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Ni kusazgirako kwa [[arithmetic|masamu ghakwamba]], icho chikwiza na [[Variable (mathematics)|vyambura-kumanyikwa]] na nchito zinyake padera pa nchito za masamu ghakwamba, nga [[addition|kusazga]] na [[multiplication|kwandaniska]]. [[Elementary algebra|Algebra ya pulayimale]] ndiyo nthowa yikuru ya algebra iyo yikusambizgika mu masukulu. Iwo ukusanda mazgu gha masamu mwakugwiliskira nchito vyakusintha vya vigaŵa vyambura kumanyikwa, na kukhumba kumanya kuti ni mikhaliro wuli iyo mazgu agha ghali ghaunenesko. Kuti ŵacite nthena, ŵakugwiriskira nchito nthowa zakupambana-pambana zakusinthira vyakuyaniska kuti ŵapature vinthu vyakusintha vya vigaŵa. [[Linear algebra|Algebra ya mzere]] ni chigaŵa chakukolerana chomene na algebra ya pulayimale, icho chikufufuza vyakuyaniska vya mzere na kunozgeka kwake, ivyo vikuchemeka ''[[system of linear equations|magulu gha vyakuyaniska vya mzere]]''. Chikupereka nthowa zakusanga vipimo ivyo vikwaniska vyakuyaniska vyose mu gulu pa nyengo yimoza, na kusambira gulu la vigaŵa ivi. <!-- paragraphs 1 and 2 are transcluded into [[Outline of algebra]] --> [[Abstract algebra|Algebra yakudumura]] yikusambira [[Algebraic structure|magulu gha algebra]], ivyo vikupangika na gulu la vinthu vya masamu pamoza na nchito yimoza panji zinandi izo zikulongosoreka pa gulu ilo. Ni kusazgirako kwa algebra ya pulayimale na ya mzere, chifukwa chikuzomerezga vinthu vinyake padera pa vipendeko na nchito zambura kuŵa za masamu ghakwamba. Chikupambaniska pakati pa mitundu yakupambana-pambana ya magulu gha algebra, nga [[Group (mathematics)|magulu]], [[Ring (mathematics)|mphete]], na [[Field (mathematics)|minda]], kuyana na unandi wa nchito izo zikugwiriskirika ntchito na madango agho ghakulondezgeka, ghakuchemeka [[axioms|madango ghakuzomerezgeka]]. [[Universal algebra|Algebra ya wonse]] na [[category theory|sambiro la mikhaliro]] vikupereka vipangiro vyakuwaneko kuti vifufuze vipimo vyambura kuwoneka ivyo vikulongosora magulu ghakupambana-pambana gha algebra. Nthowa za algebra zikasambika dankha mu [[ancient period|nyengo yakale]] kuti zithaske masuzgo ghapadera mu vigaŵa nga [[geometry]]. Ichi chikasintha mu vilimika vya m'ma 800 na [[Muḥammad ibn Mūsā al-Khwārizmī]], uyo wakanozga algebra kuŵa chigaŵa chakujipeleka cha masamu, chakupambana na geometry. Ŵasandi ŵakwamba ŵakalongosoranga vyakuyaniska na vyakuvitatuza mwakugwiliskira nchito mazgu na vifupikizgo, m'paka mu vilimika vya m'ma 1500 na 1600, apo nthowa yakukhwima ya viwimbo (symbols) yikapangika. Pakati pa vilimika vya m'ma 1800, uzelu wa algebra ukasazgirapo kuluska sambiro la vyakuyaniska pera na kusazgako mitundu yakupambana-pambana ya nchito na magulu gha algebra. Algebra yikukhwaskana na vigaŵa vinandi vya masamu, nga geometry, [[topology]], [[number theory|sambiro la vipendeko]], na [[calculus]], kweniso vigaŵa vinyake, nga [[logic]] na [[empirical sciences|kasandiro kakuzenga pa vyakuwonekera]]. == Ng'anamuro na Muko wa Lizgu == Algebra ni nthambi ya masamu iyo yikusambira magulu gha algebra na nchito izo ghakugwiliskira ntchito.<ref>{{multiref | {{harvnb|Merzlyakov|Shirshov|2020|loc=Lead section}} | {{harvnb|Gilbert|Nicholson|2004|p=[https://books.google.com/books?id=paINAXYHN8kC&pg=PA4 4]}} }}</ref> Gulu la algebra ni gulu la vinthu vya masamu ilo lilije kuŵa lambura kanthu, nga vipendeko vyambura kugaŵika, pamoza na nchito za algebra izo zikulongosoreka pa gulu ilo, nga kusazga na kwandaniska.<ref>{{multiref | {{harvnb|Fiche|Hebuterne|2013|p=[https://books.google.com/books?id=TqkckiuuXg8C&pg=PT326 326]}} | {{harvnb|Merzlyakov|Shirshov|2020|loc=§ The Subject Matter of Algebra, Its Principal Branches and Its Connection with Other Branches of Mathematics.}} | {{harvnb|Gilbert|Nicholson|2004|p=[https://books.google.com/books?id=paINAXYHN8kC&pg=PA4 4]}} }}</ref>{{efn|When understood in the widest sense, an algebraic operation is a [[function (mathematics)|function]] from a [[Cartesian product#n-ary Cartesian power|Cartesian power of a set into that set]], expressed formally as {{tmath|1= \omega: A^n \to A }}. The addition of real numbers is an example of an algebraic operation: it takes two numbers as input and produces one number as output. It has the form {{nowrap|<math>+: \R^2 \to \R</math>.<ref>{{harvnb|Baranovich|2023|loc=Lead section}}</ref>}}}} Algebra yikufufuza malango, mikhaliro yose, na mitundu ya magulu gha algebra. Mu magulu ghanyake gha algebra, yikuwoneseska umo vinthu vyakusintha (vyambura-kumanyikwa) vikugwiriskirika ntchito mu vyakuyaniska na umo vingachitikira kuvisintha.<ref>{{multiref | {{harvnb|Pratt|2022|loc=Lead section, § 1. Elementary Algebra, § 2. Abstract Algebra, § 3. Universal Algebra}} | {{harvnb|Merzlyakov|Shirshov|2020|loc=§ The Subject Matter of Algebra, Its Principal Branches and Its Connection with Other Branches of Mathematics.}} }}</ref>{{efn|Algebra is covered by division 512 in the [[Dewey Decimal Classification]]<ref>{{harvnb|Higham|2019|p=[https://books.google.com/books?id=ferEDwAAQBAJ&pg=PA296 296]}}</ref> and subclass QA 150{{hyphen}}272.5 in the [[Library of Congress Classification]].<ref>{{harvnb|Library of Congress|p=3}}</ref> It encompasses several areas in the [[Mathematics Subject Classification]].<ref>{{harvnb|zbMATH Open|2024}}</ref>}} Kanandi algebra yikupulikiskika kuŵa kusazgirako kwa [[arithmetic|masamu ghakwamba]].<ref>{{multiref | {{harvnb|Maddocks|2008|p=129}} | {{harvnb|Burgin|2022|p=[https://books.google.com/books?id=rWF2EAAAQBAJ&pg=PA45 45]}} }}</ref> Masamu ghakwamba ghakusambira nchito nga kusazga, [[subtraction|kuwuskapo]], kwandaniska, na [[Division (mathematics)|kugaŵa]], mu chigaŵa chinyake cha vipendeko, nga vipendeko vyaunenesko.<ref name="auto1">{{multiref | {{harvnb|Romanowski|2008|pp=302–303}} | {{harvnb|HC Staff|2022}} | {{harvnb|MW Staff|2023}} | {{harvnb|Bukhshtab|Pechaev|2020}} }}</ref> [[Elementary algebra|Algebra ya pulayimale]] njiyo mlingo wakwamba wa kudumuka. Nga umo masamu ghakwamba ghakucitira, yikujikanizga ku mitundu yinyake ya vipendeko na nchito. Yikusazgirapo nchito izi mwakuzomerezga unandi wambura kumanyikwa mu mtundu wa vyambura-kumanyikwa padera pa vipendeko.<ref>{{multiref | {{harvnb|Maddocks|2008|pp=129–130}} | {{harvnb|Pratt|2022|loc=Lead section, § 1. Elementary Algebra}} | {{harvnb|Wagner|Kieran|2018|p=[https://books.google.com/books?id=uW4ECwAAQBAJ&pg=PT225 225]}} }}</ref> Mlingo wapachanya wa kudumuka ukusangika mu [[abstract algebra|algebra yakudumura]], iyo yikumara yayi pa chigaŵa chinyake ndipo yikuwoneseska magulu gha algebra nga [[Group (mathematics)|magulu]] na [[Ring (mathematics)|mphete]]. Yikuluta kuluska nchito zamasamu ghakwamba mwakusazgaposo mitundu yinyake ya nchito.<ref>{{multiref | {{harvnb|Maddocks|2008|pp=131–132}} | {{harvnb|Pratt|2022|loc=§ 2. Abstract Algebra}} | {{harvnb|Wagner|Kieran|2018|p=[https://books.google.com/books?id=uW4ECwAAQBAJ&pg=PT225 225]}} }}</ref> [[Universal algebra|Algebra ya wonse]] njakudumura comenecomene chifukwa yikupulikira yayi magulu gha algebra ghapadera, kweni yikufufuza mikhaliro ya magulu gha algebra mwaunenesko.<ref>{{multiref | {{harvnb|Pratt|2022|loc=§ 3. Universal Algebra}} | {{harvnb|Grillet|2007|p=[https://link.springer.com/chapter/10.1007/978-0-387-71568-1_15 559]}} | {{harvnb|Denecke|Wismath|2018|p=[https://books.google.com/books?id=2UlZDwAAQBAJ&pg=PR5 v]}} | {{harvnb|Cohn|2012|p=[https://books.google.com/books?id=6tbuCAAAQBAJ&pg=PR13 xiii]}} }}</ref> [[File:Image-Al-Kitāb al-muḫtaṣar fī ḥisāb al-ğabr wa-l-muqābala.jpg|upright=.8|thumb|alt=Title page of The Compendious Book on Calculation by Completion and Balancing|Lizgu lakuti ''algebra'' likufuma ku mutu wa buku la [[al-Khwarizmi]] lakuti {{transliteration|ar|[[Al-Jabr]]}}.<ref>{{multiref | {{harvnb|Cresswell|2010|p=[https://books.google.com/books?id=J4i3zV4vnBAC&pg=PA11 11]}} | {{harvnb|OUP Staff}} | {{harvnb|Menini|Oystaeyen|2017|p=722}} }}</ref>]] Lizgu lakuti ''algebra'' nyengo zinyake likugwiriskirika ntchito mwakucepa kuti likung'anamurenge waka algebra ya pulayimale panji algebra yakudumura yekha.<ref>{{multiref | {{harvnb|Weisstein|2003|p=46}} | {{harvnb|Walz|2016|loc=[https://www.spektrum.de/lexikon/mathematik/algebra/12062 Algebra]}} }}</ref> Para likugwiriskirika ntchito nga zina lakuŵerengeka, algebra ni mtundu unyake wa gulu la algebra uwo ukukhwaskana na malo gha [[vector space|vector]] agho ghali na mtundu unyake wa nchito ya viŵiri viŵiri, iyo yikuchemeka [[bilinear map|nchito yakuŵiriska]].<ref>{{multiref | {{harvnb|Weisstein|2003|p=46}} | {{harvnb|Brešar|2014|p=[https://books.google.com/books?id=PkvPBAAAQBAJ&pg=PR33 xxxiii]}} | {{harvnb|Golan|1995|pp=[https://link.springer.com/chapter/10.1007/978-94-015-8502-6_18 219–227]}} }}</ref> Kulingana na umo vikuyowoyekera, algebra yingayowoyaso za vigaŵa vinyake vya algebra, nga [[Lie algebra]] panji [[associative algebra|algebra yakukolerana]].<ref>{{harvnb|EoM Staff|2017}}</ref> Lizgu lakuti ''algebra'' likufuma ku lizgu la Chiarabu lakuti {{lang|ar|الجبر}} ({{transliteration|ar|al-jabr}}), ilo pakwamba likang'anamuranga opareshoni yakuchizgira viwangwa. Mu vilimika vya m'ma 800 C.E., lizgu ili likaŵa na ng'anamuro la masamu apo [[Muhammad ibn Musa al-Khwarizmi]], uyo wakasambiranga masamu ku Persia, wakagwiriskira ntchito lizgu ili kuti wazunure nthowa yakusinthira vyakuyaniska. Wakagwiriskira ntchito lizgu ili pa mutu wa buku lake, ilo mutu wake ukung'anamulika kuti {{transliteration|ar|[[Al-Jabr|al-Kitāb al-Mukhtaṣar fī Ḥisāb al-Jabr wal-Muqābalah]]}} [Buku Lakulongosora Kupenda mwa Kumalizga na Kulinganiza]. Mutu uwu ukang'anamulika mu Chilatini kuti {{lang|la|Liber Algebrae et Almucabola}}.{{efn|The exact meaning of the term {{transliteration|ar|al-jabr}} in al-Khwarizmi's work is disputed. In some passages, it expresses that a quantity diminished by subtraction is restored to its original value, similar to how a bonesetter restores broken bones by bringing them into proper alignment.<ref>{{multiref | {{harvnb|Oaks|Alkhateeb|2007|pp=45–46, 58}} | {{harvnb|Gandz|1926|p=437}} }}</ref>}} Lizgu ili likanjira mu Chingelezi mu vilimika vya m'ma 1500 kufuma ku Chiitaliya, Chisipanishi, na Chilatini cha mu nyengo ya Ŵamitundu.<ref>{{multiref | {{harvnb|Cresswell|2010|p=[https://books.google.com/books?id=J4i3zV4vnBAC&pg=PA11 11]}} | {{harvnb|OUP Staff}} | {{harvnb|Menini|Oystaeyen|2017|p=722}} | {{harvnb|Hoad|1993|p=10}} }}</ref> Pakwamba, ng'anamuro lake likaŵa waka pa fundo yakuti [[theory of equations|kufundizga vyakuyaniska]], ndikuti, uzeru wa kusintha [[polynomial equations|vyakuyaniska vyakuvinandi]] mwakukhumba kuvitatuza. Ichi chikasintha mu vilimika vya m'ma 1800{{efn|These changes were in part triggered by discoveries that solved many of the older problems of algebra. For example, the proof of the [[fundamental theorem of algebra]] demonstrated the existence of complex solutions of polynomials<ref name="auto7">{{multiref | {{harvnb|Tanton|2005|p=10}} | {{harvnb|Kvasz|2006|p=308}} | {{harvnb|Corry|2024|loc=§ The Fundamental Theorem of Algebra}} }}</ref> and the introduction of [[Galois theory]] characterized the polynomials that have [[solution in radicals|general solutions]].<ref name="auto2">{{multiref | {{harvnb|Kvasz|2006|pp=314–345}} | {{harvnb|Merzlyakov|Shirshov|2020|loc=§ Historical Survey}} | {{harvnb|Corry|2024|loc=§ Galois Theory, § Applications of Group Theory}} }}</ref>}} apo uzelu wa algebra ukasazgirapo kuti ukwatire kusambira mitundu yakupambana-pambana ya nchito na magulu gha algebra pamoza na [[axiom|madango ghakuzomerezgeka]] ghawo, malango agho ghakulondezgeka.<ref>{{multiref | {{harvnb|Tanton|2005|p=10}} | {{harvnb|Corry|2024|loc=§ Structural Algebra}} | {{harvnb|Hazewinkel|1994|pp=[https://books.google.com/books?id=PE1a-EIG22kC&pg=PA73 73–74]}} }}</ref> == Vigaŵa Vikuru == === Algebra ya Pulayimale === {{main|Elementary algebra}} [[File:algebraic equation notation.svg|thumb|right|class=skin-invert-image|alt=Diagram of an algebraic expression|Umo mazgu gha algebra ghakulembeka:<br />&nbsp; 1 – chikwezgo (exponent)<br />&nbsp; 2 – muwandaniso (coefficient)<br />&nbsp; 3 – chigaŵa (term)<br />&nbsp; 4 – chiwimbo cha nchito (operator)<br />&nbsp; 5 – chigaŵa cambura-kusintha (constant term)<br />&nbsp; <math>c</math> – cambura-kusintha (constant)<br />&nbsp; <math>x</math> <math>y</math> – vyambura-kumanyikwa (variables)]] Algebra ya pulayimale, iyo yikuchemekaso algebra ya sukulu, ndiyo ni algebra yakale chomene ndiposo yakuzirwa chomene.<ref>{{multiref | {{harvnb|Arcavi|Drijvers|Stacey|2016|p=[https://books.google.com/books?id=N2R9DAAAQBAJ&pg=PA2 2]}} | {{harvnb|Benson|2003|pp=[https://books.google.com/books?id=nNbnCwAAQBAJ&pg=PA111 111–112]}} }}</ref> Ni generalization ya masamu ghakwamba iyo yikuthemba pa vyakusintha (vyambura-kumanyikwa) na kusanda umo mazgu gha masamu ghangasinthira.<ref name="auto4">{{multiref | {{harvnb|Maddocks|2008|p=129}} | {{harvnb|Berggren|2015|loc=Lead section}} | {{harvnb|Pratt|2022|loc=§ 1. Elementary Algebra}} | {{harvnb|Merzlyakov|Shirshov|2020|loc=§ 1. Historical Survey}} }}</ref> Masamu ghakwamba ni kasandiro ka nchito za manambara. Ghakufufuza umo manambara ghakusazgikira na kusinthika mwakugwiliskira ntchito kusazga, [[subtraction|kuwuskapo]], [[multiplication|kwandaniska]], [[Division (mathematics)|kugaŵa]], kuwoneska (exponentiation), kufumiska misisi (roots), na [[logarithm|logarithimu]]. Mwachiyelezgero, nchito ya kusazga yikusazga manambara ghaŵiri, ghakuchemeka vyakusazgika, kuŵa nambara yachitatu, iyo yikuchemeka [[sum|muzgoro]], nga umo <math>2 + 5 = 7</math>.<ref name="auto1"/> Algebra ya pulayimale yikuthemba pa nchito zenezo waka kweni yikuzomerezga vyambura-kumanyikwa padera pa manambara ghaŵaka. Vyambura-kumanyikwa ni viwimbo vya vinthu ivyo vindamanyikwe panji ivyo vyambura kumanyikwa. Vikupangiska kuti wanthu ŵayowoye ukoli uwo munthu wandaumanye mwakukhwima, na kuyowoya malango ghakumanyikwa agho ghali ghaunenesko, kwambura kupwelelera manambara agho ghakugwiriskirika ntchito. Mwachiyelezgero, cakuyaniska <math>2 \times 3 = 3 \times 2</math> chikuŵa cha masamu ghakwamba ndipo chikulongora kuyana kwa manambara agha ghekha. Para tikapoka manambara na vyambura-kumanyikwa, tingayowoya dango likuru ilo likulongosoreka ku kunozgeka kose kwa manambara, nga dango la kusintha malo (commutative property) la kwandaniska, ilo likulongosoreka mu cakuyaniska {{nowrap|<math>a \times b = b \times a</math>.<ref name="auto4"/>}} [[Algebraic expression|Mazgu gha algebra]] ghakupangika mwakugwiliskira nchito za masamu ghakwamba kuti akole pamoza vyambura-kumanyikwa na manambara. Mwakuyana na umo vikuŵira, vilembo vichoko nga ni <math>x</math>, <math>y</math>, na <math>z</math> vikwimira vyambura-kumanyikwa. Mu vinthu vinyake, viwimbo vyapasi (subscripts) vikusazgikako kupambaniska vyambura-kumanyikwa, nga <math>x_1</math>, <math>x_2</math>, na <math>x_3</math>. Vilembo vichoko-choko nga ni <math>a</math>, <math>b</math>, na <math>c</math> kanandi ghakugwiriskirika ntchito pa vyambura-kusintha (constants) na vyakusazgirako pa kwandaniska (coefficients).{{efn|Constants represent fixed numbers that do not change during the study of a specific problem.<ref>{{harvnb|Sobolev|2015}}</ref>}} Mazgu ghakuti <math>5x + 3</math> ni mazgu gha algebra ghakupangika mwa kuchulukizga nambara 5 na cambura-kusintha <math>x</math> na kusazgako nambara 3 ku ivyo vikusangika. Vyakuwoneska vinyake vya mazgu gha algebra ni <math>32xyz</math> na {{nowrap|<math>64x_1{}^2 + 7x_2 - c</math>.<ref>{{multiref | {{harvnb|Maddocks|2008|pp=129–130}} | {{harvnb|Young|2010|p=[https://books.google.com/books?id=9HRLAn326zEC&pg=RA1-PA999 999]}} | {{harvnb|Majewski|2004|p=347}} | {{harvnb|Pratt|2022|loc=§ 1. Elementary Algebra}} | {{harvnb|Sorell|2000|p=[https://books.google.com/books?id=EksSDAAAQBAJ&pg=PA19 19]}} }}</ref>}} Mazgu ghanyake gha algebra ghakuŵa nga mazgu ghakukhwaskana na mazgu ghaŵiri pamoza. [[Equation|Cakuyaniska]] ni mazgu ghakupangika mwa kuyerezgera mazgu ghaŵiri, kuyowoya kuti ghakuyana waka. Ichi chingalongoreka mwakugwiliskira nchito chiwimbo cha kuyana ({{tmath|1= = }}), nga <math>5x^2 + 6x = 3y + 4</math>. [[Inequation|Vyambura-kuyana]] vikukhwaskana na mtundu wakupambana wa kuyerezgera, kuyowoya kuti vigaŵa viŵiri ivi ni vyakupambana. Ichi chingalongoreka mwakugwiliskira ntchito viwimbo nga chiwimbo cha kuchepa ({{tmath|1= < }}), chiwimbo cha kuluska ({{tmath|1= > }}), na chiwimbo cha kupambana ({{tmath|1= \neq }}). Kupambana na mazgu ghanyake, mazgu agha ghangaŵa ghaunenesko panji ghautesi, ndipo unenesko wawo ukuthemba pa mtengo wa vinthu ivyo vikusintha. Mwachiyelezgero, mazgu ghakuti <math>x^2 = 4</math> ni ghaunenesko usange <math>x</math> ni 2 panji −2, ndipo ghautesi mwakupambanako. Ma equation ghakukhala na vyambura-kumanyikwa vingagaŵika mu ma equation ghakumanyikwa (identity equations) na ma equation ghakukhazikika (conditional equations). Ma equation ghakumanyikwa ghali ghaunenesko pa vyose ivyo vingapelekeka ku vyambura-kumanyikwa, nga cakuyaniska {{tmath|1= 2x + 5x = 7x }}. Ma equation ghakukhazikika ghakuŵa ghaunenesko waka pa vinyake vyakusintha. Mwachiyelezgero, cakuyaniska <math>x + 4 = 9</math> ni chaunenesko waka usange <math>x</math> ni 5.<ref>{{multiref | {{harvnb|Musser|Peterson|Burger|2013|p=16}} | {{harvnb|Goodman|2001|p=[https://books.google.com/books?id=TvY7DQAAQBAJ&pg=PA5 5]}} | {{harvnb|Williams|2022}} }}</ref> Chakulinga chikuru cha algebra ya pulayimale nkhumanya mtengo uwo mazgu ghakuyowoyeka ghaunenesko. Ici cingacitika mwa kusintha na kugwiliskira nchito mazgu mwakuyana na malango ghanyake. Fundo yikuru njakuti nchito yiliyose iyo yikuchitika ku chigaŵa chimoza cha cakuyaniska yikweneraso kuchitika ku chigaŵa chinyake. Mwachiyelezgero, usange munthu wawuskako 5 ku chigaŵa cha kumaryero, wakwenerato kuwuskako 5 ku chigaŵa cha kumalyero kuti ŵalinganiske vigaŵa vyose viŵiri. Chilato cha ndondomeko izi nkhupatura chinthu icho munthu wakukhumba ku chigaŵa chimoza, ndondomeko iyo yikumanyikwa kuti nkhumazga cakuyaniska kwa chinthu icho chikusintha. Mwachiyelezgero, cakuyaniska <math>x - 7 = 4</math> chingamazgika kwa <math>x</math> mwa kusazgako 7 ku vigaŵa vyose viŵiri, ivyo vikupatura <math>x</math> ku chigaŵa cha kumaryero na kusanga cakuyaniska {{tmath|1= x = 11 }}.<ref>{{multiref | {{harvnb|Maddocks|2008|p=130}} | {{harvnb|McKeague|1986|pp=[https://books.google.com/books?id=sq7iBQAAQBAJ&pg=PA51 51–54]}} | {{harvnb|Pratt|2022|loc=§ 1. Elementary Algebra}} | {{harvnb|Merzlyakov|Shirshov|2020|loc=§ 1. Historical Survey}} }}</ref> Pali nthowa zinyake zinandi izo zikugwiriskirika ntchito kumazga ma equation. [[Simplification (algebra)|Kupepuska]] kukugwiriskirika ntchito kuti chiŵike mazgu ghakusuzga na ghanyake ghakuyana kweni ghapusu. Mwachiyelezgero, mazgu ghakuti <math>7x - 3x</math> ghangaŵikika na mazgu ghakuti <math>4x</math> chifukwa <math>7x - 3x = (7-3)x = 4x</math> mwa dango la [[distributive property|kugaŵanya]].<ref>{{multiref | {{harvnb|Tan|Steeb|Hardy|2012|p=[https://books.google.com/books?id=UDb0BwAAQBAJ&pg=PA306 306]}} | {{harvnb|Lamagna|2019|p=[https://books.google.com/books?id=8PSDDwAAQBAJ&pg=PA150 150]}} }}</ref> Pa mazgu agho ghali na vyambura-kumanyikwa vinandi, kuŵikirapo m'malo mwake (substitution) ni nthowa yakumanyikwa yakusinthira chinthu chimoza na mazgu ghakuyana ghambura kusazgako cambura-kusintha ico. Mwachiyelezgero, usange munthu wamanya kuti <math>y = 3x</math>, wangapepuska mazgu ghakuti <math>7xy</math> na kusanga {{tmath|1= 21x^2 }}. Munthowa yakuyana, usange munthu wamanya mtengo wa cambura-kusintha chimoza, wangagwiriskira ntchito umo kumanya mtengo wa vinyake.<ref>{{multiref | {{harvnb|Berggren|2015|loc=§ Solving Systems of Algebraic Equations}} | {{harvnb|McKeague|2014|p=[https://books.google.com/books?id=nI7iBQAAQBAJ&pg=PA386 386]}} | {{harvnb|McKeague|1986|p=[https://books.google.com/books?id=sq7iBQAAQBAJ&pg=PA148 148]}} }}</ref> [[File:Graph (y = 0.5x - 1).svg|thumb|class=skin-invert-image|alt=Graph of equation "y = 0.5x − 1"|Ma equation gha algebra ghangagwiriskirika ntchito kulongosora vithuzi vya geometry. Mtengo wose wa <math>x</math> na <math>y</math> uwo ukumazga cakuyaniska ukupulikiskika kuŵa songo. Vikulembeka nga mzere wa cikuwundi, wakukwera, mu giraf yakucanya.]] Ma equation gha algebra ghangamasulika mu [[geometry]] kuti ghalongosore viŵelengero vya malo mu mtundu wa [[graph of a function|giraf]]. Vinthu vyakupambana-pambana ivyo vili mu equation vikupulikikwa nga ni [[Cartesian coordinate system|maryeruzgo]], ndipo vigaŵa ivyo vikumazga equation vikung'anamulika nga ni fundo za giraf. Mwachiyelezgero, usange <math>x</math> yikuŵikika pa zero mu equation {{tmath|1= y=0.5x - 1 }}, mbwenu <math>y</math> yikwenera kuŵa negative one kuti equation yiŵe yaunenesko. Ichi chikung'anamura kuti mafupa gha <math>(x, y)</math> ghakuti <math>(0, -1)</math> ni chigaŵa cha giraf ya equation. Mafupa gha <math>(x, y)</math> ghakuti {{tmath|1= (0, 7) }}, mwakupambanako, ghakumazga yayi equation ndipo ntheura ghali yayi chigaŵa cha giraf. Grafu yikukhwaska chiŵelengero chose cha x,y paŵiri awo ŵakumazga equation.<ref>{{multiref | {{harvnb|Maddocks|2008|pp=130–131}} | {{harvnb|Rohde|Jain|Poddar|Ghosh|2012|p=[https://books.google.com/books?id=vk2XbZpsBOwC&pg=PT89 89]}} | {{harvnb|Walz|2016|loc=[https://www.spektrum.de/lexikon/mathematik/algebra/12062 Algebra]}}}}</ref> ==== Ma Polynomial ==== {{main|Polynomial}} [[Polynomial|Polynomial]] ni mazgu ghakuchitika na chigaŵa chimoza panji vinandi ivyo vikusazgika panji kuwuskika pakati pawo, nga {{tmath|1= x^4+3xy^2+5x^3-1 }}. Chigaŵa chilichose ni cambura-kusintha, cambura-kumanyikwa, panji muzgoro wa cambura-kusintha na vyambura-kumanyikwa. Cambura-kumanyikwa chilichose chingakwezgeka ku chikwezgo cha cipendeko cambura kupambika (positive integer). Polynomial ya chigaŵa chimoza yikuchemeka [[monomial]], apo polynomial za vigaŵa viŵiri na vitatu zikuchemeka [[binomial]] na [[trinomial]]. [[Degree of a polynomial|Digiri ya polynomial]] ni mtengo wapachanya wa muzgoro wa vikwezgo vya vyambura-kumanyikwa (pakati pa vigaŵa vyake) (4 mu chiyelezgero ichi pacanya).<ref>{{multiref | {{harvnb|Bracken|Miller|2014|pp=386–387}} | {{harvnb|Kaufmann|Schwitters|2011|p=220}} | {{harvnb|Markushevich|2015}} }}</ref> Ma polynomial gha digiri yimoza ghakuchemeka ''ma polynomial gha mzere''. Algebra ya mzere yikusambira magulu gha ma polynomial gha mzere.<ref>{{multiref | {{harvnb|Sahai|Bist|2002|p=[https://books.google.com/books?id=yjkgNYfApj4C&pg=PA21 21]}} | {{harvnb|Maddocks|2008|p=131}} | {{harvnb|Barrera-Mora|2023|pp=[https://books.google.com/books?id=Xmu8EAAAQBAJ&pg=PR9 ix, 1–2]}} }}</ref> Polynomial yikuchemeka ''univariate'' panji ''multivariate'', kuyana na usange yikugwiriskira ntchito cambura-kumanyikwa chimoza panji vinandi.<ref>{{harvnb|Geddes|Czapor|Labahn|2007|p=[https://books.google.com/books?id=9fOUwkkRxT4C&pg=PA46 46]}}</ref> [[Factorization|Kugaŵaniska]] ni nthowa yakugwiriskira ntchito kupepuska ma polynomial, kupangiska kuti chiŵe chapusu kuvisanda na kumanya vigaŵa ivyo vikuŵa zero. Kugaŵaniska nkhulembaso polynomial kuŵa muzgoro wa vigaŵaniso vinandi. Mwachiyelezgero, polynomial <math>x^2 - 3x - 10</math> yingagaŵaniskika kuŵa {{tmath|1= (x + 2)(x - 5) }}. Polynomial yose njizero pekha usange chimoza mwa vigaŵaniso vyake ni zero, ndikuti, usange <math>x</math> ni −2 panji 5.<ref>{{multiref | {{harvnb|Lukas|2022|pp=[https://books.google.com/books?id=1-dvEAAAQBAJ&pg=PA47 47–49]}} | {{harvnb|Berggren|2015|loc=§ Algebraic Expressions, § Solving Algebraic Equations}} }}</ref> Pambere vilimika vya m'ma 1800 vindafike, vigaŵa vinandi vya algebra vikaŵanga vya equation ya polynomial, equation iyo yikasangika para munthu wakuyaniska polynomial na zero. Kuyezgayezga kwakwamba kwa kumazga ma equation gha polynomial kukaŵa kwakuti ŵalongore vyakumazga mu mazgu gha misisi ya nth. Muzgoro wa equation ya polynomial ya digiri yachiŵiri ukuperekeka na fomula ya quadratic<ref>{{multiref | {{harvnb|Berggren|2015|loc=§ Solving algebraic equations}} | {{harvnb|Corry|2024|loc=§ Classical algebra}} }}</ref> <math display="block">x = \frac{-b \pm \sqrt {b^2-4ac\ }}{2a}.</math> Mayankho gha madigiri ghatatu na ghanayi ghakupelekeka na mafomula gha [[cubic formula|cubic]] na [[quartic formula|quartic]]. Palije mayankho ghakumanyikwa ghakumazgira madigiri ghapachanya, nga umo vikawonekera mu vilimika vya m'ma 1800 na [[Abel–Ruffini theorem|fundo ya Abel-Ruffini]].<ref name="auto3"/> Nanga ni para mayankho ghakumanyikwa ghalipo yayi, mayankho ghakuyana waka ghangasangika mwakugwiliskira nchito vipangizo vya manambara nga [[Newton–Raphson method|nthowa ya Newton-Raphson]].<ref>{{harvnb|Igarashi|Altman|Funada|Kamiyama|2014|p=[https://books.google.com/books?id=58ySAwAAQBAJ&pg=PA103 103]}}</ref> [[Fundamental theorem of algebra|Fundo yikuru ya algebra]] yikuti equation yiliyose ya univariate polynomial ya digiri yiwemi iyo yili na coefficients yeneco panji yakusuzga yili na yankho limoza lakusuzga. Ntheura, polynomial yiliyose ya digiri yiwemi yingagaŵika mu ma [[polynomial factorization|polynomial gha mzere]]. Fundo yikuzirwa iyi yikakhozgeka kukwambilira kwa vilimika vya m'ma 1800, kweni yikupereka yayi nthowa yiliyose yakusangirapo vyakumazga.<ref>{{multiref | {{harvnb|Berggren|2015|loc=§ Solving algebraic equations}} | {{harvnb|Tanton|2005|p=10}} | {{harvnb|Kvasz|2006|p=308}} | {{harvnb|Corry|2024|loc=§ The Fundamental Theorem of Algebra}} }}</ref> === Algebra ya Mzere === {{main|Linear algebra}} Algebra ya mzere yikwamba na kusambira [[System of linear equations|ndondomeko za ma equation gha mzere]].<ref>{{multiref | {{harvnb|Maddocks|2008|p=131}} | {{harvnb|Barrera-Mora|2023|pp=[https://books.google.com/books?id=Xmu8EAAAQBAJ&pg=PR9 ix, 1–2], }} }}</ref> [[Linear equation|Equation njakumzere]] usange yingalembeka mu njila ya {{tmath|1= a_1x_1 + a_2x_2 + ... + a_nx_n = b}}, apo {{tmath|1= a_1 }}, {{tmath|1= a_2 }}, ..., <math>a_n</math> na <math>b</math> ni vyambura-kusintha. Vyakuyelezgera ni <math>x_1 - 7x_2 + 3x_3 = 0</math> na {{tmath|1= \textstyle \frac{1}{4} x - y = 4 }}. ''Ndondomeko ya ma equation gha mzere'' ni gulu la ma equation gha mzere agho munthu wakukhumba kusanga vyakumazga vyakuyana pakati pawo.<ref>{{multiref | {{harvnb|Anton|Rorres|2013|pp=2–3}} | {{harvnb|Maddocks|2008|p=131}} | {{harvnb|Voitsekhovskii|2011}} }}</ref> [[Matrix (mathematics)|Ma matrix]] ni magulu ghakuŵungana gha manambara mwakachilato (rows na columns) agho ghakambiliranga kwiziliska nga chiwimbo chakufinya na chakuyana mwakukwana cha ndondomeko za ma equation gha mzere.<ref>{{multiref | {{harvnb|Saikia|2008|p=[https://books.google.com/books?id=KhM7BAAAQBAJ&pg=PA1 1]}} | {{harvnb|Lal|2017|p=[https://books.google.com/books?id=FwPNDgAAQBAJ&pg=PA31 31]}} | {{harvnb|Mirakhor|Krichene|2014|p=[https://books.google.com/books?id=G6XNAwAAQBAJ&pg=PT107 107]}} }}</ref> Mwachiyelezgero, ndondomeko ya ma equation <math display="block"> \begin{align} 9x_1 + 3x_2 - 13x_3 &= 0 \\ 2.3x_1 + 7x_3 &= 9 \\ -5x_1 - 17x_2 &= -3 \end{align} </math> yingalembeka nga <math display="block">AX=B,</math> apo {{tmath|1= A }}, <math>X</math> na <math>B</math> ni ma matrix <math display="block">A=\begin{bmatrix}9 & 3 & -13 \\ 2.3 & 0 & 7 \\ -5 & -17 & 0 \end{bmatrix}, \quad X= \begin{bmatrix}x_1 \\ x_2 \\ x_3 \end{bmatrix},\quad B = \begin{bmatrix}0 \\ 9 \\ -3 \end{bmatrix}.</math> Kuyana na vinjeru vya chiŵelengero cha mizere na mizati, ma matrix ghangasazgika, ghangandaniskika, ndipo nyengo zinyake ghangapiluskika (ghangawendeskeka mwakupiluka).{{efn|Kupiluskika (inversion) nkhung'anamura kusanga matrix yinyake iyo, para yandaniskika na matrix yakwamba, yikupeleka matrix ya "identity"—iyo njakuyana na cipendeko 1 pa nkhani ya kwandaniska manambara.}} Nthowa zose zakumazgira ndondomeko za mzere zingalongosoreka nga vyakuwendeska matrix mwakugwiliskira nchito izi. Mwachiyelezgero, kumazga ndondomeko yamucanya nkhupenja matrix yakupiluskika <math>A^{-1}</math> iyo <math>A^{-1}A = I,</math> apo <math>I</math> ni [[identity matrix|matrix ya identity]]. Penepapo, kwandaniska ku mkono wamazere mbali zose ziŵiri za equation ya matrix yamucanya na <math>A^{-1},</math> munthu wakusanga muzgoro wa ndondomeko ya ma equation gha mzere nga<ref>{{multiref | {{harvnb|Brown|2015|pp=[https://books.google.com/books?id=POlVBgAAQBAJ&pg=PA30 30–31]}} | {{harvnb|Waerden|2003|pp=70–72}} }}</ref> <math display="block">X=A^{-1}B.</math> Nthowa zakumazgira ndondomeko za ma equation gha mzere zikwambira ku izo zili zapafupi kumanya, nga kwiza-mu-malo-mwa (substitution)<ref>{{multiref | {{harvnb|Young|2010|pp=[https://books.google.com/books?id=9HRLAn326zEC&pg=PA697 697–698]}} | {{harvnb|Maddocks|2008|p=131}} | {{harvnb|Sullivan|2010|pp=[https://books.google.com/books?id=6NKaDwAAQBAJ&pg=PA53 53–54]}} }}</ref> na kuwuskapo (elimination),<ref>{{multiref | {{harvnb|Anton|Rorres|2013|pp=7–8}} | {{harvnb|Sullivan|2010|pp=[https://books.google.com/books?id=6NKaDwAAQBAJ&pg=PA55 55–56]}} | {{harvnb|Atanasiu|Mikusinski|2019|p=[https://books.google.com/books?id=VbySDwAAQBAJ&pg=PA75 75]}}}}</ref> kufika ku vipangizo vyapachanya ivyo vikugwiliskira ntchito ma matrix, nga [[Cramer's rule|dango la Cramer]], [[Gaussian elimination|kuwuskapo kwa Gauss]], na [[LU decomposition|kugaŵaniska kwa LU]].<ref>{{multiref | {{harvnb|Maddocks|2008|p=131}} | {{harvnb|Anton|Rorres|2013|pp=7–8, 11, 491}} }}</ref> Ndondomeko zinyake za ma equation nizambura-kuyana (inconsistent),<ref name="auto10">{{multiref | {{harvnb|Anton|Rorres|2013|pp=3–7}} | {{harvnb|Mortensen|2013|pp=[https://books.google.com/books?id=KYDrCAAAQBAJ&pg=PA73 73–74]}} | {{harvnb|Young|2023|pp=[https://books.google.com/books?id=pMSZEAAAQBAJ&pg=PA714 714–715]}} }}</ref> ndikuti, vyakumazga vilipo yayi chifukwa ma equation ghakususkana wene.{{efn|Mwachiyelezgero, ma equation <math>x_1 - 3x_2 = 0</math> na <math>x_1 - 3x_2 = 7</math> ghakususkana wene chifukwa palije mtengo wa <math>x_1</math> na <math>x_2</math> uwo ungamazga ma equation ghaŵiri ghara pa nyengo yimoza.<ref name="auto10"/>}} Ndondomeko zakuyana zili na yankho limoza lakupambanapambana panji viŵelengero vyambura kumazgika vya vyakumazga.<ref name="auto11">{{multiref | {{harvnb|Maddocks|2008|p=131}} | {{harvnb|Harrison|Waldron|2011|p=[https://books.google.com/books?id=_sisAgAAQBAJ&pg=PT464 464]}} | {{harvnb|Anton|2013|p=[https://books.google.com/books?id=neYGCwAAQBAJ&pg=PA255 255]}} }}</ref>{{efn|Usange ndondomeko yakuyana ya ma equation yili na yankho limoza pera, ivi vikukhozga pa chiŵelengero cha vyambura-kumanyikwa na ma [[independent equation|equation ghakujipima paŵiri]]. Ma equation ghakuti ghakujipima paŵiri usange ghakupeleka yayi mzimu umoza ndipo ghangafuma yayi kuchimoza na chinyake. Yankho limoza likuŵako usange chiŵelengero cha vyambura-kumanyikwa nchakuyana na chiŵelengero cha ma equation ghakujipima paŵiri. [[Underdetermined system|Ndondomeko zambura kumazgikirathu]], kusambazgana na izi, zili na vyambura-kumanyikwa vinandi kuluska ma equation ghakujipima paŵiri ndipo zili na viŵelengero vyambura kumazgika vya vyakumazga usange nizakuyana.<ref name="auto11"/>}} Kusambira [[vector space|malo gha vector]] na [[linear map|mapu gha mzere]] nkhukuru mu algebra ya mzere. Malo gha vector ni gulu la algebra ilo likupangika na gulu (set) lino lili na kusazga uko kukupangiska kuŵa [[abelian group|gulu la abelian]] na kwandaniska na cipendeko (scalar multiplication) uko kukuyanapo na kusazga (wonani [[vector space|malo gha vector]] kuti mumanye vinandi). Mapu gha mzere ni nchito (function) pakati pa malo gha vector iyo yikuyanapo na kusazga na kwandaniska na cipendeko. Pa nkhani ya [[finite-dimensional vector space|malo gha vector ghakumalira]], ma vector na mapu gha mzere ghangayimilirika na ma matrix. Ichi chikung'anamura kuti masambiro gha ma matrix na malo gha vector ghakumalira ghakuyana waka. Comenecomene, malo gha vector ghakupereka nthowa yachitatu yakulongosolera na kugwiliskira ntchito ndondomeko za ma equation gha mzere.<ref>{{multiref | {{harvnb|Valenza|2012|p=[https://books.google.com/books?id=7x8MCAAAQBAJ&pg=PR7 vii]}} | {{harvnb|Chahal|2018|loc=[https://books.google.com/books?id=BGR8DwAAQBAJ&pg=PT10 § 1.1 What is Linear Algebra?]}} | {{harvnb|Solomon|2014|pp=[https://books.google.com/books?id=BpvSBQAAQBAJ&pg=PA57 57–58, 61–62]}} | {{harvnb|Ricardo|2009|p=[https://books.google.com/books?id=s7bMBQAAQBAJ&pg=PA389 389]}} }}</ref> Kwiza pa mkhalidwe uwu, matrix ni chithunzithunzi cha mapu gha mzere: usange munthu wakusankha [[Basis (linear algebra)|msingi]] wanyake wakulongosolera ma vector agho ghakusinthika, mbwenu ivyo vikulembeka mu matrix vikupereka vyakufumapo vya kugwiliskira ntchito mapu gha mzere ku ma vector gha msingi.<ref>{{multiref | {{harvnb|Solomon|2014|p=[https://books.google.com/books?id=BpvSBQAAQBAJ&pg=PA57 57]}} | {{harvnb|Ricardo|2009|pp=[https://books.google.com/books?id=s7bMBQAAQBAJ&pg=PA395 395–396]}} }}</ref> [[File:Linear Function Graph.svg|thumb|alt=Graph of two linear equations|Ma equation gha mzere agho ghali na vyambura-kumanyikwa viŵiri ghangang'anamulika nga [[Line (geometry)|mizere]]. Yankho la ndondomeko ya ma equation gha mzere ni apo mizere yikukhwaskana.]] Ndondomeko za ma equation zingang'anamulika nga vithunzithunzi vya geometry. Ku ndondomeko zakuŵa na vyambura-kumanyikwa viŵiri, equation yiliyose yikwimira [[Line (geometry)|mzere]] mu [[two-dimensional space|malo gha mibaru yiŵiri]]. Apo mizere yiŵiri yikukhwaskana ndipo ni yankho la ndondomeko yose chifukwa apa ndipapera apo pakumazga equation yakwamba na yachiŵiri pamoza. Ku ndondomeko zambura-kuyana, mizere yiŵiri yikwenda mwakuyana kwambura kukhwaskana, ndikuti, palije yankho chifukwa yikukhwaskana yayi nakale. Usange ma equation ghaŵiri ngambura kujipima paŵiri, ghakulongosora mzere umoza wene, ndikuti, yankho la equation yimoza njakumazgaso equation yinyake. Vyakuyanapo ivi vikupangiska kuti munthu wasange vyakumazga mwakuwona pa giraf, kulemba ma equation na kumanya apo ghakukhwaskana.<ref>{{multiref | {{harvnb|Anton|Rorres|2013|pp=3–5}} | {{harvnb|Young|2010|pp=[https://books.google.com/books?id=9HRLAn326zEC&pg=PA696 696–697]}} | {{harvnb|Sneyd|Fewster|McGillivray|2022|p=[https://books.google.com/books?id=zqd3EAAAQBAJ&pg=PA211 211]}} }}</ref> Fundo zenezi zikugwira ntchito so ku ndondomeko za ma equation zakuŵa na vyambura-kumanyikwa vinandi, kweni kupambana nkhwakuti ma equation agha ghakulongosora yayi mizere kweni vithunzithunzi vyapachanya kuluska. Mwachiyelezgero, ma equation gha vyambura-kumanyikwa vitatu ghakuyana na [[Plane (mathematics)|mabwalo]] mu [[three-dimensional space|malo gha mibaru yitatu]], ndipo apo mabwalo ghose ghakukhwaskana ndipo pakumazga ndondomeko ya ma equation.<ref>{{multiref | {{harvnb|Anton|Rorres|2013|pp=3–5}} | {{harvnb|Young|2010|p=[https://books.google.com/books?id=9HRLAn326zEC&pg=PA713 713]}} | {{harvnb|Sneyd|Fewster|McGillivray|2022|p=[https://books.google.com/books?id=zqd3EAAAQBAJ&pg=PA211 211]}} }}</ref> === Algebra Yakudumura === {{main|Abstract algebra}} Algebra yakudumura, iyo yikuchemekaso algebra ya sono,<ref>{{multiref | {{harvnb|Gilbert|Nicholson|2004|p=[https://books.google.com/books?id=paINAXYHN8kC&pg=PA1 1]}} | {{harvnb|Dominich|2008|p=[https://books.google.com/books?id=uEedNKV3nlUC&pg=PA19 19]}} }}</ref> njakusambira [[algebraic structures|magulu gha algebra]]. Gulu la algebra ni chiwongo cha kupulikiska [[Operation (mathematics)|nchito]] pa [[mathematical object|vinthu vya masamu]], nga kusazga kwa vipendeko. Apo algebra ya pulayimale na algebra ya mzere zikugwira ntchito pakati pa vipimo vya magulu gha algebra ghakupambanapambana, algebra yakudumura yikutora nthowa yikuru kuluska, yakuyaniska umo magulu gha algebra ghakupambanirana na mitundu yose ya magulu gha algebra iyo yiliko, nga [[Group (mathematics)|magulu]], [[Ring (mathematics)|mphete]], na [[Field (mathematics)|minda]].<ref>{{multiref | {{harvnb|Maddocks|2008|pp=131–132}} | {{harvnb|Pratt|2022|loc=Lead section, § 2. Abstract Algebra}} | {{harvnb|Gilbert|Nicholson|2004|pp=[https://books.google.com/books?id=paINAXYHN8kC&pg=PA1 1–3]}} | {{harvnb|Dominich|2008|p=[https://books.google.com/books?id=uEedNKV3nlUC&pg=PA19 19]}} }}</ref> Kupambana kukuru pakati pa mitundu iyi ya magulu gha algebra nkhu chiŵelengero cha nchito izo zikugwiliskira ntchito na madango agho ghakuzomerezgeka.<ref name="auto9"/> Mu [[mathematics education|masambizgo gha masamu]], algebra yakudumura yikwimira kalasi yapachanya ya ku yunivesite iyo ŵakusambira masamu ŵakusambira pamanyuma pakumazga makalasi gha algebra ya mzere.<ref>{{harvnb|Hausberger|2020|loc=Abstract Algebra Teaching and Learning}}</ref> [[File:Binary operations as black box.svg|thumb|class=skin-invert-image|alt=Diagram of binary operation|Magulu ghanandi gha algebra ghakuzirwa pa nchito zaŵiri (binary operations), izo zikutora vinthu viŵiri kuŵa vyakwiza-mu nchito ndipo vikuvikoleranga kuŵa chinthu chimoza kuŵa vyakufumamo, nga umo kusazga na kwandaniska vikuchitira.]] Pa mkhalidwe wakuzomerezgeka, gulu la algebra ni [[Set (mathematics)|gulu la vinthu]]{{efn|Gulu la vinthu ni chiŵungano cha vinthu vyakupambanapambana ivyo vilije njila yakukhwaskana, nga vipendeko, ma vector, panji magulu ghanyake. [[Set theory|Sambiro la magulu]] likulongosora madango na mikhaliro ya magulu.<ref>{{multiref | {{harvnb|Tanton|2005|p=460}} | {{harvnb|Murthy|2012|p=[https://books.google.com/books?id=CBc8BAAAQBAJ&pg=PA3 1.3]}} }}</ref>}} lakuzikapo, pamoza na nchito yimoza panji zinandi.{{efn|Kuyana na malongosoro ghanyake, magulu gha algebra ghakusazgapo chinthu chakupambana nga chigaŵa chinyake chakusazgikapo, nga chinthu cha identity pa nkhani ya kwandaniska.<ref name="auto5">{{harvnb|Ovchinnikov|2015|p=[https://books.google.com/books?id=UMbXBgAAQBAJ&pg=PA27 27]}}</ref>}} Algebra yakudumura yikukhumbisiska comenecomene [[binary operation|nchito zaŵiri]],{{efn|Magulu ghanyake gha algebra agho ghakusambirika na algebra yakudumura ghali na [[unary operation|nchito yimoza]] kusazgikapo pa nchito zaŵiri. Mwachiyelezgero, [[normed vector space|malo gha vector ghakuŵa na muyeso]] ghali na [[Norm (mathematics)|muyeso]] (norm), uwo ni nchito yimoza iyo yikugwiliskikira comenecomene kukhwaskanya vector na utali wake.<ref>{{harvnb|Grillet|2007|p=[https://books.google.com/books?id=LJtyhu8-xYwC&pg=PA247 247]}}</ref>}} izo zikutora vinthu viŵiri vilivyose mu gulu lakuzikapo kuŵa vyakwiza-mu, ndipo zikuvipeleka ku chinthu chinyake mu gulu ili kuŵa chakufumamo.<ref>{{multiref | {{harvnb|Whitelaw|1995|p=[https://books.google.com/books?id=f2hyf0QoB_0C&pg=PA61 61]}} | {{harvnb|Nicholson|2012|p=[https://books.google.com/books?id=w-GaLpapRcEC&pg=PA70 70]}} | {{harvnb|Fiche|Hebuterne|2013|p=[https://books.google.com/books?id=TqkckiuuXg8C&pg=PT326 326]}} | {{harvnb|Pratt|2022|loc=Lead section, § 2. Abstract Algebra}} }}</ref> Mwachiyelezgero, gulu la algebra <math>\langle \N, + \rangle</math> lili na [[natural numbers|vipendeko vyakuŵelenjera]] ({{tmath|1= \N }}) kuŵa gulu lakuzikapo na kusazga ({{tmath|1= + }}) kuŵa nchito yake yaŵiri.<ref name="auto5"/> Gulu lakuzikapo lingaŵa na vinthu vinyake kupambuka vipendeko, ndipo nchito zake nizakukakikizgika yayi ku nchito zaumaliro za masamu pera.<ref>{{multiref | {{harvnb|Maddocks|2008|pp=131–132}} | {{harvnb|Pratt|2022|loc=Lead section, § 2. Abstract Algebra}} }}</ref> Mwachiyelezgero, gulu lakuzikapo la [[symmetry group|gulu la symmetry]] la chinthu cha geometry likupangika na [[geometric transformation|kusintha kwa geometry]], nga [[rotation|kuzingilizga]], apo munsi mwake chinthu chikukhalilira [[Invariant (mathematics)|chambura-kusintha]]. Nchito yake yaŵiri ni [[function composition|kukolerana kwa mapu]], iyo yikutora vyakusintha viŵiri kuŵa vyakwiza-mu ndipo yili na chakusintha icho chikufuma pa kugwiliskira ntchito chakusintha chakwamba kulondezgeka na chachiŵiri kuŵa chakufumamo.<ref>{{multiref | {{harvnb|Olver|1999|pp=[https://books.google.com/books?id=1GlHYhNRAqEC&pg=PA55 55–56]}} | {{harvnb|Abas|Salman|1994|pp=[https://books.google.com/books?id=5snsCgAAQBAJ&pg=PA58 58–59]}} | {{harvnb|Häberle|2009|p=[https://books.google.com/books?id=McvSa-cFZCMC&pg=PA640 640]}} }}</ref> ==== Sambiro la Magulu ==== {{main|Group theory}} Algebra yakudumura yikupatuliska magulu gha algebra kuyana na madango panji [[axiom|maxiom]] agho nchito zake zikuzomerezga na chiŵelengero cha nchito izo zikugwiliskira ntchito. Mtundu wa chiyambipo comenecomene ni gulu (group), ilo lili na nchito yimoza ndipo likukhumba kuti nchito iyi njakukolerana ([[Associative property|associative]]) ndiposo yili na [[identity element|chinthu cha identity]] na [[inverse element|vinthu vyakupiluska]]. Nchito njakukolerana usange kalongozgero ka kugwiliskira ntchito kanandi kalije mphampha, ndikuti, usange {{nowrap|<math>(a \circ b) \circ c</math>{{efn|Viwimbo <math>\circ</math> na <math>\star</math> vikugwiliskika mu nkhani iyi kwimira nchito yiliyose iyo yingayana panji yambakuyana na nchito za masamu.<ref>{{harvnb|Gilbert|Nicholson|2004|p=[https://books.google.com/books?id=paINAXYHN8kC&pg=PA4 4]}}</ref>}}}} nchakuyana na <math>a \circ (b \circ c)</math> ku vinthu vyose. Nchito yili na chinthu cha identity panji chinthu chambura-kusintha usange chinthu chimoza ''e'' chilipo icho chikusintha yayi mtengo wa chinthu chilichose chinyake, ndikuti, usange {{tmath|1= a \circ e = e \circ a = a }}. Nchito yili na vinthu vyakupiluska usange ku chinthu chilichose <math>a</math> pali chinthu chakuwelengana <math>a^{-1}</math> icho chikuwuskapo vya {{tmath|1= a }}. Usange chinthu chikugwira ntchito pa icho chakupiluska chake mbwenu muzgoro ni chinthu chambura-kusintha ''e'', chakulongosoreka mwakuzomerezgeka nga {{tmath|1= a \circ a^{-1} = a^{-1} \circ a = e }}. Gulu la algebra lililose ilo likukwaniska vikhumbikwa ivi ni gulu.<ref>{{multiref | {{harvnb|Kargapolov|Merzlyakov|2016|loc=§ Definition}} | {{harvnb|Khattar|Agrawal|2023|pp=[https://books.google.com/books?id=7-nIEAAAQBAJ&pg=PA4 4–6]}} | {{harvnb|Maddocks|2008|pp=131–132}} | {{harvnb|Pratt|2022|loc=Lead section, § 2. Abstract Algebra}} | {{harvnb|Neri|2019|p=[https://books.google.com/books?id=NMOlDwAAQBAJ&pg=PA258 258]}} }}</ref> Mwachiyelezgero, <math>\langle \Z, + \rangle</math> ni gulu ilo lapangika na gulu la [[integers|vipendeko vyambura kugaŵika]] pamoza na nchito ya kusazga. Chinthu chambura-kusintha ni 0 ndipo chinthu chakupiluska cha cipendeko chilichose <math>a</math> ni {{nowrap|<math>-a</math>.<ref>{{multiref | {{harvnb|Khattar|Agrawal|2023|pp=[https://books.google.com/books?id=7-nIEAAAQBAJ&pg=PA6 6–7]}} | {{harvnb|Maddocks|2008|pp=131–132}} | {{harvnb|Adhikari|Adhikari|2013|p=[https://books.google.com/books?id=lBO7BAAAQBAJ&pg=PA72 72]}}}}</ref>}} Vipendeko vyakuŵelenjera pamoza na kusazga, kususkana na ivi, vikupanga yayi gulu chifukwa vili pera na vipendeko vyakuzomerezgeka ndipo ntheura vikusoŵa vinthu vyakupiluska.<ref>{{multiref | {{harvnb|McWeeny|2002|p=[https://books.google.com/books?id=x3fjIXY93TsC&pg=PA6 6]}} | {{harvnb|Kramer|Pippich|2017|p=[https://books.google.com/books?id=nvM-DwAAQBAJ&pg=PA49 49]}} }}</ref> [[Group theory|Sambiro la magulu]] likusanda umo magulu ghaliri, pamoza na fundo za musingi nga [[fundamental theorem of finite abelian groups|fundo yikuru ya magulu gha abelian ghakumalira]] na [[Feit–Thompson theorem|fundo ya Feit-Thompson]].<ref>{{multiref | {{harvnb|Tanton|2005|p=242}} | {{harvnb|Bhattacharya|Jain|Nagpaul|1994|p=[https://books.google.com/books?id=hiQ8e0b48swC&pg=PA141 141]}} | {{harvnb|Weisstein|2003|p=[https://books.google.com/books?id=D_XKBQAAQBAJ&pg=PA1020 1020]}} }}</ref> Iyi yachiŵiri yikaŵa njira yikuru yakwambilira mu chimoza mwa vinthu vikuru comenecomene mu masamu vya vilimika vya m'ma 1900: nchito yakugwirira pamoza, iyo yikatora mapeji ghakuluska 10,000 mu majenali ndipo yikafuma comenecomene pakati pa 1960 na 2004, iyo yikafiskira ku [[classification of finite simple groups|kupatuliska magulu ghapusu ghakumalira]] kwakukwana.<ref>{{multiref | {{harvnb|Elwes|2006}} | {{harvnb|Wilson|2009|p=2}} }}</ref> ==== Sambiro la Mphete na Sambiro la Munda ==== {{main|Ring theory|Field (mathematics)}} Mphete ni gulu la algebra lino lili na nchito ziŵiri izo zikugwira ntchito mwakuyana na kusazga na kwandaniska kwa vipendeko ndipo zikuchemeka na kulembeka mwakuyana. Mphete ni [[commutative group|gulu lakusinthana]] pasi pa kusazga: kusazga kwa mphete nkhwakukolerana, kwakusinthana, ndipo kuli na chinthu cha identity na vinthu vyakupiluska. Kwandaniska nkhwakukolerana ndiposo [[distributivity|kwakugaŵira]] ku kusazga; ndikuti, <math>a (b + c) = a b + a c</math> na <math>(b + c) a = b a + c a.</math> Kweniso, kwandaniska nkhwakukolerana ndipo kuli na [[identity element|chinthu cha identity]] icho chikuchemeka comenecomene {{math|1}}.<ref>{{multiref | {{harvnb|Weisstein|2003|p=2579}} | {{harvnb|Maxwell|2009|pp=[https://books.google.com/books?id=yD0irRUE_u4C&pg=PA73 73–74]}} | {{harvnb|Pratt|2022|loc=§ 2.3 Rings}} }}</ref>{{efn|Ŵalembi ŵanyake ŵakukhumba yayi kuŵako kwa chinthu cha identity mu kwandaniska. Mphete iyo yilije chinthu cha identity mu kwandaniska nyengo zinyake yikuchemeka {{not a typo|[[rng (algebra)|rng]].}}<ref>{{harvnb|Silverman|2022|p=[https://books.google.com/books?id=PKFnEAAAQBAJ&pg=PA64 64]}}</ref>}} Kwandaniska nkhukhumbikwa yayi kuŵa kwakusinthana; usange nkhwakusinthana, munthu wali na [[commutative ring|mphete yakusinthana]].<ref>{{harvnb|Geddes|Czapor|Labahn|2007|p=[https://books.google.com/books?id=9fOUwkkRxT4C&pg=PA24 24]}}</ref> [[ring of integers|Mphete ya vipendeko vyambura kugaŵika]] ({{tmath|1= \Z }}) ni yimoza mwa mphete zapusu comenecomene izo zili zakusinthana.<ref>{{harvnb|Smith|2015|p=[https://books.google.com/books?id=MXu9CgAAQBAJ&pg=PA161 161]}}</ref> ''[[field (mathematics)|Munda]]'' ni mphete yakusinthana iyo {{tmath|1\ne 0}}{{efn|Ichi chikung'anamura kuti kwandaniska na kusazga vikugwiliskira ntchito vinthu vyakupambanapambana vya identity.<ref>{{harvnb|Moh|1992|pp=[https://books.google.com/books?id=maK3sbTVhsoC&pg=PA102 102–103]}}</ref>}} ndipo chinthu chilichose ichi mbura kuŵa zero chili na [[multiplicative inverse|chakupiluska cha kwandaniska]].<ref>{{multiref | {{harvnb|Geddes|Czapor|Labahn|2007|p=[https://books.google.com/books?id=9fOUwkkRxT4C&pg=PA24 24]}} | {{harvnb|Weisstein|2003|pp=1047, 2579}} | {{harvnb|Pratt|2022|loc=§ 2.4 Fields}} }}</ref> Mphete ya vipendeko vyambura kugaŵika njambura kupanga munda chifukwa yikusoŵa vyakupiluska vya kwandaniska. Mwachiyelezgero, chakupiluska cha kwandaniska cha <math>7</math> ni {{tmath|1= \tfrac{1}{7} }}, icho ndi cipendeko cambura kugaŵika yayi. [[rational numbers|Vipendeko vyakugaŵikika]], [[real numbers|vipendeko vyeneco]], na [[complex numbers|vipendeko vyakusuzga]] vilivyose vikupanga munda na nchito za kusazga na kwandaniska.<ref>{{multiref | {{harvnb|Irving|2004|pp=77, 236}} | {{harvnb|Weisstein|2003|pp=1047, 2579}} | {{harvnb|Hohn|2013|pp=[https://books.google.com/books?id=9XlFu4XQ6nUC&pg=PA83 83–84]}} }}</ref> [[Ring theory|Sambiro la mphete]] ni kusambira mphete, kupenja vinthu nga [[subring|mphete zamunsi]], [[quotient ring|mphete za mgaŵano]], [[polynomial ring|mphete za polynomial]], na [[Ideal (ring theory)|ma ideal]] pamoza na fundo nga [[Hilbert's basis theorem|fundo ya msingi ya Hilbert]].<ref>{{multiref | {{harvnb|Serovajsky|2020|loc=§ Room 4B.5 Rings}} | {{harvnb|Kleiner|2007|p=[https://books.google.com/books?id=udj-1UuaOiIC&pg=PA63 63]}} | {{harvnb|Kline|1990|p=[https://books.google.com/books?id=8YaBuGcmLb0C&pg=PA1153 1153]}} }}</ref> Sambiro la munda likukhwaskana na minda, kupenja [[field extension|kutandarizga kwa munda]], [[algebraic closure|kujara kwa algebra]], na [[finite fields|minda yakumalira]].<ref>{{multiref | {{harvnb|Waerden|2003|pp=110–114, 231, 246}} | {{harvnb|Karpilovsky|1989|p=[https://books.google.com/books?id=-2WR0fw9gLMC&pg=PA45 45]}} | {{harvnb|Kleiner|2007|p=[https://books.google.com/books?id=udj-1UuaOiIC&pg=PA63 63]}} }}</ref> [[Galois theory|Sambiro la Galois]] likupenja uzeru pakati pa sambiro la munda na sambiro la magulu, likujizika pa [[fundamental theorem of Galois theory|fundo yikuru ya sambiro la Galois]].<ref>{{multiref | {{harvnb|Lang|2005|pp=[https://books.google.com/books?id=Fge-BwqhqIYC&pg=PA261 261–262]}} | {{harvnb|Cox|2012|pp=[https://books.google.com/books?id=vBKrOch1AkYC&pg=PA161 161–162]}} }}</ref> ==== Sambiro la Kukhwaskana Pakati pa Magulu gha Algebra ==== [[File:Magma to group2.svg|thumb|class=skin-invert-image|alt=Diagram of relations between some algebraic structures|Chithunzithunzi cha ukhwaskano pakati pa magulu ghanyake gha algebra. Mwachiyelezgero, mbali yake yapachanya kumalyo yikulongora kuti [[Magma (algebra)|magma]] yikuŵa [[semigroup|semigroup]] usange nchito yake njakukolerana.]] Kupambuka magulu, mphete, na minda, kuli magulu ghanandi ghanyake gha algebra agho ghakusambirika na algebra. Ghakusazgamo [[Magma (algebra)|ma magma]], [[semigroup|ma semigroup]], [[monoid|ma monoid]], [[abelian group|magulu gha abelian]], [[commutative ring|mphete zakusinthana]], [[Module (mathematics)|ma module]], [[Lattice (order)|ma lattice]], [[vector space|malo gha vector]], [[Algebra over a field|algebra pa munda]], na magulu [[associative|ghakukolerana]] na [[non-associative algebras|ghambura kukolerana]]. Ghakupambana pakati pawo pa mtundu wa vinthu ivyo ghakulongosora na vikhumbikwa ivyo nchito zawo zikufiska. Ghanandi ghakukhwaskana wene pakati pawo mu ntchito yakuti gulu la musingi lingasinthika kuŵa gulu lakuzikirapo comenecomene mwakusazgirapo vikakiro.<ref name="auto9">{{multiref | {{harvnb|Pratt|2022|loc=Lead section, § 2. Abstract Algebra}} | {{harvnb|Merzlyakov|Shirshov|2020|loc=The Subject Matter of Algebra, Its Principal Branches and Its Connection with Other Branches of Mathematics.}} | {{harvnb|Bourbaki|1998|pp=[https://books.google.com/books?id=STS9aZ6F204C&pg=PA428 428–430, 446]}} }}</ref> Mwachiyelezgero, magma yikuŵa semigroup usange nchito yake njakukolerana.<ref>{{harvnb|Cooper|2011|p=[https://books.google.com/books?id=Fybzl6QB62gC&pg=PA60 60]}}</ref> [[Homomorphism|Ma homomorphism]] ni vipangizo vyakupenjera vinjeru vya mzimu mwakuyaniska magulu ghaŵiri gha algebra.<ref>{{multiref | {{harvnb|Rowen|2006|p=[https://books.google.com/books?id=AhEPCgAAQBAJ&pg=PA12 12]}} | {{harvnb|Pratt|2022|loc=§ 3.3 Birkhoff's Theorem}} | {{harvnb|Grätzer|2008|p=34}} }}</ref> Homomorphism ni mapu ghakufuma ku gulu lakuzikapo la gulu limoza la algebra kuya ku gulu lakuzikapo la gulu linyake la algebra, ghakusunga mikhaliro yinyake ya mzimu. Usange magulu ghaŵiri gha algebra ghakugwiliskira ntchito nchito zaŵiri ndipo ghali mu mtundu <math>\langle A, \circ \rangle</math> na <math>\langle B, \star \rangle</math> mbwenu mapu <math>h: A \to B</math> ni homomorphism usange ghakukwaniska ivi: {{tmath|1= h(x \circ y) = h(x) \star h(y) }}. Kuŵako kwa homomorphism kukulongora kuti nchito <math>\star</math> mu gulu lachiŵiri la algebra yikugwira ntchito yakuyana na iyo nchito <math>\circ</math> yikugwira mu gulu lakwamba la algebra.<ref>{{multiref | {{harvnb|Pratt|2022|loc=§ 3.3 Birkhoff's Theorem}} | {{harvnb|Rowen|2006|p=[https://books.google.com/books?id=AhEPCgAAQBAJ&pg=PA12 12]}} | {{harvnb|Gowers|Barrow-Green|Leader|2010|pp=[https://books.google.com/books?id=ZOfUsvemJDMC&pg=PA27 27–28]}} | {{harvnb|Adhikari|2016|pp=[https://books.google.com/books?id=MIAXDQAAQBAJ&pg=PA5 5–6]}} }}</ref> [[Isomorphisms|Ma isomorphism]] ni mtundu wapadera wa homomorphism uwo ukulongora kuyanako kukuru pakati pa magulu ghaŵiri gha algebra. Isomorphism ni homomorphism [[bijective|yakwenerana pa chimoza-na-chimoza]], ndikuti, yikupanga ukhwaskano wa chimoza-na-chimoza pakati pa vinthu vya magulu ghaŵiri gha algebra. Ichi chikung'anamura kuti chinthu chilichose cha gulu lakwamba la algebra chikuya ku chinthu chimoza chapadera mu gulu lachiŵiri, kwambura vinthu vyakusoŵa mapu mu gulu lachiŵiri.<ref>{{multiref | {{harvnb|Neri|2019|pp=[https://books.google.com/books?id=NMOlDwAAQBAJ&pg=PA278 278–279]}} | {{harvnb|Ivanova|Smirnov|2012}} | {{harvnb|Deo|2018|p=[https://books.google.com/books?id=HjtRDwAAQBAJ&pg=PA295 295]}} | {{harvnb|Ono|2019|p=[https://books.google.com/books?id=SR2nDwAAQBAJ&pg=PA84 84]}}}}</ref> [[File:Venn A subset B.svg|thumb|alt=Venn diagram of a set and its subset|[[Subalgebra|Vigulu vyamunsi vya algebra]] vikufinyikizga nchito zake ku chigaŵa cha gulu lakuzikapo la gulu la algebra lakwamba.]] Chipangizo chinyake cha kuyaniska nkhukhwaskana pakati pa gulu la algebra na [[Subalgebra#Subalgebras in universal algebra|chigulu chamunsi cha algebra]] chake.<ref name="auto8">{{multiref | {{harvnb|Indurkhya|2013|pp=[https://books.google.com/books?id=foTrCAAAQBAJ&pg=PA217 217–218]}} | {{harvnb|Pratt|2022|loc=§ 3.3 Birkhoff's Theorem}} | {{harvnb|Grätzer|2008|p=34}} }}</ref> Gulu la algebra na chigulu chamunsi chake vikugwiliskira ntchito nchito zakuyana,{{efn|Kuyana na malongosoro ghanyake, chigulu chamunsi chingaŵaso na nchito zichoko.<ref name="auto6">{{harvnb|Indurkhya|2013|pp=[https://books.google.com/books?id=foTrCAAAQBAJ&pg=PA217 217–218]}}</ref>}} izo zikulondezga maxiom ghakuyana. Kupambana kwapera nkhwakuti gulu lakuzikapo la chigulu chamunsi ni chigaŵa cha gulu lakuzikapo la gulu la algebra.{{efn|Ichi chikung'anamura kuti vinthu vyose vya gulu lakwamba nivyaso vinthu vya gulu lachiŵiri kweni gulu lachiŵiri lingaŵa na vinthu ivyo vilipo yayi mu gulu lakwamba.<ref>{{harvnb|Efimov|2014}}</ref>}} Nchito zose mu chigulu chamunsi zikukhumbikwa kuŵa [[Closure (mathematics)|zakujara]] mu gulu lake lakuzikapo, ndikuti, zikufumiska pera vinthu ivyo vili mu gulu ili.<ref name="auto8"/> Mwachiyelezgero, gulu la [[Parity (mathematics)|vipendeko vyakwenerana]] pamoza na kusazga ni chigulu chamunsi cha gulu lose la vipendeko vyambura kugaŵika pamoza na kusazga. Ichi nchakuti chifukwa muzgoro wa vipendeko viŵiri vyakwenerana ni cipendeko cakwenerana kavili. Kweni gulu la vipendeko vyambura kwenerana pamoza na kusazga nichigulu chamunsi yayi chifukwa nichambura kujara: kusazga vipendeko viŵiri vyambura kwenerana vikufumiska cipendeko chakwenerana, icho ndi chigaŵa yayi cha gulu ilo lasankhika.<ref name="auto6"/> [[Universal algebra|Algebra ya wonse]] ni sambiro la magulu gha algebra mwaŵukuru. Nga chigaŵa cha vinjeru vyake vyakuwonera vinthu vyakuzomerezgeka, yikupwelelera yayi vinthu vyeneco ivyo vikupanga magulu ghakuzikapo ndipo yikuwona nchito izo zili na vyakwiza-mu vinandi kuluska viŵiri, nga [[ternary operation|nchito zitatu]]. Yikupereka chiwongo cha kupenja vinjeru vya mzimu ivyo magulu ghakupambanapambana gha algebra ghali navyo pamoza.<ref>{{multiref | {{harvnb|Pratt|2022|loc=§ 3. Universal Algebra}} | {{harvnb|Cohn|2012|p=[https://books.google.com/books?id=6tbuCAAAQBAJ&pg=PR13 xiii]}} }}</ref>{{efn|Nthowa yakupambanako pachoko yikupulikiska algebra ya wonse kuŵa sambiro la mtundu umoza wa magulu gha algebra ghakumanyikwa nga ma algebra ghawonse. Ma algebra ghawonse ghakulongosoreka mwakuzirwa kuti ghasazgemo magulu ghanyake ghanandi gha algebra. Mwachiyelezgero, magulu na mphete ni mitundu yapadera ya algebra ya wonse.<ref>{{multiref | {{harvnb|Smirnov|2020}} | {{harvnb|Grätzer|2008|pp=7–8}} | {{harvnb|Bahturin|2013|p=[https://books.google.com/books?id=8RbvCAAAQBAJ&pg=PA346 346]}} }}</ref>}} Chimoza mwa vinjeru vya mzimu ivi vikukhwaskana na [[Identity (mathematics)#Logic and universal algebra|vinthu vyakuyana]] (identities) ivyo nivyanadi mu magulu ghakupambanapambana gha algebra. Mu mkhalidwe uwu, chinthu chakuyana ni equation [[Universal quantification|yawonse]] panji equation iyo nyanadi ku vinthu vyose vya gulu lakuzikapo. Mwachiyelezgero, kusinthana (commutativity) ni equation yawonse iyo yikuti <math>a \circ b</math> nichakuyana na <math>b \circ a</math> ku vinthu vyose.<ref>{{multiref | {{harvnb|Pratt|2022|loc=§ 3.2 Equational Logic}} | {{harvnb|Mal’cev|1973|pp=210–211}} }}</ref> [[Variety (universal algebra)|Mtundu wakuyana]] (variety) ni gulu la magulu ghose gha algebra agho ghakukwaniska vinthu vinyake vyakuyana. Mwachiyelezgero, usange magulu ghaŵiri gha algebra ghakukwaniska kusinthana mbwenu ghose ghaŵiri ni chigaŵa cha mtundu wakuyana uwo ukuyana nawo.<ref>{{multiref | {{harvnb|Mal’cev|1973|pp=210–211}} | {{harvnb|Cohn|2012|p=[https://books.google.com/books?id=6tbuCAAAQBAJ&pg=PA162 162]}} | {{harvnb|Rosen|2012|p=[https://books.google.com/books?id=-oVvEAAAQBAJ&pg=PA779 779]}} | {{harvnb|Hazewinkel|1994|p=[https://books.google.com/books?id=PE1a-EIG22kC&pg=PA406 406]}} }}</ref>{{efn|Mtundu uliwose wa gulu la algebra ukupanga yayi mtundu wakuyana. Mwachiyelezgero, magulu na mphete vyose vikupanga mtundu wakuyana kweni minda njambura kupanga.<ref>{{harvnb|Cohn|1995|p=[https://books.google.com/books?id=u-4ADgUgpSMC&pg=PA8 8]}}</ref>}}{{efn|Kupambuka vinthu vyakuyana, algebra ya wonse yikukhumbikwaso na vinjeru vya mzimu ivyo vikukhwaskana na [[quasi-identity|vinthu vyakuyana pachoko]] (quasi-identities). Chinthu chakuyana pachoko ni chinthu chakuyana icho chikukhumbikwa pera pasi pa vikhumbikwa vinyake (ivyo vikuŵa mu mtundu wa [[Horn clause|chigaŵa cha Horn]]<ref>{{harvnb|Mal’cev|1973|p=211}}</ref>). Ni kutandarizga kwa chinthu chakuyana mu mzimu wakuti chinthu chilichose chakuyana ni chinthu chakuyana pachoko kweni chinthu chilichose chakuyana pachoko ni yayi chinthu chakuyana. [[Quasivariety|Mtundu wakuyana pachoko]] ni gulu la magulu ghose gha algebra agho ghakukwaniska vinthu vinyake vyakuyana pachoko.<ref>{{multiref | {{harvnb|Mal’cev|1973|pp=210–211}} | {{harvnb|Pratt|2022|loc=§ 3. Universal Algebra}} | {{harvnb|Artamonov|2003|p=[https://books.google.com/books?id=sLDGY4Hk8V0C&pg=PA873 873]}} }}</ref>}} [[Category theory|Sambiro la mikhaliro]] likupenja umo vinthu vya masamu vikukhwaskirana na chinyake mwakugwiliskira ntchito mzimu wa [[Category (mathematics)|mikhaliro]] (categories). Mkhaliro ni chiŵungano cha vinthu pamoza na chiŵungano cha [[morphisms|vilongozgi]] panji "mivi" pakati pa vinthu ivi. Viŵungano ivi viŵiri vikwenera kukwaniska vikhumbikwa vinyake. Mwachiyelezgero, vilongozgi vingakolerana, panji ku ''kolerana'': usange muvi ukuŵako kufuma ku chinthu <math>a</math> kuya ku chinthu {{tmath|1= b }}, ndipo muvi unyake kufuma ku chinthu <math>b</math> kuya ku chinthu {{tmath|1= c }}, mbwenu pakwenera kuŵakoso muvi kufuma ku chinthu <math>a</math> kuya ku chinthu {{tmath|1= c }}. Kukolerana kwa vilongozgi kukukhumbikwa kuŵa kwakukolerana, ndipo pakwenera kuŵako "muvi wa identity" ku chinthu chilichose.<ref>{{multiref | {{harvnb|Weisstein|2003|pp=347–348}} | {{harvnb|Gowers|Barrow-Green|Leader|2010|pp=[https://books.google.com/books?id=ZOfUsvemJDMC&pg=PA6 6, 165]}} | {{harvnb|Cheng|2023|p=102}} }}</ref> Mikhaliro yikugwiliskika comenecomene mu masamu gha sono chifukwa yikupereka chiwongo chakukoleranya kuti chilongosore na kupenja vinjeru vinandi vya musingi vya masamu. Mwachiyelezgero, magulu ya vinthu ghangalongosoreka na [[category of sets|mkhaliro wa magulu]], ndipo gulu lililose lingawoneka kuŵa vilongozgi vya mkhaliro uwo uli na chinthu chimoza pera.<ref>{{multiref | {{harvnb|Gowers|Barrow-Green|Leader|2010|pp=[https://books.google.com/books?id=ZOfUsvemJDMC&pg=PA6 6, 165]}} | {{harvnb|Borceux|1994|p=[https://books.google.com/books?id=YfzImoopB-IC&pg=PA20 20]}} | {{harvnb|Laos|1998|p=[https://books.google.com/books?id=1r7dSn4ZqogC&pg=PA100 100]}} | {{harvnb|Cheng|2023|pp=128–131}} }}</ref> == Mbiri == {{main|History of algebra|Timeline of algebra}} [[File:Rhind Mathematical Papyrus.jpg|thumb|alt=Rhind Papyrus|[[Rhind Mathematical Papyrus|Papyrus ya Rhind Mathematical]] kufuma ku [[ancient Egypt|Egypt yakale]], iyo yikuŵa ya {{circa|1650 BCE}}, ni chimoza cha vyolálemba vyakale comenecomene ivyo vikudumbiskana masuzgo gha algebra.]] Chiyambi cha algebra chili mu kuyezgayezga kwakumazga masuzgo gha masamu agho ghakukhwaskana na kuŵelenga na viŵelengero vyambura kumanyikwa. Vyakukula ivi vikachitika mu nyengo yakale mu [[Babylonia]], [[Ancient Egypt|Egypt]], [[Ancient Greece|Greece]], [[Ancient China|China]], na [[Ancient India|India]]. Chimoza mwa vyolálemba vyakale comenecomene pa masuzgo gha algebra ni [[Rhind Mathematical Papyrus|Papyrus ya Rhind Mathematical]] kufuma ku Egypt yakale, iyo yikalembeka pafupifupi mu 1650&nbsp;BCE.{{efn|Zuŵa lenelene nkhwakususkana, ndipo ŵalongozgi ŵanyake ŵa mbiri ŵakuti liŵe pafupifupi mu 1550&nbsp;BCE.<ref>{{multiref | {{harvnb|Corry|2024|loc=§ Problem-Solving in Egypt and Babylon}} | {{harvnb|Brezinski|Meurant|Redivo-Zaglia|2022|p=[https://books.google.com/books?id=4IGhEAAAQBAJ&pg=PA34 34]}} }}</ref>}} Yikudumbiskana vyakumazga vya [[linear equations|ma equation gha mzere]], nga umo vikulongosoreka mu masuzgo nga "Chinthu; chigaŵa chake chachinayi chikusazgikapo pa icho. Chikuŵa 15. Kasi chinthu ni chiwuli?" Mabuwe gha dongo gha ku Babylon kufuma pa nyengo yeneyiyo ghakulongosora nthowa zakumazga ma equation gha mzere na [[Quadratic equation|polynomial gha digiri yachiŵiri]], nga nthowa ya [[completing the square|kukwaniska cikwezgo]].<ref>{{multiref | {{harvnb|Tanton|2005|p=9}} | {{harvnb|Kvasz|2006|p=290}} | {{harvnb|Corry|2024|loc=§ Problem Solving in Egypt and Babylon}} }}</ref> Vinandi mwa vinjeru ivi vikafika ku Ŵagiriki ŵakale. Kwambira mu vilimika vya 6 BCE, chikhumbo chawo chikuru chikaŵa geometry m'malo mwa algebra, kweni ŵakagwiliskira ntchito nthowa za algebra kumazga masuzgo gha geometry. Mwachiyelezgero, ŵakasandanga vithunzithunzi vya geometry apo utali na malo ghake vikatoleka kuŵa viŵelengero vyambura kumanyikwa ivyo vikwenera kusangika, nga umo vikawonekera mu nthowa ya [[Pythagoras]] ya [[difference of two squares|mphambano wa vikwezgo viŵiri]] na munyuma mu buku la [[Euclid's Elements|Euclid's Elements]].<ref>{{multiref | {{harvnb|Tanton|2005|p=9}} | {{harvnb|Kvasz|2006|p=290}} | {{harvnb|Corry|2024|loc=§ The Pythagoreans and Euclid}} }}</ref> Mu vilimika vya 3 CE, [[Diophantus]] wakapeleka malongosoro ghakuzura gha umo wangamazgira ma equation gha algebra mu magazini ghakuchemeka ''[[Arithmetica]]''. Ndiyo wakaŵa wakwamba kuyezgayezga kugwiliskira ntchito viwimbo (symbolic notation) kulongosora ma polynomial.<ref>{{multiref | {{harvnb|Merzlyakov|Shirshov|2020|loc=§ Historical Survey}} | {{harvnb|Sialaros|2018|p=[https://books.google.com/books?id=2PZYDwAAQBAJ&pg=PT55 55]}} | {{harvnb|Corry|2024|loc=§ Diophantus}} }}</ref> Ntchito ya Diophantus yikakhwaskira kukula kwa algebra ku Ŵaarabu, apo nthowa zake zinandi zikawonekera mu vinjeru na vipangizo ivyo vikagwiliskika mu algebra ya Chiarabu ya nyengo za pakati.<ref>{{multiref | {{harvnb|Hettle|2015|pp=139–141, 160–161}} | {{harvnb|Christianidis|Megremi|2019|pp=16–17}} }}</ref> Ku China wakale, ''[[The Nine Chapters on the Mathematical Art]]'', buku ilo likalembeka pa nyengo yakufuma ku vilimika vya 10 BCE kufika ku vilimika vya 2 CE,<ref>{{harvnb|Burgin|2022|p=[https://books.google.com/books?id=rWF2EAAAQBAJ&pg=PA10 10]}}</ref> likasandaso nthowa zakupambanapambana zakumazgira ma equation gha algebra, kusazgamo kugwiliskira ntchito vinthu vyakuyana na matrix.<ref>{{harvnb|Higgins|2015|p=[https://books.google.com/books?id=QANiCgAAQBAJ&pg=PA89 89]}}</ref> [[File:Al-Khwarizmi portrait.jpg|thumb|upright=0.6|left|Chithunzi cha kuyezgayezga cha [[Al-Khwarizmi]], chakufuma pa sitembu ya Soviet]] Nkhwakususkana usange vyakukula ivi vyakale ni chigaŵa cha algebra panji ni vyakwambiliranji pera. Vikapeleka vyakumazga vya masuzgo gha algebra kweni vikaghanaghanira yayi mwamzimu wakudumura na wawonse, m'malo mwake vikakhalilira pa mkhalidwe pakuyowoya na kugwiliskika padera pera.<ref>{{multiref | {{harvnb|Kvasz|2006|pp=290–291}} | {{harvnb|Sialaros|2018|p=[https://books.google.com/books?id=2PZYDwAAQBAJ&pg=PT55 55]}} | {{harvnb|Boyer|Merzbach|2011|p=[https://books.google.com/books?id=bR9HAAAAQBAJ&pg=PA161 161]}} | {{harvnb|Derbyshire|2006|p=[https://books.google.com/books?id=mLqaAgAAQBAJ&pg=PT39 31]}} }}</ref> Ichi chikasintha na msandi wa masamu wa ku Persia, [[Al-Khwarizmi]],{{efn|Ŵalongozgi ŵanyake ŵa mbiri ŵakumuwona kuŵa "wiske wa algebra" apo ŵanyake ŵakupeleka zina ili ku Diophantus.<ref>{{multiref | {{harvnb|Boyer|Merzbach|2011|p=[https://books.google.com/books?id=bR9HAAAAQBAJ&pg=PA161 161]}} | {{harvnb|Derbyshire|2006|p=[https://books.google.com/books?id=mLqaAgAAQBAJ&pg=PA31 31]}} }}</ref> }} uyo wakafumiska buku lake ''[[The Compendious Book on Calculation by Completion and Balancing]]'' mu 825 CE. Al-Khwarizmi wakapeleka malongosoro ghakwamba ghakuzomerezgeka ghakumazgira ma equation mwakughaŵika mu mitundu 6 yakuzomerezgeka{{Efn|Mitundu iyi ni <math> bx = c </math>, <math> ax^2 = bx </math>, <math> ax^2 = c </math>, <math> ax^2 + bx = c </math>, <math> ax^2 + c = bx </math>, na <math> ax^2 = bx + c </math>.{{sfn|Bradley|2006|p=[http://books.google.com/books?id=EIdtVPeD7GcC&pg=PA95 95]}}}} ndiposo kupereka ndondomeko zakuzomerezgeka, mwakuyila-kuyila, za vyakuvimazga. Mwakuwuskapo nthowa izi ku vithunzithunzi vyapadera vya geometry na kuwona viŵelengero vyambura kumanyikwa kuŵa vinthu vyawonse vya algebra, wakakhozga chiwongo cha kugwira ntchito chakuzomerezgeka. Kusintha uku, kufuma ku kumazga masuzgo ghapadera kuya ku kukhozga nthowa yawonse, nkhwakasintha algebra kuŵa sambiro lakujimira paokha.<ref>{{multiref | {{harvnb|Tanton|2005|p=10}} | {{harvnb|Kvasz|2006|pp=291–293}} | {{harvnb|Merzlyakov|Shirshov|2020|loc=§ Historical Survey}} }}</ref> Vyakukhwaskira vinyake vyakuzirwa ku algebra vikafuma ku msandi wa masamu wa Chiarabu [[Thābit ibn Qurra]] naye so mu vilimika vya 9 CE na msandi wa masamu wa ku Persia [[Omar Khayyam]] mu vilimika vya 11 na 12.<ref>{{multiref | {{harvnb|Waerden|2013|pp=3, 15–16, 24–25}} | {{harvnb|Jenkins|2010|p=[https://books.google.com/books?id=giEkCQAAQBAJ&pg=PA82 82]}} | {{harvnb|Pickover|2009|p=[https://books.google.com/books?id=JrslMKTgSZwC&pg=PA90 90]}} }}</ref> Ku India, [[Brahmagupta]] wakasanda umo wangamazgira ma equation gha digiri yachiŵiri na ndondomeko za ma equation gha vyambura-kumanyikwa vinandi mu vilimika vya 7 CE. Pakati pa vyakukula vyake vikaŵako kugwiliskira ntchito zero na vipendeko vyakusuzga (negative numbers) mu ma equation gha algebra.<ref>{{multiref | {{harvnb|Tanton|2005|pp=9–10}} | {{harvnb|Corry|2024|loc=§ The Equation in India and China}} }}</ref> Ŵasandi ŵa masamu ŵa ku India [[Mahāvīra (mathematician)|Mahāvīra]] mu vilimika vya 9 na [[Bhāskara II]] mu vilimika vya 12 ŵakakhozgaso nthowa na vinjeru vya Brahmagupta.<ref>{{multiref | {{harvnb|Seshadri|2010|p=[https://books.google.com/books?id=w_JdDwAAQBAJ&pg=PA156 156]}} | {{harvnb|Emch|Sridharan|Srinivas|2005|p=[https://books.google.com/books?id=qfJdDwAAQBAJ&pg=PA20 20]}} }}</ref> Mu 1247, msandi wa masamu wa ku China [[Qin Jiushao]] wakalemba buku la ''[[Mathematical Treatise in Nine Sections]]'', ilo likusazgamo [[Horner's method|nthowa yakuŵelenga]] ya [[Polynomial evaluation|kuŵelenga mtengo wa ma polynomial]], kusazgamo ma polynomial gha madigiri ghapachanya.<ref>{{multiref | {{harvnb|Smorynski|2007|p=[https://books.google.com/books?id=qY657eFq7UgC&pg=PA137 137]}} | {{harvnb|Zwillinger|2002|p=[https://books.google.com/books?id=gE_MBQAAQBAJ&pg=PA812 812]}} }}</ref> {{multiple image | perrow = 2 | total_width = 350 | image1 = Francois Viete.jpeg | alt1 = Drawing of François Viète | image2 = Frans Hals - Portret van René Descartes (cropped).jpg | alt2 = Painting of René Descartes | footer = [[François Viète]] (kumalyo) na [[René Descartes]] ŵakasanga viwimbo vyakwenerana kulongosora ma equation mwamzimu wakudumura na wachidango. }} Msandi wa masamu wa ku Italy [[Fibonacci]] wakiza na vinjeru na nthowa za Al-Khwarizmi ku Ulaya mu mabuku ghake, kusazgamo ''[[Liber Abaci]]''.<ref>{{multiref | {{harvnb|Waerden|2013|pp=32–35}} | {{harvnb|Tanton|2005|p=10}} | {{harvnb|Kvasz|2006|p=293}} }}</ref> Mu 1545, msandi wa masamu wa mitundu yinandi wa ku Italy [[Gerolamo Cardano]] wakafumiska buku lake ''[[Ars Magna (Cardano book)|Ars Magna]]'', ilo likakhwaskira vinthu vinandi mu algebra, likadumbiskana [[imaginary numbers|vipendeko vya mung'anamuro]], ndipo likaŵa lakwamba kupeleka nthowa zawonse zakumazgira ma equation gha [[Cubic equation|digiri yitatu]] na [[quartic equation|digiri yinayi]].<ref>{{multiref | {{harvnb|Tanton|2005|p=10}} | {{harvnb|Kvasz|2006|p=293}} | {{harvnb|Corry|2024|loc=§ Cardano and the Solving of Cubic and Quartic Equations}} | {{harvnb|Miyake|2002|p=[https://books.google.com/books?id=G0P2BwAAQBAJ&pg=PA268 268]}} }}</ref> Mu vilimika vya 16 na 17, ŵasandi ŵa masamu ŵa ku France [[François Viète]] na [[René Descartes]] ŵakiza na malembelo na viwimbo kwimira vyambura-kumanyikwa na nchito, kupangiska kuti ma equation ghalembeke mwamzimu wachidango na wakudumura. Awo ŵakaŵako panthazi pawo ŵakajighemezga pa malongosoro ghakuyowoya gha masuzgo na vyakumazga.<ref>{{multiref | {{harvnb|Tanton|2005|p=10}} | {{harvnb|Kvasz|2006|pp=291–292, 297–298, 302}} | {{harvnb|Merzlyakov|Shirshov|2020|loc=§ Historical Survey}} | {{harvnb|Corry|2024|loc=§ Viète and the Formal Equation, § Analytic Geometry}} }}</ref> Ŵalongozgi ŵanyake ŵa mbiri ŵakuwona kukula uku kuŵa mzuŵa wakuzirwa mu mbiri ya algebra ndipo ŵakuwona ivyo vikaŵako pambere kuŵa mbiri-ntchakwamba ya algebra chifukwa vikasoŵanga mzimu wakudumura uwo ukujimira pa kugwiliskira ntchito viwimbo.<ref>{{multiref | {{harvnb|Hazewinkel|1994|p=[https://books.google.com/books?id=PE1a-EIG22kC&pg=PA73 73]}} | {{harvnb|Merzlyakov|Shirshov|2020|loc=§ Historical Survey}} }}</ref> Mu vilimika vya 17 na 18, kuyezgayezga kwakuluska kukachitika kupenja vyakumazga vyawonse ku ma polynomial gha digiri yankonde na yapachanya. Vyose ivi vikafiliskika.<ref name="auto3">{{multiref | {{harvnb|Tanton|2005|p=10}} | {{harvnb|Merzlyakov|Shirshov|2020|loc=§ Historical Survey}} | {{harvnb|Corry|2024|loc=§ Impasse with Radical Methods}} }}</ref> Kumapeleko gha vilimika vya 18, msandi wa masamu wa ku Germany [[Carl Friedrich Gauss]] wakalongosora fundo yikuru ya algebra, iyo yikulongosora kuŵako kwa [[Zero of a function|vizero]] vya ma polynomial gha digiri yiliyose kwambura kupeleka yankho lawonse.<ref name="auto7"/> Kwambilira kwa vilimika vya 19, msandi wa masamu wa ku Italy [[Paolo Ruffini]] na msandi wa masamu wa ku Norway [[Niels Henrik Abel]] [[Abel–Ruffini theorem|ŵakakhozga]] kuti palije yankho lawonse ilo lilipo ku ma polynomial gha digiri yankonde na yapachanya.<ref name="auto3"/> Kwiza pa na pamanyuma pachoko pa vyakusanga vyawo, msandi wa masamu wa ku France [[Évariste Galois]] wakakhozga icho pamanyuma chikachemeka [[Galois theory|sambiro la Galois]], ilo likapeleka kupenja kwakukuzura kwa vyakumazga vya ma polynomial apo so likakhozga msingi wa [[group theory|sambiro la magulu]].<ref name="auto2"/> Ŵasandi ŵa masamu paukhwakuŵa ŵakamanya kuzirwa kwa sambiro la magulu ku magulu ghanyake gha masamu ndipo ŵakaligwiliskira ntchito ku vipangizo nga geometry na sambiro la vipendeko.<ref>{{multiref | {{harvnb|Corry|2024|loc=§ Applications of Group Theory}} | {{harvnb|Bueno|French|2018|pp=[https://books.google.com/books?id=kmZaDwAAQBAJ&pg=PA73 73–75]}} }}</ref> [[File:Garrett Birkhoff.jpeg|thumb|alt=Photo of Garrett Birkhoff|[[Garrett Birkhoff]] wakakhozga vinjeru vinandi vya msingi vya algebra ya wonse.|left|upright=0.8]] Kwambira pakati pa vilimika vya 19, chikhumbo mu algebra chikasintha kufuma ku kusambira ma polynomial ivyo vikakhwaskana na algebra ya pulayimale kuya ku kupenja kwakukuru kwa magulu gha algebra, ndipo ichi chikawoneka pakufuma kwa [[abstract algebra|algebra yakudumura]]. Nthowa iyi yikapenja msingi wa maxiom wa nchito za algebra zakupambanapambana.<ref>{{multiref | {{harvnb|Merzlyakov|Shirshov|2020|loc=§ Historical Survey}} | {{harvnb|Tanton|2005|p=10}} | {{harvnb|Corry|2024|loc=§ Structural Algebra}} | {{harvnb|Hazewinkel|1994|pp=[https://books.google.com/books?id=PE1a-EIG22kC&pg=PA73 73–74]}} }}</ref> Kusangika kwa ndondomeko nyifya za algebra izo zikuzirwa pa nchito na vinthu vyakupambanapambana vikalondezga kukula uku, nga [[Boolean algebra]], [[Vector space|algebra ya vector]], na [[matrix algebra|algebra ya matrix]].<ref>{{multiref | {{harvnb|Merzlyakov|Shirshov|2020|loc=§ Historical Survey}} | {{harvnb|Tanton|2005|p=10}} | {{harvnb|Corry|2024|loc=§ Matrices, § Quaternions and Vectors}} }}</ref> Vyakukula vyakuzirwa vyakwamba mu algebra yakudumura vikapangika na ŵasandi ŵa masamu ŵa ku Germany [[David Hilbert]], [[Ernst Steinitz]], na [[Emmy Noether]] pamoza na msandi wa masamu wa ku Austria [[Emil Artin]]. Ŵakasanda mitundu yakupambanapambana ya magulu gha algebra ndipo ŵakaghapatuliska kuyana na maxiom ghawo ghakuzikapo kuŵa mitundu, nga magulu, mphete, na minda.<ref>{{multiref | {{harvnb|Merzlyakov|Shirshov|2020|loc=§ Historical Survey}} | {{harvnb|Corry|2024|loc=§ Hilbert and Steinitz, § Noether and Artin}} | {{harvnb|Hazewinkel|1994|pp=[https://books.google.com/books?id=PE1a-EIG22kC&pg=PA73 73–74]}} }}</ref> Mzimu wa nthowa yikuru comenecomene iyo yikukhwaskana na algebra ya wonse ukaghanaghanika na msandi wa masamu wa ku England [[Alfred North Whitehead]] mu buku lake la 1898 ''A Treatise on Universal Algebra''. Kwambira mu vya 1930, msandi wa masamu wa ku America [[Garrett Birkhoff]] wakatandarizga vinjeru ivi ndipo wakakhozga vinjeru vinandi vya msingi vya gulu ili la sambiro.<ref>{{multiref | {{harvnb|Grätzer|2008|p=[https://books.google.com/books?id=8lNkXPJas4wC&pg=PR7 vii]}} | {{harvnb|Chang|Keisler|1990|p=[https://books.google.com/books?id=uiHq0EmaFp0C&pg=PA603 603]}} | {{harvnb|Knoebel|2011|p=[https://books.google.com/books?id=VWS_sgO2uvgC&pg=PA5 5]}} | {{harvnb|Hazewinkel|1994|pp=[https://books.google.com/books?id=PE1a-EIG22kC&pg=PA74 74–75]}} }}</ref> Kusangika kwa algebra ya wonse kukalongozgera ku kufuma kwa vipimo vinyake vinyifya ivyo vikang'anamuka pa kupanga algebra ya masamu ghanyake{{em dash}}ndikuti, kugwiliskira ntchito nthowa za algebra ku magulu ghanyake gha masamu. Algebra ya topology yikafuma mu vilimika vyakwamba vya 20, kusambira magulu gha algebra nga [[topological groups|magulu gha topology]] na [[Lie groups|magulu gha Lie]].<ref>{{multiref | {{harvnb|Hazewinkel|1994|pp=[https://books.google.com/books?id=PE1a-EIG22kC&pg=PA74 74–75]}} | {{harvnb|Kleiner|2007|p=[https://books.google.com/books?id=udj-1UuaOiIC&pg=PA100 100]}} | {{harvnb|Carlson|2024|loc=§ History of topology}} }}</ref> Mu vya 1940 na 50, [[homological algebra|algebra ya homology]] yikafuma, kugwiliskira ntchito nthowa za algebra kusambira [[Homology (mathematics)|homology]].<ref>{{multiref | {{harvnb|Hazewinkel|1994|pp=[https://books.google.com/books?id=PE1a-EIG22kC&pg=PA74 74–75]}} | {{harvnb|Weibel|1995|p=[https://books.google.com/books?id=UtIhAwAAQBAJ&pg=PR11 xi, 4]}} }}</ref> Pafupifupi nyengo yeneyiyo, [[category theory|sambiro la mikhaliro]] likafuma ndipo lyakhala likugwira ntchito yikuru mu [[foundations of mathematics|msingi wa masamu]].<ref>{{multiref | {{harvnb|Krömer|2007|p=[https://books.google.com/books?id=41bHxtHxjUAC&pg=PA61 61]}} | {{harvnb|Laos|1998|p=[https://books.google.com/books?id=1r7dSn4ZqogC&pg=PA100 100]}} }}</ref> Vyakukula vinyake vikaŵa kupangika kwa [[model theory|sambiro la vimodel]] na kusambira [[free algebra|algebra zamahara]].<ref>{{multiref | {{harvnb|Hazewinkel|1994|pp=[https://books.google.com/books?id=PE1a-EIG22kC&pg=PA74 74–75]}} | {{harvnb|Pratt|2022|loc=§ 6. Free Algebras}} }}</ref> {{clear}} == Kugwiliskika Ntchito == {{see also|Applied mathematics}} Chikoliro cha algebra nkhutandarika comenecomene, mu masamu mwene na mu kugwiliskika kwake ku magulu ghanyake gha masamu.<ref>{{multiref | {{harvnb|Houston|2004|p=[https://books.google.com/books?id=jsWL_XJt-dMC&pg=PA319 319]}} | {{harvnb|Neri|2019|p=[https://books.google.com/books?id=NMOlDwAAQBAJ&pg=PR12 xii]}} | {{harvnb|Lidl|Pilz|1997|pp=[https://books.google.com/books?id=_49AmSWo4_AC&pg=PR7 vii–viii]}} }}</ref> Kupanga masamu ghanyake kuŵa gha algebra nkhu ndondomeko ya kugwiliskira ntchito nthowa na vinjeru vya algebra ku [[branches of mathematics|magulu ghanyake gha masamu]], nga [[geometry]], [[topology]], [[number theory|sambiro la vipendeko]], na [[calculus]]. Ichi chikuchitika mwakugwiliskira ntchito viwimbo mu mtundu wa vyambura-kumanyikwa kulongosora vinjeru vya masamu pa vipimo vikuru, kupangiska kuti ŵasandi ŵa masamu ŵapange vimodel vyakuzomerezgeka ivyo vikulongosora umo vinthu vikukhwaskirana na kukolerana wene.<ref>{{multiref | {{harvnb|Kleiner|2007|p=[https://books.google.com/books?id=udj-1UuaOiIC&pg=PA100 100]}} | {{harvnb|Pratt|2022|loc=§ 5. Algebraization of Mathematics}} | {{harvnb|Maddocks|2008|p=130}} | {{harvnb|Pratt|2022|loc=§ 5. Algebraization of Mathematics}} | {{harvnb|Mancosu|1999|pp=[https://books.google.com/books?id=60qaEePdqcoC&pg=PA84 84–85]}} }}</ref> [[File:Sphere Quadric.png|thumb|alt=Rendered image of a sphere|Equation ya algebra <math>x^2 + y^2 + z^2 = 1</math> yikulongosora [[sphere|sphere]] ku [[Origin (mathematics)|malo ghakwambira]] ghali na radius ya 1.]] Nchito yimoza, iyo yikusangika mu geometry, ni kugwiliskira ntchito mazgu gha algebra kulongosora vithunzithunzi vya geometry. Mwachiyelezgero, equation <math>y = 3x - 7</math> yikulongosora mzere mu malo gha mibaru yiŵiri apo equation <math>x^2 + y^2 + z^2 = 1</math> yikuyana na [[sphere|sphere]] mu malo gha mibaru yitatu. Vyakuzirwa comenecomene ku [[algebraic geometry|geometry ya algebra]] ni [[algebraic varieties|mitundu yakuyana ya algebra]],{{efn|Mitundu yakuyana ya algebra iyo yikusambirika mu geometry njakupambana na mitundu yakuyana yikuru iyo yikusambirika mu algebra ya wonse.<ref>{{multiref | {{harvnb|Pratt|2022|loc=§ 1.4 Cartesian geometry, § 3. Universal Algebra}} | {{harvnb|Danilov|2006|p=[https://books.google.com/books?id=-QMWR-x66XUC&pg=PA174 174]}} }}</ref>}} izo ni vyakumazga vya [[systems of polynomial equations|ndondomeko za ma equation gha polynomial]] ivyo vingagwiliskika kulongosora vithunzithunzi vyapasuzgika vya geometry.<ref>{{multiref | {{harvnb|Pratt|2022|loc=§ 5.1 Algebraic Geometry}} | {{harvnb|Danilov|2006|pp=[https://books.google.com/books?id=-QMWR-x66XUC&pg=PA172 172, 174]}} }}</ref> Kughanaghanira mwa algebra kungamazgaso masuzgo gha geometry. Mwachiyelezgero, munthu wangamanya usange na apo mzere wakulongosoreka na <math>y = x + 1</math> ukukhwaskana na dindi (circle) ilo likulongosoreka na <math>x^2 + y^2 = 25</math> mwakumazga ndondomeko ya ma equation ghakupangika na ma equation ghaŵiri agha.<ref>{{harvnb|Vince|2007|p=[https://books.google.com/books?id=B574tQbP6WcC&pg=PA133 133]}}</ref> Topology yikusambira vinjeru vya vithunzithunzi vya geometry panji [[topological space|malo gha topology]] ivyo vikukhalilira mwambura kusintha para vichitikirwa [[continuous deformation|kusintha kwakulutilira]]. [[Algebraic topology|Topology ya algebra]] yikuzirwa pa vinjeru vya algebra nga sambiro la magulu kupatuliska malo gha topology. Mwachiyelezgero, [[homotopy groups|magulu gha homotopy]] ghakupatuliska malo gha topology kuyana na kuŵako kwa [[Loop (topology)|majoro]] panji [[Hole#In mathematics|maenja]] mwa iwo.<ref>{{multiref | {{harvnb|Pratt|2022|loc=§ 5.3 Algebraic Topology}} | {{harvnb|Rabadan|Blumberg|2019|pp=[https://books.google.com/books?id=2967DwAAQBAJ&pg=PA49 49–50]}} | {{harvnb|Nakahara|2018|p=[https://books.google.com/books?id=p2C1DwAAQBAJ&pg=PA121 121]}} | {{harvnb|Weisstein|2003|pp=52–53}} }}</ref> Sambiro la vipendeko likukhwaskana na vinjeru na ukhwaskano pakati pa vipendeko vyambura kugaŵika. [[Algebraic number theory|Sambiro la vipendeko la algebra]] likugwiliskira ntchito nthowa na vinjeru vya algebra ku chipangizo ichi cha kupenja. Vyakuyelezgera ni kugwiliskira ntchito mazgu gha algebra kulongosora madango ghawonse, nga [[Fermat's Last Theorem|fundo yaumaliro ya Fermat]], na kugwiliskira ntchito magulu gha algebra kusanda mkhalidwe wa vipendeko, nga [[ring of integers|mphete ya vipendeko vyambura kugaŵika]].<ref>{{multiref | {{harvnb|Pratt|2022|loc=§ 5.2 Algebraic Number Theory}} | {{harvnb|Jarvis|2014|p=[https://books.google.com/books?id=0j0qBAAAQBAJ&pg=PA1 1]}} | {{harvnb|Viterbo|Hong|2011|p=[https://books.google.com/books?id=d89QRR24jbMC&pg=PA127 127]}} }}</ref> Chipangizo chakukhwaskana ichi cha [[combinatorics|combinatorics]] chikugwiliskira ntchito nthowa za algebra kumazga masuzgo ghakukhwaskana na kuŵelenga, kunozga, na kukoleranya vinthu vyakupambanapambana. Chiyelezgero mu [[algebraic combinatorics|combinatorics ya algebra]] ni kugwiliskira ntchito sambiro la magulu kusanda [[Graph (discrete mathematics)|ma graph]] na symmetries.<ref>{{multiref | {{harvnb|Gowers|Barrow-Green|Leader|2010|pp=[https://books.google.com/books?id=ZOfUsvemJDMC&pg=PA550 550, 561]}} | {{harvnb|Godsil|2017|p=[https://books.google.com/books?id=hLs6DwAAQBAJ&pg=PR8 viii]}} | {{harvnb|Betten|Kohnert|Laue|Wassermann|2013|p=[https://books.google.com/books?id=G1TmCAAAQBAJ&pg=PP9 ix]}} }}</ref> Vinjeru vya algebra vikuzirwaso ku calculus, iyo yikugwiliskira ntchito mazgu gha masamu kupenja [[rates of change|liŵiro la kusintha]] na [[Integral|kuwungana]]. Yikuzirwa pa algebra, mwachiyelezgero, kupulikiska umo mazgu agha ghangasinthika na mzimu uwo vyambura-kumanyikwa vikugwira mwa iwo.<ref>{{multiref | {{harvnb|Kilty|McAllister|2018|pp=x, 347, 589}} | {{harvnb|Bressoud|2021|p=[https://books.google.com/books?id=GkgHEAAAQBAJ&pg=PA64 64]}} }}</ref> [[Algebraic logic|Logic ya algebra]] yikugwiliskira ntchito nthowa za algebra kulongosora na kusanda magulu na vinjeru ivyo vili musingi wa [[logical reasoning|kughanaghanira kwa logic]],<ref>{{multiref | {{harvnb|Halmos|1956|p=363}} | {{harvnb|Burris|Legris|2021|loc=§ 1. Introduction}} }}</ref> kupenja vyose viŵiri, magulu ghenegho gha masamu na kugwiliskika kwawo ku masuzgo ghakuwoneka gha logic.<ref>{{harvnb|Andréka|Németi|Sain|2001|pp=[https://link.springer.com/chapter/10.1007/978-94-017-0452-6_3 133–134]}}</ref> Yikusazgamo kusambira [[Boolean algebra]] kulongosora [[propositional logic]]<ref>{{multiref | {{harvnb|Andréka|Madarász|Németi|2020|loc=§ Concrete Algebraic Logic}} | {{harvnb|Pratt|2022|loc=§ 5.4 Algebraic Logic}} | {{harvnb|Plotkin|2012|pp=[https://books.google.com/books?id=-v3xCAAAQBAJ&pg=PA155 155–156]}} | {{harvnb|Jansana|2022|loc=Lead section}} }}</ref> pamoza na kupanga na kusanda magulu gha algebra ghakuyana na [[Logic#Systems_of_logic|ndondomeko za logic]] zapasuzgika kuluska.<ref>{{multiref | {{harvnb|Andréka|Madarász|Németi|2020|loc=§ Abstract Algebraic Logic}} | {{harvnb|Jansana|2022|loc=§ 4. Algebras}} }}</ref> [[File:Rubik's cube.svg|thumb|upright=0.8|alt=Picture of Rubik's cube|Mbali za [[Rubik's Cube]] zingazingilizgika kusintha kunozgeka kwa vipande vyakupambanapambana mitundu (colored patches). Vipimo ivyo vikufuma pamanyuma (permutations) vikupanga gulu ilo likuchemeka [[Rubik's Cube group|gulu la Rubik's Cube]].<ref>{{harvnb|Joyner|2008|p=92}}</ref>]] Nthowa za algebra zikugwiliskikaso comenecomene mu magulu ghanyake, nga sayansi za chilengechilenge. Mwachiyelezgero, zikugwiliskika kulongosora [[scientific laws|madango gha kasandiro]] na kumazga ma equation mu [[physics]], [[chemistry]], na [[biology]].<ref>{{multiref | {{harvnb|Houston|2004|p=[https://books.google.com/books?id=jsWL_XJt-dMC&pg=PA319 319]}} | {{harvnb|Neri|2019|p=[https://books.google.com/books?id=NMOlDwAAQBAJ&pg=PR12 xii]}} | {{harvnb|Anton|Rorres|2010|p=[https://books.google.com/books?id=1PJ-WHepeBsC&pg=PA327 327]}} }}</ref> Kugwiliskika kwakuyana kukusangikaso mu magulu nga [[economics]], [[geography]], [[engineering]] (kusazgamo [[electronics]] na [[robotics]]), na [[computer science]] kulongosora ukhwaskano, kumazga masuzgo, na kupanga vimodel vya ndondomeko.<ref>{{multiref | {{harvnb|Neri|2019|p=[https://books.google.com/books?id=NMOlDwAAQBAJ&pg=PR12 xii]}} | {{harvnb|Aleskerov|Ersel|Piontkovski|2011|pp=[https://books.google.com/books?id=ipcSD8ZGB8cC&pg=PA1 1–9]}} | {{harvnb|Straffin|1980|p=[https://www.jstor.org/stable/2689388 269]}} | {{harvnb|Menini|Oystaeyen|2017|p=[https://books.google.com/books?id=3mlQDwAAQBAJ&pg=PR5 v]}} | {{harvnb|Lovett|2015|p=[https://books.google.com/books?id=jRUqCgAAQBAJ&pg=PR9 ix]}} | {{harvnb|Lidl|Pilz|1997|pp=[https://books.google.com/books?id=_49AmSWo4_AC&pg=PR7 vii–viii]}} }}</ref> Algebra ya mzere yikugwira ntchito yikuru mu [[artificial intelligence]] na [[machine learning]], mwachiyelezgero, mwakukhozgera kuwendeska na kusanda [[dataset|masetu gha data]] ghakuru mwakuzomerezgeka.<ref>{{multiref | {{harvnb|Wheeler|2023|p=[https://books.google.com/books?id=IqQIEQAAQBAJ&pg=PA29 29, 36–37]}} | {{harvnb|Gallier|Quaintance|2020|pp=[https://books.google.com/books?id=jWLcDwAAQBAJ&pg=PA1 1–2]}} }}</ref> Magulu ghakupambanapambana ghakuzirwa pa magulu gha algebra ghakusambirika na algebra yakudumura. Mwachiyelezgero, sayansi za vinthu nga [[crystallography]] na [[quantum mechanics]] zikugwiliskira ntchito comenecomene sambiro la magulu,<ref>{{multiref | {{harvnb|Klimov|2014|p=[https://books.google.com/books?id=DZK3DwAAQBAJ&pg=PR9 ix]}} | {{harvnb|Bengtsson|Życzkowski|2017|pp=313–353}} }}</ref> ilo likugwiliskikaso kusambira ma puzzle nga [[Sudoku]] na [[Rubik's Cube]],<ref>{{harvnb|Terras|2019|pp=63–64, 142}}</ref> na [[Mathematics of paper folding|origami]].<ref>{{harvnb|Hull|2021|p=[https://books.google.com/books?id=LdX7DwAAQBAJ&pg=PA180 180]}}</ref> Vyose viŵiri [[coding theory|sambiro la ma code]] na [[cryptology]] zikuzirwa pa algebra yakudumura kumazga masuzgo ghakukhwaskana na [[data transmission|kutuma data]], nga kujiwezga na vikwaskiro (noise) na kukhozgera [[data security|chitetezo cha data]].<ref>{{multiref | {{harvnb|Lidl|Pilz|1997|pp=183–184, 239–240}} | {{harvnb|Carstensen|Fine|Rosenberger|2011|pp=[https://books.google.com/books?id=Xo6iSxRfXz0C&pg=PA326 326–327]}} }}</ref> == Masambizgo == {{See also|Mathematics education}} [[File:Balance scale.svg|thumb|upright=1.3|class=skin-invert-image|alt=Diagram of a balance scale|[[Balance scales|Vipimiro vyakulinganya]] vikugwiliskika mu masambizgo gha algebra kovwira ŵasambiri kupulikiska umo ma equation ghangasinthika kuti ghamanye viŵelengero vyambura kumanyikwa.<ref>{{multiref | {{harvnb|Kieran|2006|p=[https://books.google.com/books?id=OTCsKu0BZ0kC&pg=PA15 15]}} | {{harvnb|Kaput|2018|p=[https://books.google.com/books?id=1GUPEAAAQBAJ&pg=PA186 186]}} |{{harvnb|Gardella|DeLucia|2020|pp=[https://books.google.com/books?id=HBXFDwAAQBAJ&pg=PA19 19–22]}} }}</ref>]] Masambizgo gha algebra ghakuzirwa comenecomene pa algebra ya pulayimale, chimoza mwa vifukwa ivyo algebra ya pulayimale yikuchemekaso "algebra ya sukulu". Comenecomene, yikwambiskika yayi kwambira mu [[secondary education|masambizgo ghapachanya]] chifukwa yikukhumba kumanya makora masamu ghakwamba apo yikwizaso na vyakusuzga vinyake vipya ivyo vikukhwaskana na kughanaghanira kwakudumura na kwawonse.<ref>{{multiref | {{harvnb|Arcavi|Drijvers|Stacey|2016|p=xiii}} | {{harvnb|Dekker|Dolk|2011|p=[https://books.google.com/books?id=7sVFaMhwackC&pg=PA69 69]}} }}</ref> Yikukhumba kuzgoŵeska ŵasambiri na mbali yakuzomerezgeka ya masamu mwakuŵawovwira kupulikiska viwimbo vya masamu, mwachiyelezgero, umo vyambura-kumanyikwa vingagwiliskika kwimira viŵelengero vyambura kumanyikwa. Kususka kwinyake ku ŵasambiri nkhwakuti, kupambana na kuŵelenga kwaumaliro, mazgu gha algebra ghakusuzga comenecomene kumazgika mwakwenderana. M'malo mwake, ŵasambiri ŵakukhumbikwa kusambira umo ŵangaghasinthira kuyana na madango ghanyake, kanandi kuti ŵamanye chiŵelengero chambura kumanyikwa.<ref>{{multiref | {{harvnb|Arcavi|Drijvers|Stacey|2016|pp=2–5}} | {{harvnb|Drijvers|Goddijn|Kindt|2011|pp=[https://books.google.com/books?id=7sVFaMhwackC&pg=PA8 8–10, 16–18]}} }}</ref> Vipangizo vinyake vyakwiziska ŵasambiri ku mbali yakudumura ya algebra vikuzirwa pa vimodel vyakuwoneka na kulongora ma equation, kusazgamo vyakuyelezgera vya geometry, vipangizo vyakugwira nawo nchito nga vikoli panji makapu, na "makina gha nchito" (function machines) ivyo vikulongora ma equation kuŵa [[flow diagram|maonekero gha kuluta patsogolo]]. Nthowa yimoza yikugwiliskira ntchito [[balance scales|vipimiro vyakulinganya]] kuŵa nthowa yakuwoneka yakovwira ŵasambiri kupulikiska masuzgo ghakwamba gha algebra. Uzito wa vinthu vinyake pa chipimiro nchambura kumanyikwa ndipo ukwimira vyambura-kumanyikwa. Kumazga equation kukuyana na kusazga na kuwuskapo vinthu ku mbali zose ziŵiri mwakuti mbali zikhalilire mu ulinganyi mpaka chinthu chimoza pera icho chikhala pa mbali yimoza ni chinthu chambura kumanyikwa uzito wake.<ref>{{multiref | {{harvnb|Kieran|2006|p=[https://books.google.com/books?id=OTCsKu0BZ0kC&pg=PA15 15]}} | {{harvnb|Kaput|2018|p=[https://books.google.com/books?id=1GUPEAAAQBAJ&pg=PA186 186]}} |{{harvnb|Gardella|DeLucia|2020|pp=[https://books.google.com/books?id=HBXFDwAAQBAJ&pg=PA19 19–22]}} | {{harvnb|Star|Foegen|Larson|McCallum|2015|pp=16–17}} }}</ref> [[Word problem (mathematics education)|Masuzgo gha mazgu]] ni chipangizo chinyake chakulongora umo algebra yikugwiliskika ku vinthu vyaunenesko vya moyo. Mwachiyelezgero, ŵasambiri ŵangapika mu mkhalidwe uwo mbale wa Naomi wali na machiyembe ghakuŵirapo kuŵiri kuluska Naomi. Pakuti ŵaŵiri wose pamoza ŵali na machiyembe 12, ŵasambiri ŵakupikika kuti ŵasange equation ya algebra iyo yikulongosora mkhalidwe uwu ({{tmath|1= 2x + x = 12 }}) na kumanya machiyembe ghaŵi agho Naomi wali nagho {{nowrap|({{tmath|1= x = 4 }}).<ref>{{multiref | {{harvnb|Arcavi|Drijvers|Stacey|2016|pp=58–59}} | {{harvnb|Drijvers|Goddijn|Kindt|2011|p=[https://books.google.com/books?id=7sVFaMhwackC&pg=PA13 13]}} }}</ref>}} Pa vipimo vya yunivesite, ŵasambiri ŵa masamu ŵakukhwaskana na mitu yapachanya ya algebra kufuma ku algebra ya mzere na algebra yakudumura. Makalasi ghakwamba gha [[undergraduate|digiri yakwamba]] mu algebra ya mzere ghakuzirwa pa ma matrix, malo gha vector, na mapu gha mzere. Para ŵamalizga, ŵasambiri comenecomene ŵakwiziskika ku algebra yakudumura, uko ŵakusambira magulu gha algebra nga magulu, mphete, na minda, pamoza na ukhwaskano pakati pawo. Masambiro (curriculum) ghakuzirwa comenecomene ghakukhwaskaso vithuzi vyapadera vya magulu gha algebra, nga ndondomeko za vipendeko vyakugaŵikika, vipendeko vyeneco, na ma polynomial.<ref>{{harvnb|Hausberger|Zandieh|Fleischmann|2021|pp=147–148}}</ref> == Vinyake Vyakukhwaskana == {{div col|colwidth=30em}} * {{annotated link|Commutative algebra}} * {{annotated link|Computer algebra}} * {{annotated link|Exterior algebra}} * {{annotated link|F-algebra}} * {{annotated link|Geometric algebra}} * {{annotated link|Non-associative algebra}} * {{annotated link|Outline of algebra}} * {{annotated link|Representation theory}} * {{annotated link|Tensor}} {{div col end}} == References == === Notes === {{notelist}} === Citations === {{reflist}} === Sources === {{refbegin|30em}} * {{cite book |last1=Abas |first1=Syed Jan |last2=Salman |first2=Amer Shaker |title=Symmetries Of Islamic Geometrical Patterns |date=1994 |publisher=World Scientific |isbn=978-981-4502-21-4 |url=https://books.google.com/books?id=5snsCgAAQBAJ |language=en |access-date=March 12, 2024}}{{cbignore}} * {{cite book |last1=Adhikari |first1=Mahima Ranjan |title=Basic Algebraic Topology and its Applications |publisher=Springer |isbn=978-81-322-2843-1 |url=https://books.google.com/books?id=MIAXDQAAQBAJ&pg=PA5 |language=en |date=2016 |access-date=August 5, 2024}}{{cbignore}} * {{cite book |last1=Adhikari |first1=Mahima Ranjan |last2=Adhikari |first2=Avishek |title=Basic Modern Algebra with Applications |publisher=Springer |isbn=978-81-322-1599-8 |url=https://books.google.com/books?id=lBO7BAAAQBAJ&pg=PA72 |language=en |date=2013 |access-date=August 5, 2024}}{{cbignore}} * {{cite book |last1=Aleskerov |first1=Fuad |last2=Ersel |first2=Hasan |last3=Piontkovski |first3=Dmitri |title=Linear Algebra for Economists |date=2011 |publisher=Springer |isbn=978-3-642-20570-5 |url=https://books.google.com/books?id=ipcSD8ZGB8cC&pg=PA1 |language=en |access-date=March 11, 2024}}{{cbignore}} * {{cite web |last1=Andréka |first1=H. |last2=Madarász |first2=J. X. |last3=Németi |first3=I. |title=Algebraic Logic |url=https://encyclopediaofmath.org/wiki/Algebraic_logic |website=Encyclopedia of Mathematics |publisher=Springer |access-date=October 23, 2023 |date=2020 |archive-date=January 24, 2024 |archive-url=https://web.archive.org/web/20240124094606/https://encyclopediaofmath.org/wiki/Algebraic_logic |url-status=live}} * {{cite book |last1=Andréka |first1=H. |last2=Németi |first2=I. |last3=Sain |first3=I. |title=Handbook of Philosophical Logic |date=2001 |publisher=Springer |isbn=978-94-017-0452-6 |chapter-url=https://link.springer.com/chapter/10.1007/978-94-017-0452-6_3 |language=en |chapter=Algebraic Logic |doi=10.1007/978-94-017-0452-6_3 |access-date=January 24, 2024 |archive-date=January 24, 2024 |archive-url=https://web.archive.org/web/20240124094523/https://link.springer.com/chapter/10.1007/978-94-017-0452-6_3 |url-status=live}} * {{cite book |last1=Anton |first1=Howard |title=Elementary Linear Algebra |date=2013 |publisher=John Wiley & Sons |isbn=978-1-118-67730-8 |url=https://books.google.com/books?id=neYGCwAAQBAJ&pg=PA255 |language=en |access-date=January 18, 2024}}{{cbignore}} * {{cite book |last1=Anton |first1=Howard |last2=Rorres |first2=Chris |title=Elementary Linear Algebra: Applications Version |publisher=John Wiley & Sons |isbn=978-0-470-43205-1 |url=https://books.google.com/books?id=1PJ-WHepeBsC&pg=PA327 |language=en |date=2010}} * {{cite book |last1=Anton |first1=Howard |last2=Rorres |first2=Chris |title=Elementary Linear Algebra: Applications Version |date=2013 |publisher=John Wiley & Sons |isbn=978-1-118-47422-8 |url=https://books.google.com/books?id=D9xoDwAAQBAJ |language=en |access-date=January 18, 2024}}{{cbignore}} * {{cite book |last1=Arcavi |first1=Abraham |last2=Drijvers |first2=Paul |last3=Stacey |first3=Kaye |title=The Learning and Teaching of Algebra: Ideas, Insights and Activities |date=2016 |publisher=Routledge |isbn=978-1-134-82077-1 |url=https://books.google.com/books?id=XGR9DAAAQBAJ |language=en |access-date=January 24, 2024}}{{cbignore}} * {{cite book |last1=Artamonov |first1=V. A. |editor1-last=Hazewinkel |editor1-first=M. |editor-link=Michiel Hazewinkel |title=Handbook of Algebra |date=2003 |publisher=Elsevier |isbn=978-0-08-053297-4 |chapter-url=https://books.google.com/books?id=sLDGY4Hk8V0C&pg=PA873 |language=en |chapter=Quasivarieties |access-date=January 21, 2024}}{{cbignore}} * {{cite book |last1=Atanasiu |first1=Dragu |last2=Mikusinski |first2=Piotr |title=A Bridge To Linear Algebra |date=2019 |publisher=World Scientific |isbn=978-981-12-0024-3 |url=https://books.google.com/books?id=VbySDwAAQBAJ&pg=PA75 |language=en |access-date=March 12, 2024}}{{cbignore}} * {{cite book |last1=Bahturin |first1=Y. |title=Basic Structures of Modern Algebra |publisher=Springer |isbn=978-94-017-0839-5 |url=https://books.google.com/books?id=8RbvCAAAQBAJ&pg=PA346 |language=en |date=2013 |access-date=August 30, 2024}}{{cbignore}} * {{cite web |last1=Baranovich |first1=T. M. |title=Algebraic Operation |url=https://encyclopediaofmath.org/wiki/Algebraic_operation |website=Encyclopedia of Mathematics |publisher=Springer |access-date=January 11, 2023 |date=2023 |archive-date=August 23, 2023 |archive-url=https://web.archive.org/web/20230823194536/https://encyclopediaofmath.org/wiki/Algebraic_operation |url-status=live}} * {{cite book |last1=Barrera-Mora |first1=Fernando |title=Linear Algebra: A Minimal Polynomial Approach to Eigen Theory |date=2023 |publisher=Walter de Gruyter GmbH & Co KG |isbn=978-3-11-113591-5 |url=https://books.google.com/books?id=Xmu8EAAAQBAJ&pg=PR9 |language=en |access-date=January 18, 2024}}{{cbignore}} * {{cite book |last1=Bengtsson |first1=Ingemar |last2=Życzkowski |first2=Karol |author-link2=Karol Życzkowski |title=Geometry of Quantum States: An Introduction to Quantum Entanglement |title-link=Geometry of Quantum States |edition=2nd |year=2017 |publisher=Cambridge University Press |isbn=978-1-107-02625-4}}{{cbignore}} * {{cite book |last1=Benson |first1=Donald C. |title=A Smoother Pebble: Mathematical Explorations |date=2003 |publisher=Oxford University Press |isbn=978-0-19-514436-9 |url=https://books.google.com/books?id=nNbnCwAAQBAJ&pg=PA111 |language=en |access-date=January 16, 2024}}{{cbignore}} * {{cite web |last1=Berggren |first1=John L. |title=Elementary Algebra |url=https://www.britannica.com/science/elementary-algebra |website=Encyclopædia Britannica |access-date=January 14, 2024 |language=en |date=2015 |archive-date=January 14, 2024 |archive-url=https://web.archive.org/web/20240114180506/https://www.britannica.com/science/elementary-algebra |url-status=live}} * {{cite book |editor1-last=Betten |editor1-first=Anton |editor2-last=Kohnert |editor2-first=Axel |editor3-last=Laue |editor3-first=Reinhard |editor4-last=Wassermann |editor4-first=Alfred |title=Algebraic Combinatorics and Applications |publisher=Springer |isbn=978-3-642-59448-9 |url=https://books.google.com/books?id=G1TmCAAAQBAJ&pg=PP9 |language=en |date=2013}} * {{cite book |last1=Bhattacharya |first1=P. B. |last2=Jain |first2=S. K. |last3=Nagpaul |first3=S. R. |title=Basic Abstract Algebra |publisher=Cambridge University Press |isbn=978-0-521-46629-5 |url=https://books.google.com/books?id=hiQ8e0b48swC&pg=PA141 |language=en |date=1994}} * {{cite book |last1=Borceux |first1=Francis |title=Handbook of Categorical Algebra: Basic category theory |publisher=Cambridge University Press |isbn=978-0-521-44178-0 |url=https://books.google.com/books?id=YfzImoopB-IC&pg=PA20 |language=en |date=1994}} * {{cite book |last1=Bourbaki |first1=N. |author-link=Nicolas Bourbaki |title=Algebra I: Chapters 1-3 |publisher=Springer |isbn=978-3-540-64243-5 |url=https://books.google.com/books?id=STS9aZ6F204C&pg=PA446 |language=en |date=1998}} * {{cite book |last1=Boyer |first1=Carl B. |last2=Merzbach |first2=Uta C. |title=A History of Mathematics |date=2011 |publisher=John Wiley & Sons |isbn=978-0-470-63056-3 |url=https://books.google.com/books?id=bR9HAAAAQBAJ&pg=PA161 |language=en |access-date=January 27, 2024}}{{cbignore}} * {{cite book |last1=Bracken |first1=Laura J. |last2=Miller |first2=Edward S. |title=Elementary Algebra |publisher=Cengage Learning |isbn=978-0-618-95134-5 |date=2014}} * {{cite book |last=Bradley |first=Michael J. |year=2006 |url=http://books.google.com/books?id=EIdtVPeD7GcC |publisher=Chelsea House Publishers |title=The Birth of Mathematics: Ancient Times To 1300}} * {{cite book |last1=Bressoud |first1=David M. |title=Calculus Reordered: A History of the Big Ideas |publisher=Princeton University Press |isbn=978-0-691-21878-6 |url=https://books.google.com/books?id=GkgHEAAAQBAJ&pg=PA64 |language=en |date=2021 |access-date=September 4, 2024}}{{cbignore}} * {{cite book |last1=Brezinski |first1=Claude |last2=Meurant |first2=Gérard |last3=Redivo-Zaglia |first3=Michela |title=A Journey through the History of Numerical Linear Algebra |publisher=SIAM |isbn=978-1-61197-723-3 |url=https://books.google.com/books?id=4IGhEAAAQBAJ&pg=PA34 |language=en |date=2022 |access-date=August 12, 2024}}{{cbignore}} * {{cite book |last1=Brešar |first1=Matej |title=Introduction to Noncommutative Algebra |publisher=Springer |isbn=978-3-319-08693-4 |url=https://books.google.com/books?id=PkvPBAAAQBAJ&pg=PR33 |language=en |date=2014 |access-date=June 14, 2024}}{{cbignore}} * {{cite book |last1=Brown |first1=Jonathon D. |title=Linear Models in Matrix Form: A Hands-On Approach for the Behavioral Sciences |publisher=Springer |isbn=978-3-319-11734-8 |url=https://books.google.com/books?id=POlVBgAAQBAJ&pg=PA30 |language=en |date=2015}} * {{cite book |last1=Bueno |first1=Otávio |last2=French |first2=Steven |title=Applying Mathematics: Immersion, Inference, Interpretation |publisher=Oxford University Press |isbn=978-0-19-881504-4 |url=https://books.google.com/books?id=kmZaDwAAQBAJ&pg=PA73 |language=en |date=2018 |access-date=July 28, 2024}}{{cbignore}} * {{cite web |last1=Bukhshtab |first1=A. A. |last2=Pechaev |first2=V. I. |title=Arithmetic |url=https://encyclopediaofmath.org/wiki/Arithmetic |website=Encyclopedia of Mathematics |publisher=Springer |access-date=October 23, 2023 |date=2020 |archive-date=October 4, 2009 |archive-url=https://web.archive.org/web/20091004230123/http://eom.springer.de/a/a013260.htm |url-status=live}} * {{cite book |last1=Burgin |first1=Mark |title=Trilogy Of Numbers And Arithmetic – Book 1: History Of Numbers And Arithmetic: An Information Perspective |date=2022 |publisher=World Scientific |isbn=978-981-12-3685-3 |url=https://books.google.com/books?id=rWF2EAAAQBAJ&pg=PA45 |language=en |access-date=January 13, 2024}}{{cbignore}} * {{cite web |last1=Burris |first1=Stanley |last2=Legris |first2=Javier |title=The Algebra of Logic Tradition |url=https://plato.stanford.edu/entries/algebra-logic-tradition/ |website=The Stanford Encyclopedia of Philosophy |publisher=Metaphysics Research Lab, Stanford University |access-date=January 22, 2024 |date=2021 |archive-date=January 29, 2024 |archive-url=https://web.archive.org/web/20240129081715/https://plato.stanford.edu/entries/algebra-logic-tradition/ |url-status=live}} * {{cite web |last1=Carlson |first1=Stephan C. |title=Topology – Homology, Cohomology, Manifolds |url=https://www.britannica.com/science/topology/Algebraic-topology |website=Encyclopædia Britannica |access-date=2 October 2024 |language=en |date=2024}} * {{cite book |last1=Carstensen |first1=Celine |last2=Fine |first2=Benjamin |last3=Rosenberger |first3=Gerhard |title=Abstract Algebra: Applications to Galois Theory, Algebraic Geometry, and Cryptography |publisher=Walter de Gruyter |isbn=978-3-11-025008-4 |url=https://books.google.com/books?id=Xo6iSxRfXz0C&pg=PA326 |language=en |date=2011}} * {{cite book |last1=Chahal |first1=J. S. |title=Fundamentals of Linear Algebra |publisher=CRC Press |isbn=978-0-429-75810-2 |url=https://books.google.com/books?id=BGR8DwAAQBAJ&pg=PT10 |language=en |date=2018 |access-date=August 29, 2024}}{{cbignore}} * {{cite book |last1=Chang |first1=C. C. |last2=Keisler |first2=H. J. |title=Model Theory |date=1990 |publisher=Elsevier |isbn=978-0-08-088007-5 |url=https://books.google.com/books?id=uiHq0EmaFp0C&pg=PA603 |language=en |access-date=January 27, 2024}}{{cbignore}} * {{cite book |last=Cheng |first=Eugenia |author-link=Eugenia Cheng |title=The Joy of Abstraction |year=2023 |publisher=Cambridge University Press |isbn=978-1-108-47722-2 |doi=10.1017/9781108769389}} * {{cite journal |last1=Christianidis |first1=Jean |last2=Megremi |first2=Athanasia |title=Tracing the Early History of Algebra: Testimonies on Diophantus in the Greek-speaking World (4th–7th Century CE) |journal=Historia Mathematica |volume=47 |doi=10.1016/j.hm.2019.02.002 |date=2019 |pages=16–38}} * {{cite book |last1=Cohn |first1=P. M. |author-link=Paul Cohn |title=Skew Fields: Theory of General Division Rings |publisher=Cambridge University Press |isbn=978-0-521-43217-7 |url=https://books.google.com/books?id=u-4ADgUgpSMC&pg=PA8 |language=en |date=1995}} * {{cite book |last1=Cohn |first1=P. M. |title=Universal Algebra |publisher=Springer |isbn=978-94-009-8399-1 |url=https://books.google.com/books?id=6tbuCAAAQBAJ&pg=PR13 |language=en |date=2012 |access-date=June 14, 2024}}{{cbignore}} * {{cite book |last1=Cooper |first1=Ellis D. |title=Mathematical Mechanics: From Particle to Muscle |date=2011 |publisher=World Scientific |isbn=978-981-4289-70-2 |url=https://books.google.com/books?id=Fybzl6QB62gC&pg=PA60 |language=en |access-date=January 20, 2024}}{{cbignore}} * {{cite web |last1=Corry |first1=Leo |title=Algebra |url=https://www.britannica.com/science/algebra |website=Encyclopædia Britannica |access-date=January 25, 2024 |language=en |date=2024 |archive-date=January 19, 2024 |archive-url=https://web.archive.org/web/20240119233613/https://www.britannica.com/science/algebra |url-status=live}} * {{cite book |last1=Cox |first1=David A. |author-link=David A. Cox |title=Galois Theory |publisher=John Wiley & Sons |isbn=978-1-118-21842-6 |url=https://books.google.com/books?id=vBKrOch1AkYC&pg=PA161 |language=en |date=2012}} * {{cite book |last1=Cresswell |first1=Julia |title=Oxford Dictionary of Word Origins |date=2010 |publisher=Oxford University Press |isbn=978-0-19-954793-7 |url=https://books.google.com/books?id=J4i3zV4vnBAC&pg=PA11 |language=en |access-date=January 27, 2024}}{{cbignore}} * {{cite book |last1=Danilov |first1=V. I. |title=Algebraic Geometry I: Algebraic Curves, Algebraic Manifolds and Schemes |date=2006 |publisher=Springer |isbn=978-3-540-51995-9 |chapter-url=https://books.google.com/books?id=-QMWR-x66XUC&pg=PA172 |language=en |chapter=II. Algebraic Varieties and Schemes |access-date=January 24, 2024}}{{cbignore}} * {{cite book |last1=Dekker |first1=Truus |last2=Dolk |first2=Maarten |editor1-last=Drijvers |editor1-first=Paul |title=Secondary Algebra Education: Revisiting Topics and Themes and Exploring the Unknown |date=2011 |publisher=Springer |isbn=978-94-6091-334-1 |chapter-url=https://books.google.com/books?id=7sVFaMhwackC&pg=PA5 |language=en |chapter=3. From Arithmetic to Algebra |access-date=January 24, 2024}}{{cbignore}} * {{cite book |last1=Denecke |first1=Klaus |last2=Wismath |first2=Shelly L. |title=Universal Algebra and Applications in Theoretical Computer Science |publisher=CRC Press |isbn=978-1-4822-8583-3 |url=https://books.google.com/books?id=2UlZDwAAQBAJ&pg=PR5 |language=en |date=2018 |access-date=August 30, 2024}}{{cbignore}} * {{cite book |last1=Deo |first1=Satya |title=Algebraic Topology: A Primer |publisher=Springer |isbn=978-981-10-8734-9 |url=https://books.google.com/books?id=HjtRDwAAQBAJ&pg=PA295 |language=en |date=2018 |access-date=August 5, 2024}}{{cbignore}} * {{cite book |last1=Derbyshire |first1=John |title=Unknown Quantity: A Real and Imaginary History of Algebra |date=2006 |publisher=National Academies Press |isbn=978-0-309-09657-7 |chapter-url=https://books.google.com/books?id=mLqaAgAAQBAJ&pg=PT39 |language=en |chapter=2. The Father of Algebra |access-date=January 27, 2024}}{{cbignore}} * {{cite book |last1=Dominich |first1=Sándor |title=The Modern Algebra of Information Retrieval |date=2008 |publisher=Springer |isbn=978-3-540-77659-8 |url=https://books.google.com/books?id=uEedNKV3nlUC&pg=PA19 |language=en |access-date=January 20, 2024}}{{cbignore}} * {{cite book |last1=Drijvers |first1=Paul |last2=Goddijn |first2=Aad |last3=Kindt |first3=Martin |editor1-last=Drijvers |editor1-first=Paul |title=Secondary Algebra Education: Revisiting Topics and Themes and Exploring the Unknown |date=2011 |publisher=Springer |isbn=978-94-6091-334-1 |chapter-url=https://books.google.com/books?id=7sVFaMhwackC&pg=PA5 |language=en |chapter=1. Algebra Education: Exploring Topics and Themes |access-date=January 24, 2024}}{{cbignore}} * {{cite web |last1=Efimov |first1=B. A. |title=Set theory |url=https://encyclopediaofmath.org/wiki/Set_theory |website=Encyclopedia of Mathematics |publisher=Springer |access-date=January 11, 2023 |date=2014 |archive-date=November 29, 2022 |archive-url=https://web.archive.org/web/20221129153653/https://encyclopediaofmath.org/wiki/Set_theory |url-status=live}} * {{cite web |last=Elwes |first=Richard |url=http://plus.maths.org/issue41/features/elwes/index.htmljournal |title=An enormous theorem: the classification of finite simple groups |website=[[Plus Magazine]] |date=December 2006 |access-date=2011-12-20 |archive-date=2009-02-02 |archive-url=https://web.archive.org/web/20090202092008/http://plus.maths.org/issue41/features/elwes/index.html |url-status=dead}} * {{cite book |last1=Emch |first1=Gerard G. |last2=Sridharan |first2=R. |last3=Srinivas |first3=M. D. |title=Contributions to the History of Indian Mathematics |date=2005 |publisher=Springer |isbn=978-93-86279-25-5 |url=https://books.google.com/books?id=qfJdDwAAQBAJ&pg=PA20 |language=en |access-date=January 27, 2024}}{{cbignore}} * {{cite web |author1=EoM Staff |title=Algebra |url=https://encyclopediaofmath.org/wiki/Algebra |website=Encyclopedia of Mathematics |publisher=Springer |access-date=January 11, 2023 |date=2017 |archive-date=November 29, 2022 |archive-url=https://web.archive.org/web/20221129153630/https://encyclopediaofmath.org/wiki/Algebra |url-status=live}} * {{cite book |last1=Fiche |first1=Georges |last2=Hebuterne |first2=Gerard |title=Mathematics for Engineers |date=2013 |publisher=John Wiley & Sons |isbn=978-1-118-62333-6 |url=https://books.google.com/books?id=TqkckiuuXg8C&pg=PT326 |language=en |access-date=January 13, 2024}}{{cbignore}} * {{cite book |last1=Gallier |first1=Jean H. |last2=Quaintance |first2=Jocelyn |title=Linear Algebra And Optimization With Applications To Machine Learning – Volume Ii: Fundamentals Of Optimization Theory With Applications To Machine Learning |publisher=World Scientific |isbn=978-981-12-1658-9 |url=https://books.google.com/books?id=jWLcDwAAQBAJ&pg=PA1 |language=en |date=2020}} * {{cite journal |last1=Gandz |first1=Solomon |title=The Origin of the Term "Algebra" |url=https://archive.org/details/sim_american-mathematical-monthly_1926-11_33_9/page/437 |journal=The American Mathematical Monthly |volume=33 |issue=9 |doi=10.2307/2299605 |date=1926 |pages=437–440 |jstor=2299605}} * {{cite book |last1=Gardella |first1=Francis |last2=DeLucia |first2=Maria |title=Algebra for the Middle Grades |date=2020 |publisher=IAP |isbn=978-1-64113-847-5 |url=https://books.google.com/books?id=HBXFDwAAQBAJ&pg=PA19 |language=en |access-date=January 24, 2024}}{{cbignore}} * {{cite book |last1=Geddes |first1=Keith O. |last2=Czapor |first2=Stephen R. |last3=Labahn |first3=George |title=Algorithms for Computer Algebra |publisher=Springer |isbn=978-0-585-33247-5 |url=https://books.google.com/books?id=9fOUwkkRxT4C&pg=PA46 |language=en |date=2007}} * {{cite book |last1=Gilbert |first1=William J. |last2=Nicholson |first2=W. Keith |title=Modern Algebra with Applications |date=2004 |publisher=John Wiley & Sons |isbn=978-0-471-46989-6 |url=https://books.google.com/books?id=paINAXYHN8kC&pg=PA4 |language=en |access-date=January 13, 2024}}{{cbignore}} * {{cite book |last1=Godsil |first1=Chris |title=Algebraic Combinatorics |publisher=Routledge |isbn=978-1-351-46750-6 |url=https://books.google.com/books?id=hLs6DwAAQBAJ&pg=PR8 |language=en |date=2017}} * {{cite book |last1=Golan |first1=Jonathan S. |title=Foundations of Linear Algebra |date=1995 |publisher=Springer |isbn=978-94-015-8502-6 |chapter-url=https://link.springer.com/chapter/10.1007/978-94-015-8502-6_18 |language=en |chapter=Algebras Over A Field |series=Kluwer Texts in the Mathematical Sciences |volume=11 |pages=219–227 |doi=10.1007/978-94-015-8502-6_18 |access-date=January 13, 2024 |archive-date=January 12, 2024 |archive-url=https://web.archive.org/web/20240112171825/https://link.springer.com/chapter/10.1007/978-94-015-8502-6_18 |url-status=live}} * {{cite book |last1=Goodman |first1=A. W. |title=Algebra From A To Z |volume=1 |date=2001 |publisher=World Scientific |isbn=978-981-310-266-8 |url=https://books.google.com/books?id=TvY7DQAAQBAJ&pg=PA5 |language=en |access-date=March 11, 2024}}{{cbignore}} * {{cite book |editor1-last=Gowers |editor1-first=Timothy |editor2-last=Barrow-Green |editor2-first=June |editor3-last=Leader |editor3-first=Imre |title=The Princeton Companion to Mathematics |publisher=Princeton University Press |isbn=978-1-4008-3039-8 |url=https://books.google.com/books?id=ZOfUsvemJDMC&pg=PA1 |language=en |date=2010}} * {{cite book |last1=Grätzer |first1=George |title=Universal Algebra |date=2008 |publisher=Springer |isbn=978-0-387-77487-9 |url=https://books.google.com/books?id=8lNkXPJas4wC |language=en |edition=2 |access-date=January 27, 2024}}{{cbignore}} * {{cite book |last1=Grillet |first1=Pierre Antoine |title=Abstract Algebra |date=2007 |publisher=Springer |isbn=978-0-387-71568-1 |chapter-url=https://link.springer.com/chapter/10.1007/978-0-387-71568-1_15 |language=en |chapter=Universal Algebra |series=Graduate Texts in Mathematics |volume=242 |pages=559–580 |doi=10.1007/978-0-387-71568-1_15 |access-date=January 13, 2024 |archive-date=January 12, 2024 |archive-url=https://web.archive.org/web/20240112171841/https://link.springer.com/chapter/10.1007/978-0-387-71568-1_15 |url-status=live}} * {{cite book |last1=Häberle |first1=L. |editor1-last=Fink |editor1-first=Andreas |editor2-last=Lausen |editor2-first=Berthold |editor3-last=Seidel |editor3-first=Wilfried |editor4-last=Ultsch |editor4-first=Alfred |title=Advances in Data Analysis, Data Handling and Business Intelligence |date=2009 |publisher=Springer |isbn=978-3-642-01044-6 |chapter-url=https://books.google.com/books?id=McvSa-cFZCMC&pg=PA640 |language=en |chapter=On Classification of Molecules and Species of Representation Rings |access-date=March 12, 2024}}{{cbignore}} * {{cite journal |last1=Halmos |first1=Paul R. |title=The Basic Concepts of Algebraic Logic |journal=The American Mathematical Monthly |date=1956 |volume=63 |issue=6 |pages=363–387 |doi=10.2307/2309396 |jstor=2309396 |issn=0002-9890}} * {{cite book |last1=Harrison |first1=Michael |last2=Waldron |first2=Patrick |title=Mathematics for Economics and Finance |date=2011 |publisher=Routledge |isbn=978-1-136-81921-6 |url=https://books.google.com/books?id=_sisAgAAQBAJ&pg=PT464 |language=en |access-date=January 18, 2024}}{{cbignore}} * {{cite book |last1=Hausberger |first1=Thomas |editor1-last=Lerman |editor1-first=Stephen |title=Encyclopedia of Mathematics Education |publisher=Springer |isbn=9783030157883 |edition=2 |chapter=Abstract Algebra Teaching and Learning |date=2020}} * {{cite book |last1=Hausberger |first1=Thomas |last2=Zandieh |first2=Michelle |last3=Fleischmann |first3=Yael |editor1-last=Durand-Guerrier |editor1-first=Viviane |editor2-last=Hochmuth |editor2-first=Reinhard |editor3-last=Nardi |editor3-first=Elena |editor4-last=Winsløw |editor4-first=Carl |title=Research and Development in University Mathematics Education: Overview Produced by the International Network for Didactic Research in University Mathematics |publisher=Routledge |isbn=978-1-000-36924-3 |language=en |chapter=Abstract and Linear Algebra |date=2021}} * {{cite book |last1=Hazewinkel |first1=Michiel |author-link=Michiel Hazewinkel |title=Encyclopaedia of Mathematics (Set) |date=1994 |publisher=Springer |isbn=978-1-55608-010-4 |url=https://books.google.com/books?id=PE1a-EIG22kC&pg=PA73 |language=en |access-date=January 27, 2024}}{{cbignore}} * {{cite web |author1=HC Staff |title=Arithmetic |url=https://www.ahdictionary.com/word/search.html?q=arithmetic&submit.x=58&submit.y=14 |website=American Heritage Dictionary |publisher=HarperCollins |access-date=October 19, 2023 |date=2022 |archive-date=November 8, 2023 |archive-url=https://web.archive.org/web/20231108181459/https://www.ahdictionary.com/word/search.html?q=arithmetic&submit.x=58&submit.y=14 |url-status=live}} * {{cite journal |last1=Hettle |first1=Cyrus |title=The Symbolic and Mathematical Influence of Diophantus's Arithmetica |journal=Journal of Humanistic Mathematics |volume=5 |issue=1 |doi=10.5642/jhummath.201501.08 |date=2015 |pages=139–166 |doi-access=free}} * {{cite book |last1=Higgins |first1=Peter M. |title=Algebra: A Very Short Introduction |date=2015 |publisher=Oxford University Press |isbn=978-0-19-104746-6 |url=https://books.google.com/books?id=QANiCgAAQBAJ&pg=PA89 |language=en |access-date=January 27, 2024}}{{cbignore}} * {{cite book |last1=Higham |first1=Nicholas J. |title=Handbook of Writing for the Mathematical Sciences |date=2019 |publisher=SIAM |isbn=978-1-61197-610-6 |edition=3 |url=https://books.google.com/books?id=ferEDwAAQBAJ&pg=PA296 |language=en |access-date=March 17, 2024}}{{cbignore}} * {{cite book |last1=Hoad |first1=T. F. |title=The Concise Oxford Dictionary of English Etymology |date=1993 |publisher=Oxford University Press |isbn=978-0-19-283098-2}} * {{cite book |last1=Hohn |first1=Franz E. |title=Elementary Matrix Algebra |publisher=Dover Publications |isbn=978-0-486-14372-9 |url=https://books.google.com/books?id=9XlFu4XQ6nUC&pg=PA83 |language=en |date=2013}} * {{cite book |last1=Houston |first1=Stephen D. |title=The First Writing: Script Invention as History and Process |date=2004 |publisher=Cambridge University Press |isbn=978-0-521-83861-0 |url=https://books.google.com/books?id=jsWL_XJt-dMC&pg=PA319 |language=en}}{{cbignore}} * {{cite book |last1=Hull |first1=Thomas C. |title=Origametry: Mathematical Methods in Paper Folding |publisher=Cambridge University Press |isbn=978-1-108-47872-4 |url=https://books.google.com/books?id=LdX7DwAAQBAJ&pg=PA5 |date=2021 |access-date=August 7, 2024}}{{cbignore}} * {{cite book |last1=Igarashi |first1=Yoshihide |last2=Altman |first2=Tom |last3=Funada |first3=Mariko |last4=Kamiyama |first4=Barbara |title=Computing: A Historical and Technical Perspective |date=2014 |publisher=CRC Press |isbn=978-1-4822-2741-3 |url=https://books.google.com/books?id=58ySAwAAQBAJ&pg=PA103 |language=en |access-date=January 29, 2024}}{{cbignore}} * {{cite book |last1=Indurkhya |first1=Bipin |title=Metaphor and Cognition: An Interactionist Approach |date=2013 |publisher=Springer |isbn=978-94-017-2252-0 |chapter-url=https://books.google.com/books?id=foTrCAAAQBAJ&pg=PA217 |language=en |chapter=6.5 Algebras and Structures |access-date=January 21, 2024}}{{cbignore}} * {{cite book |last1=Irving |first1=Ronald S. |title=Integers, Polynomials, and Rings: A Course in Algebra |date=2004 |publisher=Springer |isbn=978-0-387-40397-7 |url=https://books.google.com/books?id=-7OM1OtOFJgC |language=en |access-date=January 20, 2024}}{{cbignore}} * {{cite web |last1=Ivanova |first1=O. A. |last2=Smirnov |first2=D. M. |title=Isomorphism |url=https://encyclopediaofmath.org/wiki/Isomorphism |website=Encyclopedia of Mathematics |publisher=Springer |date=2012 |access-date=March 11, 2024 |archive-date=August 6, 2024 |archive-url=https://web.archive.org/web/20240806082014/https://encyclopediaofmath.org/wiki/Isomorphism |url-status=live}} * {{cite web |last1=Jansana |first1=Ramon |title=Algebraic Propositional Logic |url=https://plato.stanford.edu/entries/logic-algebraic-propositional/ |website=The Stanford Encyclopedia of Philosophy |publisher=Metaphysics Research Lab, Stanford University |access-date=January 22, 2024 |date=2022 |archive-date=December 20, 2016 |archive-url=https://web.archive.org/web/20161220155433/https://plato.stanford.edu/entries/logic-algebraic-propositional/ |url-status=live}} * {{cite book |last1=Jarvis |first1=Frazer |title=Algebraic Number Theory |date=2014 |publisher=Springer |isbn=978-3-319-07545-7 |url=https://books.google.com/books?id=0j0qBAAAQBAJ&pg=PA1 |language=en |access-date=January 24, 2024}}{{cbignore}} * {{cite book |last1=Jenkins |first1=Everett |title=The Muslim Diaspora (Volume 1, 570-1500): A Comprehensive Chronology of the Spread of Islam in Asia, Africa, Europe and the Americas |date=2010 |publisher=McFarland |isbn=978-0-7864-4713-8 |url=https://books.google.com/books?id=giEkCQAAQBAJ&pg=PA82 |language=en |access-date=January 28, 2024}}{{cbignore}} * {{cite book |last1=Joyner |first1=David |title=Adventures in Group Theory: Rubik's Cube, Merlin's Machine, and Other Mathematical Toys |publisher=Johns Hopkins University Press |isbn=978-0-8018-9012-3 |edition=2 |date=2008}} * {{cite book |last1=Kaput |first1=James J. |editor1-last=Wagner |editor1-first=Sigrid |editor2-last=Kieran |editor2-first=Carolyn |title=Research Issues in the Learning and Teaching of Algebra: the Research Agenda for Mathematics Education, Volume 4 |publisher=Routledge |isbn=978-1-135-43414-4 |chapter-url=https://books.google.com/books?id=1GUPEAAAQBAJ&pg=PA186 |language=en |chapter=Linking Representations in the Symbol Systems of Algebra |date=2018 |access-date=August 8, 2024}}{{cbignore}} * {{cite web |last1=Kargapolov |first1=M. I. |last2=Merzlyakov |first2=Yu. I. |title=Group |url=https://encyclopediaofmath.org/wiki/Group |website=Encyclopedia of Mathematics |publisher=Springer |access-date=January 11, 2023 |date=2016 |archive-date=December 5, 2022 |archive-url=https://web.archive.org/web/20221205014207/https://encyclopediaofmath.org/wiki/Group |url-status=live}} * {{cite book |last1=Karpilovsky |first1=G. |title=Topics in Field Theory |publisher=Elsevier |isbn=978-0-08-087266-7 |url=https://books.google.com/books?id=-2WR0fw9gLMC&pg=PA45 |language=en |date=1989}} * {{cite book |last1=Kaufmann |first1=Jerome E. |last2=Schwitters |first2=Karen L. |title=Elementary Algebra |publisher=Cengage Learning |isbn=978-1-4390-4917-4 |date=2011}} * {{cite book |last1=Khattar |first1=Dinesh |last2=Agrawal |first2=Neha |title=Group Theory |date=2023 |publisher=Springer and Ane Books Pvt. Ltd. |isbn=978-3-031-21307-6 |url=https://books.google.com/books?id=7-nIEAAAQBAJ&pg=PA4 |language=en |access-date=January 20, 2024}}{{cbignore}} * {{cite book |last1=Kieran |first1=Carolyn |editor1-last=Gutiérrez |editor1-first=Angel |editor2-last=Boero |editor2-first=Paolo |title=Handbook of Research on the Psychology of Mathematics Education: Past, Present and Future |publisher=Sense Publishers |isbn=978-90-77874-19-6 |chapter-url=https://books.google.com/books?id=OTCsKu0BZ0kC&pg=PA15 |language=en |chapter=Research on the Learning and Teaching of Algebra |date=2006 |access-date=August 8, 2024}}{{cbignore}} * {{cite book |last1=Kilty |first1=Joel |last2=McAllister |first2=Alex |title=Mathematical Modeling and Applied Calculus |date=2018 |publisher=Oxford University Press |isbn=978-0-19-255813-8 |url=https://books.google.com/books?id=YVRuDwAAQBAJ&pg=PA347 |language=en |access-date=January 24, 2024}}{{cbignore}} * {{cite book |last1=Kleiner |first1=Israel |title=A History of Abstract Algebra |publisher=Springer |isbn=978-0-8176-4685-1 |url=https://books.google.com/books?id=udj-1UuaOiIC&pg=PA100 |language=en |date=2007}} * {{cite book |last1=Klimov |first1=D. M. |title=Group-Theoretic Methods in Mechanics and Applied Mathematics |publisher=CRC Press |isbn=978-1-4822-6522-4 |url=https://books.google.com/books?id=DZK3DwAAQBAJ&pg=PR9 |language=en |date=2014}} * {{cite book |last1=Kline |first1=Morris |title=Mathematical Thought From Ancient to Modern Times: Volume 3 |publisher=Oxford University Press |isbn=978-0-19-506137-6 |url=https://books.google.com/books?id=8YaBuGcmLb0C&pg=PA1153 |language=en |date=1990}} * {{cite book |last1=Knoebel |first1=Arthur |title=Sheaves of Algebras Over Boolean Spaces |date=2011 |publisher=Springer |isbn=978-0-8176-4218-1 |url=https://books.google.com/books?id=VWS_sgO2uvgC&pg=PA5 |language=en |access-date=January 27, 2024}}{{cbignore}} * {{cite book |last1=Kramer |first1=Jürg |last2=Pippich |first2=Anna-Maria von |title=From Natural Numbers to Quaternions |date=2017 |publisher=Springer |isbn=978-3-319-69429-0 |url=https://books.google.com/books?id=nvM-DwAAQBAJ&pg=PA49 |language=en |access-date=January 20, 2024}}{{cbignore}} * {{cite book |last1=Krömer |first1=Ralph |title=Tool and Object: A History and Philosophy of Category Theory |publisher=Springer |isbn=978-3-7643-7524-9 |url=https://books.google.com/books?id=41bHxtHxjUAC&pg=PA61 |language=en |date=2007}} * {{cite journal |last1=Kvasz |first1=L. |title=The History of Algebra and the Development of the Form of Its Language |journal=Philosophia Mathematica |date=2006 |volume=14 |issue=3 |pages=287–317 |doi=10.1093/philmat/nkj017 |doi-access=free |issn=1744-6406}} * {{cite book |last1=Lal |first1=Ramji |title=Algebra 2: Linear Algebra, Galois Theory, Representation Theory, Group Extensions and Schur Multiplier |publisher=Springer |isbn=978-981-10-4256-0 |url=https://books.google.com/books?id=FwPNDgAAQBAJ&pg=PA31 |language=en |date=2017}}{{cbignore}} * {{cite book |last1=Lamagna |first1=Edmund A. |title=Computer Algebra: Concepts and Techniques |date=2019 |publisher=CRC Press |isbn=978-1-351-60583-0 |url=https://books.google.com/books?id=8PSDDwAAQBAJ&pg=PA150 |language=en |access-date=January 16, 2024}}{{cbignore}} * {{cite book |last1=Lang |first1=Serge |author-link=Serge Lang |title=Algebra |publisher=Springer |isbn=978-0-387-95385-4 |url=https://books.google.com/books?id=Fge-BwqhqIYC&pg=PA261 |language=en |date=2005}} * {{cite book |last1=Laos |first1=Nicolas K. |title=Topics in Mathematical Analysis and Differential Geometry |publisher=World Scientific |isbn=978-981-02-3180-4 |url=https://books.google.com/books?id=1r7dSn4ZqogC&pg=PA100 |language=en |date=1998}} * {{cite book |author1=Library of Congress |title=Library of Congress Classification: Class Q - Science |publisher=Library of Congress |url=https://www.loc.gov/aba/cataloging/classification/lcco/lcco_q.pdf |access-date=March 17, 2024 |archive-date=April 5, 2024 |archive-url=https://web.archive.org/web/20240405210545/https://www.loc.gov/aba/cataloging/classification/lcco/lcco_q.pdf |url-status=live}} * {{cite book |last1=Lidl |first1=Rudolf |last2=Pilz |first2=Günter |title=Applied Abstract Algebra |publisher=Springer |isbn=978-0-387-98290-8 |url=https://books.google.com/books?id=_49AmSWo4_AC&pg=PR7 |language=en |date=1997}} * {{cite book |last1=Lovett |first1=Stephen |title=Abstract Algebra: Structures and Applications |publisher=CRC Press |isbn=978-1-4822-4891-3 |url=https://books.google.com/books?id=jRUqCgAAQBAJ&pg=PR9 |language=en |date=2015 |access-date=July 27, 2024}}{{cbignore}} * {{cite book |last1=Lukas |first1=Andre |title=The Oxford Linear Algebra for Scientists |publisher=Oxford University Press |isbn=978-0-19-258347-5 |url=https://books.google.com/books?id=1-dvEAAAQBAJ&pg=PA47 |language=en |date=2022}}{{cbignore}} * {{cite book |last1=Maddocks |first1=J. R. |editor1-last=Lerner |editor1-first=Brenda Wilmoth |editor2-last=Lerner |editor2-first=K. Lee |title=The Gale Encyclopedia of Science |date=2008 |publisher=Thompson Gale |isbn=978-1-4144-2877-2 |edition=4th |chapter=Algebra |url=https://www.encyclopedia.com/science-and-technology/mathematics/mathematics/algebra |access-date=January 13, 2024 |archive-date=January 12, 2024 |archive-url=https://web.archive.org/web/20240112102551/https://www.encyclopedia.com/science-and-technology/mathematics/mathematics/algebra |url-status=live}} * {{cite book |last1=Majewski |first1=Miroslaw |title=MuPAD Pro Computing Essentials |date=2004 |publisher=Springer |isbn=978-3-540-21943-9 |edition=2}} * {{cite book |last1=Mal’cev |first1=A. I. |author-link=Anatoly Maltsev |title=Algebraic Systems |date=1973 |publisher=Springer |isbn=978-3-642-65374-2 |chapter-url=https://link.springer.com/chapter/10.1007/978-3-642-65374-2_5 |language=en |chapter=Quasivarieties |pages=210–266 |doi=10.1007/978-3-642-65374-2_5 |access-date=January 21, 2024 |archive-date=June 18, 2018 |archive-url=https://web.archive.org/web/20180618183135/https://link.springer.com/chapter/10.1007%2F978-3-642-65374-2_5 |url-status=live}} * {{cite book |last1=Mancosu |first1=Paolo |title=Philosophy of Mathematics and Mathematical Practice in the Seventeenth Century |date=1999 |publisher=Oxford University Press |isbn=978-0-19-513244-1 |url=https://books.google.com/books?id=60qaEePdqcoC&pg=PA84 |language=en |access-date=January 24, 2024}}{{cbignore}} * {{cite web |last1=Markushevich |first1=A. I. |title=Polynomial |url=https://encyclopediaofmath.org/wiki/Polynomial |website=Encyclopedia of Mathematics |publisher=Springer |access-date=January 11, 2023 |date=2015 |archive-date=August 6, 2024 |archive-url=https://web.archive.org/web/20240806082025/https://encyclopediaofmath.org/wiki/Polynomial |url-status=live}} * {{cite book |last1=Maxwell |first1=E. A. |title=Algebraic Structure and Matrices Book 2 |date=2009 |publisher=Syracuse University Press |isbn=978-0-521-10905-5 |url=https://books.google.com/books?id=yD0irRUE_u4C&pg=PA73 |language=en |access-date=January 20, 2024}}{{cbignore}} * {{cite book |last1=McKeague |first1=Charles P. |title=Elementary Algebra |publisher=Academic Press |isbn=978-1-4832-6384-7 |url=https://books.google.com/books?id=sq7iBQAAQBAJ&pg=PA148 |language=en |date=1986}}{{cbignore}} * {{cite book |last1=McKeague |first1=Charles P. |title=Intermediate Algebra: A Text/Workbook |date=2014 |publisher=Academic Press |isbn=978-1-4832-1417-7 |url=https://books.google.com/books?id=nI7iBQAAQBAJ&pg=PA386 |language=en |access-date=January 16, 2024}}{{cbignore}} * {{cite book |last1=McWeeny |first1=R. |title=Symmetry: An Introduction to Group Theory and Its Applications |date=2002 |publisher=Courier Corporation |isbn=978-0-486-42182-7 |url=https://books.google.com/books?id=x3fjIXY93TsC&pg=PA6 |language=en |access-date=January 20, 2024}}{{cbignore}} * {{cite book |last1=Menini |first1=Claudia |last2=Oystaeyen |first2=Freddy Van |url=https://books.google.com/books?id=3mlQDwAAQBAJ&pg=PA722 |title=Abstract Algebra: A Comprehensive Treatment |date=2017 |publisher=[[CRC Press]] |isbn=978-1-4822-5817-2 |language=en |access-date=January 27, 2024}}{{cbignore}} * {{cite web |last1=Merzlyakov |first1=Yu. I. |last2=Shirshov |first2=A. I. |title=Algebra(2) |url=https://encyclopediaofmath.org/wiki/Algebra(2) |website=Encyclopedia of Mathematics |publisher=Springer |access-date=January 11, 2023 |date=2020 |archive-date=April 7, 2023 |archive-url=https://web.archive.org/web/20230407165656/https://encyclopediaofmath.org/wiki/Algebra(2) |url-status=live}} * {{cite book |last1=Mirakhor |first1=Abbas |last2=Krichene |first2=Noureddine |title=Introductory Mathematics and Statistics for Islamic Finance |publisher=John Wiley & Sons |isbn=978-1-118-77972-9 |url=https://books.google.com/books?id=G6XNAwAAQBAJ&pg=PT107 |language=en |date=2014 |access-date=August 7, 2024}}{{cbignore}} * {{cite book |last1=Mishra |first1=Sanjay |title=Fundamentals of Mathematics: Algebra |publisher=Pearson India |isbn=978-93-325-5891-5 |language=en |date=2016}} * {{cite book |last1=Miyake |first1=Katsuya |editor1-last=Kanemitsu |editor1-first=Shigeru |editor2-last=Jia |editor2-first=Chaohua |title=Number Theoretic Methods: Future Trends |publisher=Springer |isbn=978-1-4419-5239-4 |chapter-url=https://books.google.com/books?id=G0P2BwAAQBAJ&pg=PA268 |chapter=Some Aspects on Interactions between Algebraic Number Theory and Analytic Number Theory |date=2002 |access-date=August 7, 2024}}{{cbignore}} * {{cite book |last1=Moh |first1=T. T. |title=Algebra |publisher=World Scientific |isbn=978-981-02-1195-0 |url=https://books.google.com/books?id=maK3sbTVhsoC&pg=PA102 |language=en |date=1992 }} * {{cite book |last1=Mortensen |first1=C. E. |title=Inconsistent Mathematics |date=2013 |publisher=Springer |isbn=978-94-015-8453-1 |url=https://books.google.com/books?id=KYDrCAAAQBAJ&pg=PA73 |language=en |access-date=January 18, 2024}}{{cbignore}} * {{cite book |last1=Murthy |first1=Swamy and |title=Algebra: Abstract and Modern |publisher=Pearson Education India |isbn=978-93-325-0993-1 |url=https://books.google.com/books?id=CBc8BAAAQBAJ&pg=PA3 |language=en |date=2012 |access-date=August 5, 2024}}{{cbignore}} * {{cite book |last1=Musser |first1=Gary L. |last2=Peterson |first2=Blake E. |last3=Burger |first3=William F. |title=Mathematics for Elementary Teachers: A Contemporary Approach |date=2013 |publisher=John Wiley & Sons |isbn=978-1-118-48700-6 |url=https://books.google.com/books?id=8jh7DwAAQBAJ |language=en |access-date=March 11, 2024}}{{cbignore}} * {{cite web |author1=MW Staff |title=Definition of Arithmetic |url=https://www.merriam-webster.com/dictionary/arithmetic |website=Merriam-Webster |access-date=October 19, 2023 |language=en |date=2023 |archive-date=November 14, 2023 |archive-url=https://web.archive.org/web/20231114193352/https://www.merriam-webster.com/dictionary/arithmetic |url-status=live}} * {{cite book |last1=Nakahara |first1=Mikio |title=Geometry, Topology and Physics |date=2018 |publisher=Taylor & Francis |isbn=978-1-4200-5694-5 |url=https://books.google.com/books?id=p2C1DwAAQBAJ&pg=PA121 |language=en |access-date=January 24, 2024}}{{cbignore}} * {{cite book |last1=Neri |first1=Ferrante |title=Linear Algebra for Computational Sciences and Engineering |date=2019 |publisher=Springer |isbn=978-3-030-21321-3 |url=https://books.google.com/books?id=NMOlDwAAQBAJ&pg=PR12 |language=en |access-date=January 24, 2024}}{{cbignore}} * {{cite book |last1=Nicholson |first1=W. Keith |title=Introduction to Abstract Algebra |publisher=John Wiley & Sons |isbn=978-1-118-13535-8 |url=https://books.google.com/books?id=w-GaLpapRcEC&pg=PA70 |language=en |date=2012 |access-date=August 30, 2024}}{{cbignore}} * {{cite journal |last1=Oaks |first1=Jeffrey A. |last2=Alkhateeb |first2=Haitham M. |title=Simplifying equations in Arabic algebra |journal=Historia Mathematica |volume=34 |issue=1 |doi=10.1016/j.hm.2006.02.006 |date=2007 |pages=45–61}} * {{cite book |last1=Olver |first1=Peter J. |title=Classical Invariant Theory |date=1999 |publisher=Cambridge University Press |isbn=978-0-521-55821-1 |url=https://books.google.com/books?id=1GlHYhNRAqEC&pg=PA55 |language=en |access-date=March 12, 2024}}{{cbignore}} * {{cite book |last1=Ono |first1=Hiroakira |title=Proof Theory and Algebra in Logic |publisher=Springer |isbn=978-981-13-7997-0 |url=https://books.google.com/books?id=SR2nDwAAQBAJ&pg=PA84 |language=en |date=2019}}{{cbignore}} * {{cite web |url=http://www.lexico.com/definition/algebra |archive-url=https://web.archive.org/web/20131120000000/http://www.lexico.com/definition/algebra |url-status=dead |archive-date=November 20, 2013 |title=Algebra |website=[[Lexico]] |publisher=[[Oxford University Press]] |author=OUP Staff}} * {{cite book |last1=Ovchinnikov |first1=Sergei |title=Number Systems |date=2015 |publisher=American Mathematical Society |isbn=978-1-4704-2018-5 |url=https://books.google.com/books?id=UMbXBgAAQBAJ&pg=PA27 |language=en |access-date=January 20, 2024}}{{cbignore}} * {{cite book |last1=Pickover |first1=Clifford A. |title=The Math Book: From Pythagoras to the 57th Dimension, 250 Milestones in the History of Mathematics |date=2009 |publisher=Sterling Publishing Company, Inc. |isbn=978-1-4027-5796-9 |url=https://books.google.com/books?id=JrslMKTgSZwC&pg=PA90 |language=en |access-date=January 28, 2024}}{{cbignore}} * {{cite book |last1=Plotkin |first1=B. |title=Universal Algebra, Algebraic Logic, and Databases |date=2012 |publisher=Springer |isbn=978-94-011-0820-1 |url=https://books.google.com/books?id=-v3xCAAAQBAJ&pg=PA155 |language=en |access-date=January 24, 2024}}{{cbignore}} * {{cite web |last1=Pratt |first1=Vaughan |title=Algebra |url=https://plato.stanford.edu/entries/algebra/ |website=The Stanford Encyclopedia of Philosophy |publisher=Metaphysics Research Lab, Stanford University |access-date=January 11, 2024 |date=2022 |archive-date=January 29, 2024 |archive-url=https://web.archive.org/web/20240129081755/https://plato.stanford.edu/entries/algebra/ |url-status=live}} * {{cite book |last1=Rabadan |first1=Raul |last2=Blumberg |first2=Andrew J. |title=Topological Data Analysis for Genomics and Evolution: Topology in Biology |date=2019 |publisher=Cambridge University Press |isbn=978-1-107-15954-9 |url=https://books.google.com/books?id=2967DwAAQBAJ&pg=PA49 |language=en |access-date=January 24, 2024}}{{cbignore}} * {{cite book |last1=Ricardo |first1=Henry |title=A Modern Introduction to Linear Algebra |publisher=CRC Press |isbn=978-1-4398-9461-3 |url=https://books.google.com/books?id=s7bMBQAAQBAJ&pg=PA389 |language=en |date=2009 |access-date=August 29, 2024}}{{cbignore}} * {{cite book |last1=Rohde |first1=Ulrich L. |last2=Jain |first2=G. C. |last3=Poddar |first3=Ajay K. |last4=Ghosh |first4=A. K. |title=Introduction to Differential Calculus: Systematic Studies with Engineering Applications for Beginners |date=2012 |publisher=John Wiley & Sons |isbn=978-1-118-13014-8 |url=https://books.google.com/books?id=vk2XbZpsBOwC&pg=PT89 |language=en |access-date=January 16, 2024}}{{cbignore}} * {{cite book |last1=Romanowski |first1=Perry |editor1-last=Lerner |editor1-first=Brenda Wilmoth |editor2-last=Lerner |editor2-first=K. Lee |title=The Gale Encyclopedia of Science |date=2008 |publisher=Thompson Gale |isbn=978-1-4144-2877-2 |edition=4th |chapter=Arithmetic |url=https://www.encyclopedia.com/science-and-technology/mathematics/mathematics/arithmetic |access-date=January 13, 2024 |archive-date=November 1, 2023 |archive-url=https://web.archive.org/web/20231101124957/https://www.encyclopedia.com/science-and-technology/mathematics/mathematics/arithmetic |url-status=live}} * {{cite book |last1=Rosen |first1=Kenneth |title=Discrete Maths and Its Applications Global Edition 7e |publisher=McGraw Hill |isbn=978-0-07-715151-5 |url=https://books.google.com/books?id=-oVvEAAAQBAJ&pg=PA779 |language=en |date=2012}} * {{cite book |last1=Rowen |first1=Louis Halle |title=Graduate Algebra: Commutative View: Commutative View |publisher=American Mathematical Society |isbn=978-0-8218-0570-1 |url=https://books.google.com/books?id=AhEPCgAAQBAJ&pg=PA12 |language=en |date=2006 |access-date=June 14, 2024}}{{cbignore}} * {{cite book |last1=Sahai |first1=Vivek |last2=Bist |first2=Vikas |title=Linear Algebra |publisher=CRC Press |isbn=978-0-8493-2426-0 |url=https://books.google.com/books?id=yjkgNYfApj4C&pg=PA21 |language=en |date=2002}} * {{cite book |last1=Saikia |first1=Promode Kumar |title=Linear Algebra |publisher=Pearson Education India |isbn=978-81-317-4276-1 |url=https://books.google.com/books?id=KhM7BAAAQBAJ&pg=PA1 |language=en |date=2008 |access-date=August 5, 2024}}{{cbignore}} * {{cite book |last1=Serovajsky |first1=Simon |title=Architecture of Mathematics |publisher=CRC Press |isbn=978-0-429-89353-7 |url=https://books.google.com/books?id=6EX1DwAAQBAJ&pg=SA3-PA89 |language=en |date=2020}} * {{cite book |last1=Seshadri |first1=C. S. |title=Studies in the History of Indian Mathematics |date=2010 |publisher=Springer |isbn=978-93-86279-49-1 |url=https://books.google.com/books?id=w_JdDwAAQBAJ&pg=PA156 |language=en |access-date=January 27, 2024}}{{cbignore}} * {{cite book |last1=Sialaros |first1=Michalis |title=Revolutions and Continuity in Greek Mathematics |date=2018 |publisher=Walter de Gruyter GmbH & Co KG |isbn=978-3-11-056527-0 |url=https://books.google.com/books?id=2PZYDwAAQBAJ&pg=PT55 |language=en |access-date=January 27, 2024}}{{cbignore}} * {{cite book |last1=Silverman |first1=Joseph H. |author-link=Joseph H. Silverman |title=Abstract Algebra: An Integrated Approach |publisher=American Mathematical Society |isbn=978-1-4704-6860-6 |url=https://books.google.com/books?id=PKFnEAAAQBAJ&pg=PA64 |language=en |date=2022}} * {{cite web |last1=Smirnov |first1=D. M. |title=Universal Algebra |url=https://encyclopediaofmath.org/wiki/Universal_algebra |website=Encyclopedia of Mathematics |publisher=Springer |date=2020 |access-date=August 30, 2024 |archive-date=March 1, 2024 |archive-url=https://web.archive.org/web/20240301115432/https://encyclopediaofmath.org/wiki/Universal_algebra |url-status=live}} * {{cite book |last1=Smith |first1=Jonathan D. H. |title=Introduction to Abstract Algebra |publisher=CRC Press |isbn=978-1-4987-3162-1 |url=https://books.google.com/books?id=MXu9CgAAQBAJ&pg=PA161 |language=en |date=2015 |access-date=June 14, 2024}}{{cbignore}} * {{cite book |last1=Smorynski |first1=Craig |title=History of Mathematics: A Supplement |date=2007 |publisher=Springer |isbn=978-0-387-75481-9 |url=https://books.google.com/books?id=qY657eFq7UgC&pg=PA137 |language=en |access-date=January 27, 2024}}{{cbignore}} * {{cite book |last1=Sneyd |first1=James |last2=Fewster |first2=Rachel M. |last3=McGillivray |first3=Duncan |title=Mathematics and Statistics for Science |publisher=Springer |isbn=978-3-031-05318-4 |url=https://books.google.com/books?id=zqd3EAAAQBAJ&pg=PA211 |language=en |date=2022}}{{cbignore}} * {{cite web |last1=Sobolev |first1=S. K. |title=Constant |url=https://encyclopediaofmath.org/wiki/Algebraic_logic |website=Encyclopedia of Mathematics |publisher=Springer |access-date=October 23, 2023 |date=2015 |archive-date=January 24, 2024 |archive-url=https://web.archive.org/web/20240124094606/https://encyclopediaofmath.org/wiki/Algebraic_logic |url-status=live}} * {{cite book |last1=Solomon |first1=Bruce |title=Linear Algebra, Geometry and Transformation |publisher=CRC Press |isbn=978-1-4822-9930-4 |url=https://books.google.com/books?id=BpvSBQAAQBAJ&pg=PA57 |language=en |date=2014 |access-date=August 29, 2024}}{{cbignore}} * {{cite book |last1=Sorell |first1=Tom |title=Descartes: A Very Short Introduction |date=2000 |publisher=Oxford University Press |isbn=978-0-19-285409-4 |url=https://books.google.com/books?id=EksSDAAAQBAJ&pg=PA19 |language=en |access-date=March 11, 2024}}{{cbignore}} * {{cite book |last1=Star |first1=Jon R. |last2=Foegen |first2=Anne |last3=Larson |first3=Matthew R. |last4=McCallum |first4=William G. |last5=Porath |first5=Jane |last6=Zbiek |first6=Rose Mary |title=Teaching Strategies for Improving Algebra Knowledge in Middle and High School Students |publisher=U.S. Department of Education / Institute of Education Sciences |date=2015 |oclc=5867417164}} * {{cite journal |last1=Straffin |first1=Philip D. |title=Linear Algebra in Geography: Eigenvectors of Networks |journal=Mathematics Magazine |date=1980 |volume=53 |issue=5 |pages=269–276 |doi=10.2307/2689388 |jstor=2689388 |url=https://www.jstor.org/stable/2689388 |issn=0025-570X|url-access=subscription }} * {{cite book |last1=Sullivan |first1=Michael |title=Finite Mathematics: An Applied Approach |date=2010 |publisher=John Wiley & Sons |isbn=978-0-470-87639-8 |url=https://books.google.com/books?id=6NKaDwAAQBAJ&pg=PA53 |language=en |access-date=January 18, 2024}}{{cbignore}} * {{cite book |last1=Tan |first1=Kiat Shi |last2=Steeb |first2=Willi-Hans |last3=Hardy |first3=Yorick |title=SymbolicC++:An Introduction to Computer Algebra Using Object-Oriented Programming: An Introduction to Computer Algebra Using Object-Oriented Programming |date=2012 |publisher=Springer |isbn=978-1-4471-0405-6 |url=https://books.google.com/books?id=UDb0BwAAQBAJ&pg=PA306 |language=en |access-date=January 16, 2024}}{{cbignore}} * {{cite book |last1=Tanton |first1=James |title=Encyclopedia of Mathematics |date=2005 |publisher=Facts On File |isbn=978-0-8160-5124-3}} * {{cite book |last1=Terras |first1=Audrey |title=Abstract Algebra with Applications |publisher=Cambridge University Press |isbn=978-1-107-16407-9 |date=2019}} * {{cite book |last1=Tsokos |first1=Chris P. |last2=Wooten |first2=Rebecca D. |title=The Joy of Finite Mathematics: The Language and Art of Math |publisher=Academic Press |isbn=978-0-12-802985-5 |url=https://books.google.com/books?id=zu7HBQAAQBAJ&pg=PA451 |language=en |date=2015}}{{cbignore}} * {{cite book |last1=Valenza |first1=Robert J. |title=Linear Algebra: An Introduction to Abstract Mathematics |publisher=Springer |isbn=978-1-4612-0901-0 |url=https://books.google.com/books?id=7x8MCAAAQBAJ&pg=PR7 |language=en |date=2012 |access-date=August 29, 2024}}{{cbignore}} * {{cite book |last1=Vince |first1=John |title=Vector Analysis for Computer Graphics |publisher=Springer |isbn=978-1-84628-803-6 |url=https://books.google.com/books?id=B574tQbP6WcC&pg=PA133 |language=en |date=2007 |access-date=August 5, 2024}}{{cbignore}} * {{cite book |last1=Viterbo |first1=Emanuele |last2=Hong |first2=Yi |editor1-last=Hlawatsch |editor1-first=Franz |editor2-last=Matz |editor2-first=Gerald |title=Wireless Communications Over Rapidly Time-Varying Channels |date=2011 |publisher=Academic Press |isbn=978-0-08-092272-0 |chapter-url=https://books.google.com/books?id=d89QRR24jbMC&pg=PA127 |language=en |chapter=3.4 Algebraic Number Theory |access-date=January 24, 2024}}{{cbignore}} * {{cite web |last1=Voitsekhovskii |first1=M. I. |title=Linear Equation |url=https://encyclopediaofmath.org/wiki/Linear_equation |website=Encyclopedia of Mathematics |publisher=Springer |access-date=January 10, 2024 |date=2011 |archive-date=November 23, 2023 |archive-url=https://web.archive.org/web/20231123235759/https://encyclopediaofmath.org/wiki/Linear_equation |url-status=live}} * {{cite book |last1=Waerden |first1=Bartel L. van der |author-link=Bartel Leendert van der Waerden |title=Algebra |publisher=Springer |isbn=0-387-40624-7 |volume=1 |date=2003}} * {{cite book |last1=Waerden |first1=Bartel L. van der |title=A History of Algebra: From al-Khwārizmī to Emmy Noether |date=2013 |publisher=Springer |isbn=978-3-642-51599-6 |url=https://books.google.com/books?id=W6DwCAAAQBAJ |language=en |access-date=January 27, 2024}}{{cbignore}} * {{cite book |last1=Wagner |first1=Sigrid |last2=Kieran |first2=Carolyn |title=Research Issues in the Learning and Teaching of Algebra: The Research Agenda for Mathematics Education |volume=4 |date=2018 |publisher=Routledge |isbn=978-1-135-43421-2 |url=https://books.google.com/books?id=uW4ECwAAQBAJ&pg=PT225 |language=en |access-date=January 13, 2024}}{{cbignore}} * {{cite book |last1=Walz |first1=Guido |title=Lexikon der Mathematik: Band 1: A bis Eif |date=2016 |publisher=Springer |isbn=978-3-662-53498-4 |url=https://www.spektrum.de/lexikon/mathematik/algebra/12062 |language=de |chapter=Algebra |access-date=January 13, 2024 |archive-date=January 12, 2024 |archive-url=https://web.archive.org/web/20240112171819/https://www.spektrum.de/lexikon/mathematik/algebra/12062 |url-status=live |trans-title=Encyclopedia of Mathematics: Volume 1: A to Eif}} * {{cite book |last1=Weibel |first1=Charles A. |author-link=Charles Weibel |title=An Introduction to Homological Algebra |publisher=Cambridge University Press |isbn=978-1-139-64307-8 |url=https://books.google.com/books?id=UtIhAwAAQBAJ&pg=PR11 |language=en |date=1995}} * {{cite book |last1=Weisstein |first1=Eric W. |title=CRC Concise Encyclopedia of Mathematics |date=2003 |publisher=Chapman & Hall/CRC |isbn=978-1-58488-347-0 |edition=2nd}} * {{cite book |last1=Wheeler |first1=Jeffrey Paul |title=An Introduction to Optimization with Applications in Machine Learning and Data Analytics |publisher=CRC Press |isbn=978-1-003-80359-1 |url=https://books.google.com/books?id=IqQIEQAAQBAJ&pg=PA29 |language=en |date=2023}} * {{cite book |last1=Whitelaw |first1=T. A. |title=Introduction to Abstract Algebra, Third Edition |publisher=CRC Press |isbn=978-0-7514-0147-9 |url=https://books.google.com/books?id=f2hyf0QoB_0C&pg=PA61 |language=en |date=1995}}{{cbignore}} * {{cite book |last1=Williams |first1=G. Arnell |title=Algebra the Beautiful: An Ode to Math's Least-Loved Subject |date=2022 |publisher=Basic Books |isbn=978-1-5416-0070-6 |url=https://books.google.com/books?id=581CEAAAQBAJ&pg=PT62 |language=en |access-date=March 11, 2024}}{{cbignore}} * {{cite book |last=Wilson |first=Robert A. |author-link=Robert Arnott Wilson |title=The Finite Simple Groups |publisher=[[Springer-Verlag]] |series=[[Graduate Texts in Mathematics]] |isbn=978-1-84800-987-5 |doi=10.1007/978-1-84800-988-2 |year=2009 |zbl=1203.20012 |volume=251}} * {{cite book |last1=Young |first1=Cynthia Y. |title=Precalculus |date=2010 |publisher=John Wiley & Sons |isbn=978-0-471-75684-2 |url=https://books.google.com/books?id=9HRLAn326zEC&pg=RA1-PA999 |language=en |access-date=January 16, 2024}}{{cbignore}} * {{cite book |last1=Young |first1=Cynthia Y. |title=Precalculus |date=2023 |publisher=John Wiley & Sons |isbn=978-1-119-86940-5 |url=https://books.google.com/books?id=pMSZEAAAQBAJ&pg=PA714 |language=en |access-date=January 18, 2024}}{{cbignore}} * {{cite web |author1=zbMATH Open |title=Classification |url=https://zbmath.org/classification/ |website=zbMATH Open |publisher=Mathematical Reviews and zbMATH Open |access-date=March 17, 2024 |language=en |date=2024 |archive-date=July 19, 2020 |archive-url=https://web.archive.org/web/20200719184539/https://zbmath.org/classification/ |url-status=live}} * {{cite book |last1=Zwillinger |first1=Daniel |title=CRC Standard Mathematical Tables and Formulae |date=2002 |publisher=CRC Press |isbn=978-1-4200-3534-6 |url=https://books.google.com/books?id=gE_MBQAAQBAJ&pg=PA812 |language=en |access-date=January 27, 2024}}{{cbignore}} {{Refend}} == External links == {{Wikiquote}} {{Wiktionary|algebra}} {{Wikibooks|Algebra}} {{EB1911 poster|Algebra}} {{Algebra}} {{Polynomials}} {{Areas of mathematics}} {{Authority control}} [[Category:Algebra| ]] 0kqffpvzsjaa93jqdty2uvc24q8mnua 3 6916 122227 122204 2026-09-22T08:58:27Z Tumbuka Arch 6863 /* Broken home */ Zgolo 122227 wikitext text/x-wiki {{User:MiszaBot/config |maxarchivesize = 250K |counter = 16 |algo = old(48h) |archive = User talk:Anthonymunthali44/Archive %(counter)d |minthreadstoarchive = 1 |minthreadsleft = 4 }} {{Archives}} == Article on Earth == Hello, I’m messaging you today to ask if [[Tera (Charu cha pasi)]] should be changed into [[Tera]], with [[Charu cha pasi]] being a redirect to the page, instead of it having both in the name. Thanks! [[File:Coat of arms of Cuba.svg|20px]] [[User:CubanoBoi|CubanoBoi]] [[File:Coat of arms of Cuba.svg|20px]] 19:53, 22 Julayi 2025 (UTC) :@[[User:CubanoBoi|CubanoBoi]] Hello. I adapted Tera from from the Latin Word for earth since the native "Charu cha pasi" can be used in other contexts to just refer to the ground. But from context people can figure out that Tera is referring to Earth so you can remove [[User:Anthonymunthali44|Anthonymunthali44]] ([[User talk:Anthonymunthali44|pakuchezgela]]) 20:12, 22 Julayi 2025 (UTC) ::Oh, I see, since Charu cha pasi can refer to other contexts, shouldn't the page be named "Charu cha pasi (Tera)", Charu cha pasi as the name of Earth, and (Tera) as the disambiguation? [[User:CubanoBoi|CubanoBoi]] [[File:Flag of Cuba (3-2).svg|20px|link=special:Contributions/CubanoBoi]] [[File:Coat of arms of Cuba.svg|20px|link=User talk:CubanoBoi]] 20:14, 22 Julayi 2025 (UTC) :::@[[User:CubanoBoi|CubanoBoi]] That's true. Please do that, or I can [[User:Anthonymunthali44|Anthonymunthali44]] ([[User talk:Anthonymunthali44|pakuchezgela]]) 05:54, 23 Julayi 2025 (UTC) ::::Done ✔️, thanks for helping me with this! [[User:CubanoBoi|CubanoBoi]] [[File:Flag of Cuba (3-2).svg|20px|link=special:Contributions/CubanoBoi]] [[File:Coat of arms of Cuba.svg|20px|link=User talk:CubanoBoi]] 06:31, 23 Julayi 2025 (UTC) == You may be an eligible candidate for the U4C election == <div lang="en" dir="ltr" class="mw-content-ltr"> Greetings, The [[m:Special:MyLanguage/Universal_Code_of_Conduct/Coordinating_Committee|Universal Code of Conduct Coordinating Committee (U4C)]] seeks candidates for the 2026 election. The U4C is the global committee responsible for overseeing enforcement of the [[foundation:Special:MyLanguage/Policy:Universal Code of Conduct|Universal Code of Conduct]]. Elections are held annually, if elected a committee member serves for two years. 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Please renew this right if you would like to continue using it. <i>In other languages: [[:m:Special:MyLanguage/Global reminder bot/Messages/default|click here]]</i> [[User:Leaderbot|Leaderbot]] ([[User talk:Leaderbot|pakuchezgela]]) 19:42, 1 Juni 2026 (UTC)</div> == Join Wikimedia Community User Group Malawi == Muli makola akulu? '''Wikimedia Community User Group Malawi''' welcomes Wikimedia contributors from Malawi and contributors interested in Malawi-related knowledge to participate in building a stronger Wikimedia community. We invite contributors from Tumbuka Wikipedia to become participating members of the community. If you would like to participate: # Visit the [[:Meta:Wikimedia_Community_Malawi/Founding_and_Participating|Founding and Participating Members]] page. # Open the '''Participating members''' section directly: [[:Meta:Wikimedia_Community_Malawi/Founding_and_Participating#List_of_participants]] # Add your Wikimedia username under the list of participating members. # Sign your entry by adding <nowiki>#~~~~</nowiki> after your username. Your participation will help strengthen Wikimedia projects in Malawi, including Wikipedia, Wikimedia Commons, Wikidata, and Malawian language content. Participants may contribute to community discussions, outreach activities, edit-a-thons, language projects, cultural documentation, and other free knowledge initiatives. Everyone interested in creating, improving, and sharing free knowledge is welcome to participate. Yewo chomene, [[user:Tumbuka Arch|<span style='color: #FFFFFF;background-color: #191970;'>'''''Tumbuka Arch'''''</span>]][[user talk:Tumbuka Arch|'''<span style='color: #B20000;background-color: #FFFFFF;'>^★_★^★</span>''']] 14:21, 19 Julayi 2026 (UTC) == Let's wake up Tumbuka Wiktionary == @[[User:Anthonymunthali44|Anthonymunthali44]] Can we please wake this project up? It has been almost 4 years now and it is not yet ready. It only needs few entries to get going. 10 entries from you, me and the lest of other editors then it will be published. We already requested it [https://meta.wikimedia.org/wiki/Requests_for_new_languages/Wiktionary_Tumbuka here], the main page is [https://incubator.wikimedia.org/wiki/Wt/tum/Jani_likulu here]. This how its articles [https://incubator.wikimedia.org/wiki/Wt/tum/Malawi look like here], and others are on main page. If it has some entries, I will then post on Meta. See last time I posted there and what the response [https://meta.wikimedia.org/wiki/Talk:Language_committee/2024#Request_for_Approval_of_Tumbuka_Wiktionary was this]. Thanks. [[user:Tumbuka Arch|<span style='color: #FFFFFF;background-color: #191970;'>'''''Tumbuka Arch'''''</span>]][[user talk:Tumbuka Arch|'''<span style='color: #B20000;background-color: #FFFFFF;'>^★_★^★</span>''']] 17:36, 21 Julayi 2026 (UTC) :@[[User:Tumbuka Arch|Tumbuka Arch]] alright will do so [[User:Anthonymunthali44|Anthonymunthali44]] ([[User talk:Anthonymunthali44|pakuchezgela]]) 17:38, 21 Julayi 2026 (UTC) ::taonga akulu wane [[user:Tumbuka Arch|<span style='color: #FFFFFF;background-color: #191970;'>'''''Tumbuka Arch'''''</span>]][[user talk:Tumbuka Arch|'''<span style='color: #B20000;background-color: #FFFFFF;'>^★_★^★</span>''']] 17:40, 21 Julayi 2026 (UTC) == Broken home == @[[User:Anthonymunthali44|Anthonymunthali44]] akulu, did you do any translations on translatewiki? Like changing what is already translated? If you did or anyone did, and if not you, then the whole main page is broken as you [[Chikaya chikulu 9 demo|can see]]. There is no content on main page. Anything done there reflects here in 3-7 days. It is VERY tiresome and time consuming fixing home templates to be showing new contents each day as it was. Then, it was using the standardized Tumbuka which says '''Sekutembala''', instead of '''old Tumbuka''' which uses '''Lupya'''. While the standardized Tumbuka is largedly supported and known by most morden natives, it is a fake and wrong one as it is just an English word written in Tumbuka (not translated). The Old Tumbuka that says "Lupya" is old but true and accurate. However, on translatewiki, we need to stick to one form, such as morden Tumbuka for new genZ and genAlpha people to pick it up easily. Naonga chomene akulu. [[user:Tumbuka Arch|<span style='color: #FFFFFF;background-color: #191970;'>'''''Tumbuka Arch'''''</span>]][[user talk:Tumbuka Arch|'''<span style='color: #B20000;background-color: #FFFFFF;'>^★_★^★</span>''']] 09:40, 19 Lupya 2026 (UTC) :Nthena apa pakukhumbika kuti ine na @[[User:Viyowoyero-vya-Malaŵi|Viyowoyero-vya-Malaŵi]] tinozge ivyo vyanangika, nangauli tipangenge padoko padoko chifukwa ni ntchito ikulu. [[user:Tumbuka Arch|<span style='color: #FFFFFF;background-color: #191970;'>'''''Tumbuka Arch'''''</span>]][[user talk:Tumbuka Arch|'''<span style='color: #B20000;background-color: #FFFFFF;'>^★_★^★</span>''']] 09:43, 19 Lupya 2026 (UTC) ::Nkhanangiska akulu. Mphanyi nkhafumba danga. Let me know how I can help [[User:Anthonymunthali44|Anthonymunthali44]] ([[User talk:Anthonymunthali44|pakuchezgela]]) 09:49, 19 Lupya 2026 (UTC) ::I have checked, I have a record of all things I changed and can rolled it back within 1 hour or so. Should I do so? [[User:Anthonymunthali44|Anthonymunthali44]] ([[User talk:Anthonymunthali44|pakuchezgela]]) 09:58, 19 Lupya 2026 (UTC) :Hello akulu. Nayezganga using an automated way to translate as many things that were not translated as possible but if it is now broken can you find a way to revert or should I do that? Sorry for the trouble akulu. Yewo. [[User:Anthonymunthali44|Anthonymunthali44]] ([[User talk:Anthonymunthali44|pakuchezgela]]) 09:48, 19 Lupya 2026 (UTC) :Here is the complete list of my changes. I can automate all these being reverted just say the word: :<nowiki><pre></nowiki> :COMPLETE LIST OF TERMINOLOGY CHANGES — tum (Tumbuka) MediaWiki translations MediaWiki (most important messages) group, translatewiki.net Prepared for review with Tumbuka Arch :Total changes: 108 (107 in the main batch + 1 additional fix) Each entry shows: message page, English source, ORIGINAL Tumbuka text (before), NEW Tumbuka text (after). : ====== ================================================================== ====== :1. MediaWiki:Monday/tum : English: Monday ORIGINAL: Mande NEW: Lakwamba :2. MediaWiki:Tuesday/tum : English: Tuesday ORIGINAL: Chibili NEW: Chiŵili :3. MediaWiki:Mon/tum : English: Mon ORIGINAL: Mande NEW: Lakwamba :4. MediaWiki:Tue/tum : English: Tue ORIGINAL: Chibili NEW: Chiŵili :5. MediaWiki:January-gen/tum : English: January ORIGINAL: Janyuwale NEW: Matika :6. MediaWiki:February-gen/tum : English: February ORIGINAL: Febuluwale NEW: Muswela :7. MediaWiki:March-gen/tum : English: March ORIGINAL: Malichi NEW: Nyakanyaka :8. MediaWiki:April-gen/tum : English: April ORIGINAL: Epulelo NEW: Masika :9. MediaWiki:May-gen/tum : English: May ORIGINAL: Meyi NEW: Vuna :10. MediaWiki:June-gen/tum : English: June ORIGINAL: Juni NEW: Mphepo :11. MediaWiki:August-gen/tum : English: August ORIGINAL: Ogasiti NEW: Mpupulu :12. MediaWiki:September-gen/tum : English: September ORIGINAL: Sekutembala NEW: Lupya :13. MediaWiki:October-gen/tum : English: October ORIGINAL: Okutobala NEW: Zimya :14. MediaWiki:November-gen/tum : English: November ORIGINAL: Novembala NEW: Thukila :15. MediaWiki:December-gen/tum : English: December ORIGINAL: Disembala NEW: Vula :16. MediaWiki:Jan/tum : English: Jan ORIGINAL: Janyuwale NEW: Mati :17. MediaWiki:Feb/tum : English: Feb ORIGINAL: Febuluwale NEW: Muswe :18. MediaWiki:Mar/tum : English: Mar ORIGINAL: Malichi NEW: Nyaka :19. MediaWiki:Apr/tum : English: Apr ORIGINAL: Epulelo NEW: Masi :20. MediaWiki:Jun/tum : English: Jun ORIGINAL: Juni NEW: Mphepo :21. MediaWiki:Aug/tum : English: Aug ORIGINAL: Ogasiti NEW: Mpupu :22. MediaWiki:Sep/tum : English: Sep ORIGINAL: Sekutembala NEW: Lupya :23. MediaWiki:Oct/tum : English: Oct ORIGINAL: Okutobala NEW: Zimya :24. MediaWiki:Nov/tum : English: Nov ORIGINAL: Novembala NEW: Thuki :25. MediaWiki:Dec/tum : English: Dec ORIGINAL: Disembala NEW: Vula :26. MediaWiki:Htmlform-submit/tum : English: Submit ORIGINAL: Zomelezga NEW: Ipa :27. MediaWiki:Nstab-template/tum : English: Template ORIGINAL: Nkhwaska NEW: Cikomboli :28. MediaWiki:Discussiontools-replywidget-cancel/tum : English: Cancel ORIGINAL: Kuleka NEW: Koma :29. MediaWiki:Wikibase-edit/tum : English: edit ORIGINAL: lemba NEW: lembaso :30. MediaWiki:Red-link-title/tum : English: $1 (page does not exist) ORIGINAL: $1 (jani likusangika yayi) NEW: $1 (hamba ili kulije) :31. MediaWiki:Aboutsite/tum : English: About {{SITENAME}} ORIGINAL: Vokhuzana {{SITENAME}} NEW: Vyokhwaska {{SITENAME}} :32. MediaWiki:Disclaimers/tum : English: Disclaimers ORIGINAL: Chizomelezgo NEW: Vyakuchiska :33. MediaWiki:Contribslink/tum : English: contribs ORIGINAL: Volemba NEW: vyakupelekeka :34. MediaWiki:Printableversion/tum : English: Printable version ORIGINAL: Mtundu wakuprintika NEW: Kaŵiro koti kangasindikizgika :35. MediaWiki:Searchbutton/tum : English: Search ORIGINAL: Kufufuza NEW: Penja :36. MediaWiki:Disclaimerpage/tum : English: Project:General disclaimer ORIGINAL: Project:Chilolezo NEW: Project:Vyakuchiska mwausani :37. MediaWiki:Wikimedia-developers/tum : English: Developers ORIGINAL: Ŵalembi NEW: Ŵanozgi :38. MediaWiki:Wikimedia-cookiestatement/tum : English: Cookie statement ORIGINAL: Chilolelezo chinu NEW: Chiphara cha vikondamoyo :39. MediaWiki:Mobile-frontend-home-button/tum : English: Home ORIGINAL: Menyu NEW: Pakaya :40. MediaWiki:Mobile-frontend-random-button/tum : English: Random ORIGINAL: Chisawawa NEW: Bwekabweka :41. MediaWiki:Mobile-frontend-history/tum : English: View edit history of this page. ORIGINAL: Kuona mbili ya jani lino NEW: Bekani mbiri ya kalembelo ka hamba lino :42. MediaWiki:Mobile-frontend-view/tum : English: Mobile view ORIGINAL: Kuona mwafoni NEW: Kaŵiro ka pa lamya :43. MediaWiki:Mobile-frontend-terms-text/tum : English: Terms of Use ORIGINAL: Magwiliskilo NEW: Malango gha kagwiliskiro :44. MediaWiki:Searchsuggest-search/tum : English: Search {{SITENAME}} ORIGINAL: Fufuza {{SITENAME}} NEW: Fufuza mu {{SITENAME}} :45. MediaWiki:Skin-view-edit/tum : English: Edit ORIGINAL: Kulemba NEW: Lembaso :46. MediaWiki:Talk/tum : English: Discussion ORIGINAL: Kudumbizgana NEW: Kudumba :47. MediaWiki:Searcharticle/tum : English: Go ORIGINAL: Kuluta NEW: Luta :48. MediaWiki:Views/tum : English: Views ORIGINAL: Vyakuona NEW: Mawonekero :49. MediaWiki:Jumptosearch/tum : English: search ORIGINAL: kufufuza NEW: penja :50. MediaWiki:Searchbutton/tum : English: Search ORIGINAL: Fufuza NEW: Penja :51. MediaWiki:Skin-view-edit/tum : English: Edit ORIGINAL: Lemba NEW: Lembaso :52. MediaWiki:Discussiontools-replywidget-cancel/tum : English: Cancel ORIGINAL: Leka NEW: Koma :53. MediaWiki:Privacy/tum : English: Privacy policy ORIGINAL: Ndondomeko ya webusaiti NEW: Ndondomeko ya visisi :54. MediaWiki:Privacypage/tum : English: Project:Privacy policy ORIGINAL: Project:Ndondomeko ya webusaiti NEW: Project:Ndondomeko ya visisi :55. MediaWiki:Nstab-media/tum : English: Media page ORIGINAL: Jani la vinthu NEW: Hamba la vinthu :56. MediaWiki:Nstab-special/tum : English: Special page ORIGINAL: Jani lopatulika NEW: Hamba lopatulika :57. MediaWiki:Nstab-user/tum : English: {{GENDER:$1|User page}} ORIGINAL: {{GENDER:$1|Jani la mgwiliski}} NEW: {{GENDER:$1|Hamba la mgwiliski}} :58. MediaWiki:Nstab-project/tum : English: Project page ORIGINAL: Zina la jani NEW: Zina la hamba :59. MediaWiki:Nstab-help/tum : English: Help page ORIGINAL: Jani la wovwili NEW: Hamba la wovwili :60. MediaWiki:Nstab-main/tum : English: Page ORIGINAL: Jani NEW: Hamba :61. MediaWiki:Mainpage/tum : English: Main Page ORIGINAL: Jani likulu NEW: Hamba likulu :62. MediaWiki:Mainpage-description/tum : English: Main page ORIGINAL: Jani likulu NEW: Hamba likulu :63. MediaWiki:Searchsuggest-containing/tum : English: Search for pages containing ORIGINAL: Fufuza ma jani agho muli NEW: Fufuza ma hamba agho muli :64. MediaWiki:Pageinfo-toolboxlink/tum : English: Page information ORIGINAL: Va jani lino NEW: Va hamba lino :65. MediaWiki:Randompage/tum : English: Random page ORIGINAL: Jani lililose NEW: Hamba lililose :66. MediaWiki:Lastmodifiedat/tum : English: This page was last edited on $1, at $2. ORIGINAL: Jani ili ulendo waumalilo uwo likasinthikila pakaŵa pa $1, pa $2. NEW: Hamba ili ulendo waumalilo uwo likasinthikila pakaŵa pa $1, pa $2. :67. MediaWiki:Wikibase-linkitem-linkpage/tum : English: Link with page ORIGINAL: Lumikiza na jani NEW: Lumikiza na hamba :68. MediaWiki:Wikibase-linkitem-selectlink/tum : English: Please select a site and a page that you want to link to this page. ORIGINAL: Chonde sankhani saiti na jani ilo mukukhumba kulumikiza ku jani ili. NEW: Chonde sankhani saiti na hamba ilo mukukhumba kulumikiza ku hamba ili. :69. MediaWiki:Wikibase-linkitem-input-page/tum : English: Page: ORIGINAL: Jani: NEW: Hamba: :70. MediaWiki:Vector-feature-custom-font-size-exclusion-notice/tum : English: This page always uses small font size ORIGINAL: Jani ili likugwiliska ntchito malemba ghachoko ghachoko nyengo zose NEW: Hamba ili likugwiliska ntchito malemba ghachoko ghachoko nyengo zose :71. MediaWiki:Skin-theme-exclusion-notice/tum : English: This page is always in light mode. ORIGINAL: Pa jani ili pali ungweru nyengo zose. NEW: Pa hamba ili pali ungweru nyengo zose. :72. MediaWiki:Citethispage-link/tum : English: Cite this page ORIGINAL: Ikilani umboni jani ili NEW: Ikilani umboni hamba ili :73. MediaWiki:Contactpage/tum : English: Contact page ORIGINAL: Jani la kukhwaskilanapo NEW: Hamba la kukhwaskilanapo :74. (page name not confirmed — search by English/old text below) : English: Show $1 {{PLURAL:$1|result|results}} per page ORIGINAL: Kuoneska $1 {{PLURAL:$1|chiulusko|viulusko}} pakwendela jani NEW: Kuoneska $1 {{PLURAL:$1|chiulusko|viulusko}} pakwendela hamba :75. (page name not confirmed — search by English/old text below) : English: {{PLURAL:$2|This category contains only the following page.|The following {{PLURAL:$1|page is|$1 pages are}} in this category, out of $2 total.}} ORIGINAL: {{PLURAL:$2|Mtundu uwu una majani gha ni agha ghali panthazi.|Panthazi apa pali {{PLURAL:$1|jani mu|$1majani mu}} mu mtundu uwu, kufuma mu unandi wa $2.}} NEW: {{PLURAL:$2|Mtundu uwu una majani gha ni agha ghali panthazi.|Panthazi apa pali {{PLURAL:$1|hamba mu|$1majani mu}} mu mtundu uwu, kufuma mu unandi wa $2.}} :76. (page name not confirmed — search by English/old text below) : English: Page history ORIGINAL: Mbili ya jani NEW: Mbili ya hamba :77. (page name not confirmed — search by English/old text below) : English: The page size changed by this number of bytes ORIGINAL: Ukulu wa jani wasintha na nambala iyi ya ma baiti NEW: Ukulu wa hamba wasintha na nambala iyi ya ma baiti :78. (page name not confirmed — search by English/old text below) : English: Save page ORIGINAL: Sunga jani NEW: Sunga hamba :79. (page name not confirmed — search by English/old text below) : English: Publish page ORIGINAL: Chapiska jani NEW: Chapiska hamba :80. (page name not confirmed — search by English/old text below) : English: Publish page… ORIGINAL: Chapiska jani... NEW: Chapiska hamba... :81. (page name not confirmed — search by English/old text below) : English: Pages in category "$1" ORIGINAL: Ma jani mu mtundu "$1" NEW: Ma hamba mu mtundu "$1" :82. (page name not confirmed — search by English/old text below) : English: Watch this page ORIGINAL: Wonelela jani ili NEW: Wonelela hamba ili :83. (page name not confirmed — search by English/old text below) : English: Page name: ORIGINAL: Zina la jani: NEW: Zina la hamba: :84. (page name not confirmed — search by English/old text below) : English: There is currently no text in this page. You can [[Special:Search/{{PAGENAME}}|search for this page title]] in other pages, or <span class="plainlinks">[{{fullurl:{{#Special:Log}}|page={{urlencode:{{FULLPAGENAME}}}}}} search the related logs]</span>, but you do not have permission to create this page. ORIGINAL: Pasono palije dankha mazgo ghalighose pa jani lino. Munga [[Special:Search/{{PAGENAME}}|penja mutu uwo]] mu majani ghanyake, panji <span class="plainlinks">[{{fullurl:{{#Special:Log}}|page={{urlencode:{{FULLPAGENAME}}}}}} mungapenja mu mathala ghanyake]</span>, kwene mulije chilolezo chakuyata jani lino. NEW: Pasono palije dankha mazgo ghalighose pa hamba lino. Munga [[Special:Search/{{PAGENAME}}|penja mutu uwo]] mu majani ghanyake, panji <span class="plainlinks">[{{fullurl:{{#Special:Log}}|page={{urlencode:{{FULLPAGENAME}}}}}} mungapenja mu mathala ghanyake]</span>, kwene mulije chilolezo chakuyata hamba lino. :85. (page name not confirmed — search by English/old text below) : English: Track the most recent changes to the wiki on this page. ORIGINAL: Londola vinthu ivyo vyasintha mwasono pa wiki pa jani lino. NEW: Londola vinthu ivyo vyasintha mwasono pa wiki pa hamba lino. :86. (page name not confirmed — search by English/old text below) : English: Create the page "[[$1]]" on this wiki! {{PLURAL:$2|0=|See also the page found with your search.|See also the search results found.}} ORIGINAL: Yatani jani la "[[$1]]" pa wiki yino! {{PLURAL:$2|0=|Wonaniso jani ilo lasangika mu kufufuza kwinu.|Wonaniso vyakulondezga vya kufufuza ivyo vyasangika.}}{{PLURAL:$2|}} NEW: Yatani hamba la "[[$1]]" pa wiki yino! {{PLURAL:$2|0=|Wonaniso hamba ilo lasangika mu kufufuza kwinu.|Wonaniso vyakulondezga vya kufufuza ivyo vyasangika.}}{{PLURAL:$2|}} :87. (page name not confirmed — search by English/old text below) : English: New page ORIGINAL: Jani lanyuwani NEW: Hamba lanyuwani :88. (page name not confirmed — search by English/old text below) : English: redirect page ORIGINAL: zombeska jani NEW: zombeska hamba :89. (page name not confirmed — search by English/old text below) : English: This page is a member of {{PLURAL:$1|a hidden category|$1 hidden categories}}: ORIGINAL: Jani ili ni ndimoza mwa majani {{PLURAL:$1|mtundu wakubisika|$1 mitundu yakubisika}}: NEW: Hamba ili ni ndimoza mwa majani {{PLURAL:$1|mtundu wakubisika|$1 mitundu yakubisika}}: :90. (page name not confirmed — search by English/old text below) : English: View logs for this page ORIGINAL: Kuona vochitika va jani ili NEW: Kuona vochitika va hamba ili :91. (page name not confirmed — search by English/old text below) : English: This page does not exist. The deletion, protection, and move log for the page are provided below for reference. ORIGINAL: Jani ili likusangika yayi. Kufufutika, kutchinjilizika, na kuthyeka kwa jani ili kuli pasi apa. NEW: Hamba ili likusangika yayi. Kufufutika, kutchinjilizika, na kuthyeka kwa hamba ili kuli pasi apa. :92. (page name not confirmed — search by English/old text below) : English: edit this page ORIGINAL: Sinthani jani ili NEW: Sinthani hamba ili :93. (page name not confirmed — search by English/old text below) : English: No such special page ORIGINAL: Kulije jani lapadela lanthena NEW: Kulije hamba lapadela lanthena :94. (page name not confirmed — search by English/old text below) : English: '''You have requested an invalid special page.''' A list of valid special pages can be found at [[Special:SpecialPages|{{int:specialpages}}]]. ORIGINAL: '''Mwapempha jani lapadera ilo likugwira ntchito yayi.''' Mndandanda wa majani ghapadera ghakuzomerezgeka ungasangika pa [[Special:SpecialPages|{{int:majani ghapadera}}]]. NEW: '''Mwapempha hamba lapadera ilo likugwira ntchito yayi.''' Mndandanda wa majani ghapadera ghakuzomerezgeka ungasangika pa [[Special:SpecialPages|{{int:majani ghapadera}}]]. :95. (page name not confirmed — search by English/old text below) : English: You can view and copy the source of this page. ORIGINAL: Mungawona na kukopera uko jani ili likufumira. NEW: Mungawona na kukopera uko hamba ili likufumira. :96. (page name not confirmed — search by English/old text below) : English: There is a page named "[[$1]]" on {{SITENAME}}. {{PLURAL:$2|0=|See also the other search results found.}} ORIGINAL: Pali jani lakuchemeka "[[$1]]" pa {{SITENAME}}. {{PLURAL:$2|0=|Wonaniso vyakulondezga vya ivyo mwapenjanga.}} NEW: Pali hamba lakuchemeka "[[$1]]" pa {{SITENAME}}. {{PLURAL:$2|0=|Wonaniso vyakulondezga vya ivyo mwapenjanga.}} :97. (page name not confirmed — search by English/old text below) : English: Revision history for this page on the wiki ORIGINAL: Mbiri ya kusintha kwa jani ili pa wiki NEW: Mbiri ya kusintha kwa hamba ili pa wiki :98. (page name not confirmed — search by English/old text below) : English: '''Warning: You are recreating a page that was previously deleted.''' You should consider whether it is appropriate to continue editing this page. The deletion and move log for this page are provided here for convenience: ORIGINAL: '''Chenjezgo: Mukupangaso jani ilo lilikufufutika.''' Mukwenera kughanaghanirapo usange ntchakwenelera kulutilira kulemba jani ili. Mbili ya kusisimwika na kusamuskika kwa jani ili vyapelekeka pano kuti viŵe vyambura kusuzga kulondezga: NEW: '''Chenjezgo: Mukupangaso hamba ilo lilikufufutika.''' Mukwenera kughanaghanirapo usange ntchakwenelera kulutilira kulemba hamba ili. Mbili ya kusisimwika na kusamuskika kwa hamba ili vyapelekeka pano kuti viŵe vyambura kusuzga kulondezga: :99. (page name not confirmed — search by English/old text below) : English: Redirect page ORIGINAL: Kulutiska jani kunyake NEW: Kulutiska hamba kunyake :100. (page name not confirmed — search by English/old text below) : English: Combined display of all available logs of {{SITENAME}}. You can narrow down the view by selecting a log type, the username (case-sensitive), or the affected page (also case-sensitive). ORIGINAL: Vyakuoneska vyakusazga vya mindandanda yose ya {{SITENAME}}. Mungachepeskako kuwona mwa kusankha mtundu wa vikhongwani, zina la wakugwiliskira ntchito (kuŵika vilembo vikulu na vidoko mwatcheru), panji jani ilo lakhwaskika (kuŵikaso vilembo vikulu na vidoko mwatcheru). NEW: Vyakuoneska vyakusazga vya mindandanda yose ya {{SITENAME}}. Mungachepeskako kuwona mwa kusankha mtundu wa vikhongwani, zina la wakugwiliskira ntchito (kuŵika vilembo vikulu na vidoko mwatcheru), panji hamba ilo lakhwaskika (kuŵikaso vilembo vikulu na vidoko mwatcheru). :101. (page name not confirmed — search by English/old text below) : English: ---- ''This is the discussion page for an anonymous user who has not created an account yet, or who does not use it.'' We therefore have to use the numerical IP address to identify them. Such an IP address can be shared by several users. If you are an anonymous user and feel that irrelevant comments have been directed at you, please [[Special:CreateAccount|create an account]] or [[Special:UserLogin|log in]] to avoid future confusion with other anonymous users. ORIGINAL: ---- ''Ili ni jani lakudumbiskilanapo la munthu wambura kumanyikwa uyo wandapange akaunti, panji uyo wakuyigwiliska ntchito akaunti yayi.'' Ntheura tikwenera kugwiliskira ntchito adiresi ya IP ya nambala kuti tiŵamanye. Adiresi ya IP yanthena iyi yingagaŵika na ŵanthu ŵanandi. Usange ndimwe munthu wambura kumanyikwa uyo ivi valembeka apa vikumukhwaskani yayi, chonde [[Special:CreateAccount|pangani akaunti]] panji [[Special:UserLogin|njirani]] kuti muleke kusokonezgeka na ŵanyakhe awo ŵakuseŵezeska ntchito kwambura kumanyikwa. NEW: ---- ''Ili ni hamba lakudumbiskilanapo la munthu wambura kumanyikwa uyo wandapange akaunti, panji uyo wakuyigwiliska ntchito akaunti yayi.'' Ntheura tikwenera kugwiliskira ntchito adiresi ya IP ya nambala kuti tiŵamanye. Adiresi ya IP yanthena iyi yingagaŵika na ŵanthu ŵanandi. Usange ndimwe munthu wambura kumanyikwa uyo ivi valembeka apa vikumukhwaskani yayi, chonde [[Special:CreateAccount|pangani akaunti]] panji [[Special:UserLogin|njirani]] kuti muleke kusokonezgeka na ŵanyakhe awo ŵakuseŵezeska ntchito kwambura kumanyikwa. :102. (page name not confirmed — search by English/old text below) : English: $1 × $2, $3 {{PLURAL:$3|page|pages}} ORIGINAL: $1 × $2, $3 {{PLURAL:$3|jani|majani}} NEW: $1 × $2, $3 {{PLURAL:$3|hamba|majani}} :103. (page name not confirmed — search by English/old text below) : English: {{PLURAL:$1|$1 page is|$1 pages are}} on your watchlist (plus talk pages). ORIGINAL: {{PLURAL:$1| $1 jani ili mukulilondezga| $1 majani agha mukughalondezga}} (pamoza na majani ghakuchezgelapo). NEW: {{PLURAL:$1| $1 hamba ili mukulilondezga| $1 majani agha mukughalondezga}} (pamoza na majani ghakuchezgelapo). :104. (page name not confirmed — search by English/old text below) : English: ← previous page ORIGINAL: ← jani lakumasinda NEW: ← hamba lakumasinda :105. (page name not confirmed — search by English/old text below) : English: next page → ORIGINAL: jani lapanthazi → NEW: hamba lapanthazi → :106. 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Munga [[Special:Search/{{PAGENAME}}|penja jani lino]] mu viyowoyelo vinyake, <span class="plainlinks">[{{fullurl:{{#Special:Log}}|page={{FULLPAGENAMEE}}}} penja mu ma log nghakupokelelapo], panji[{{fullurl:{{FULLPAGENAME}}|action=edit}} yatani jani lino]</span>. NEW: Palije dankha mazgo pa hamba lino. Munga [[Special:Search/{{PAGENAME}}|penja hamba lino]] mu viyowoyelo vinyake, <span class="plainlinks">[{{fullurl:{{#Special:Log}}|page={{FULLPAGENAMEE}}}} penja mu ma log nghakupokelelapo], panji[{{fullurl:{{FULLPAGENAME}}|action=edit}} yatani hamba lino]</span>. : ====== ================================================================== ====== :NOTE: 3 messages were part of the intended correction but could NOT be published (blocked by translatewiki.net site permissions on this account) and remain unchanged: : - MediaWiki:Mainpage/tum ("Main Page" -> still "Jani likulu") - MediaWiki:Nstab-mainpage/tum ("Main Page" -> still "Jani likulu") - MediaWiki:Mainpage-nstab/tum ("Main page" -> still "Jani likulu") :These three were never touched, so they cannot be the cause of anything broken. :Total published live: 108 :<nowiki></pre></nowiki> [[User:Anthonymunthali44|Anthonymunthali44]] ([[User talk:Anthonymunthali44|pakuchezgela]]) 10:24, 19 Lupya 2026 (UTC) ::@[[User:Anthonymunthali44|Anthonymunthali44]] akulu, yayi, kupanga revert yayi. Ninozgenge waka mazina gha mwezi ghekha, vyose vikhale nthena nthena. Mwanangiska chala, kuti waka ine miyezi nkhailemba mu Chitumbuka chiphya, apo imwe mwapanga mu Chitumbuka cheneko kweneso chakale. Vyose vili kale makola, ninozgenge waka mazina gha miyezi mu Chitumbuka, ndiho ghananga home page lithu. Naonga akulu, yewo. [[user:Tumbuka Arch|<span style='color: #FFFFFF;background-color: #191970;'>'''''Tumbuka Arch'''''</span>]][[user talk:Tumbuka Arch|'''<span style='color: #B20000;background-color: #FFFFFF;'>^★_★^★</span>''']] 08:58, 22 Lupya 2026 (UTC) 84tmlug9h9qa95xzlbjakqo89949jny 0 18053 122213 121940 2026-09-22T00:07:55Z InternetArchiveBot 6449 Add 1 book for [[en:Wikipedia:Verifiability|verifiability]] (20260921sim)) #IABot (v2.0.9.6) ([[User:GreenC bot|GreenC bot]] 122213 wikitext text/x-wiki Pa 6 Febuluwale 2023, pa 04:17 TRT (01:17 UTC), chindindindi cha M 7.8 chikasunkhunya kumwera na pakati kwa Turkey na kumpoto na kumanjiliro gha dazi kwa Syria..<ref>{{Cite web |last1=Subramaniam |first1=Tara |last2=Mogul |first2=Rhea |last3=Renton |first3=Adam |last4=Sangal |first4=Aditi |last5=Vales |first5=Leinz |last6=Hammond |first6=Elise |last7=Chowdhury |first7=Maureen |last8=Vera |first8=Amir |date=6 February 2023 |title=February 6, 2023 Turkey-Syria earthquake news |url=https://www.cnn.com/middleeast/live-news/turkey-earthquake-latest-020623/index.html |url-status=live |archive-url=https://web.archive.org/web/20230207044338/https://www.cnn.com/middleeast/live-news/turkey-earthquake-latest-020623/index.html |archive-date=7 February 2023 |access-date=7 February 2023 |publisher=[[CNN]]}}</ref><ref>{{Cite web |date=6 February 2023 |title=Live Updates Turkey, Syria earthquake kills thousands |url=https://apnews.com/article/turkey-earthquake-live-updates-19e7d84fefdeed4c8a355dedf23d914f |url-status=live |archive-url=https://web.archive.org/web/20230206061642/https://apnews.com/article/turkey-earthquake-live-updates-19e7d84fefdeed4c8a355dedf23d914f |archive-date=6 February 2023 |access-date=7 February 2023 |website=[[AP News]]}}</ref> Malo agha ghakaŵa pa mtunda wa makilomita 32 kumanjiliro gha dazi kwa Gaziantep. Chindindindi ichi chikaŵa na nkhongono ya Mercalli ya XI (Extreme), ndipo chikalondezgana na chindindindi cha M 7.7 pa 13:24.<ref name="gcmt">{{Cite web |date=6 February 2023 |title=Global CMT Catalog Search |url=https://www.globalcmt.org/cgi-bin/globalcmt-cgi-bin/CMT5/form?itype=ymd&yr=2023&mo=2&day=6&oyr=2023&omo=2&oday=7&jyr=1976&jday=1&ojyr=1976&ojday=1&otype=nd&nday=1&lmw=7&umw=10&lms=0&ums=10&lmb=0&umb=10&llat=-90&ulat=90&llon=-180&ulon=180&lhd=0&uhd=1000&lts=-9999&uts=9999&lpe1=0&upe1=90&lpe2=0&upe2=90&list=0 |url-status=live |archive-url=https://web.archive.org/web/20230207002705/https://www.globalcmt.org/cgi-bin/globalcmt-cgi-bin/CMT5/form?itype=ymd&yr=2023&mo=2&day=6&oyr=2023&omo=2&oday=7&jyr=1976&jday=1&ojyr=1976&ojday=1&otype=nd&nday=1&lmw=7&umw=10&lms=0&ums=10&lmb=0&umb=10&llat=-90&ulat=90&llon=-180&ulon=180&lhd=0&uhd=1000&lts=-9999&uts=9999&lpe1=0&upe1=90&lpe2=0&upe2=90&list=0 |archive-date=7 February 2023 |access-date=6 February 2023 |publisher=Global Centroid Moment Tensor}}</ref> Chindindindi ichi chikachitika pa mtunda wa makilomita 95 (59 mi) kumpoto-m'mafumiro gha dazi kwa chigaŵa chakwamba, mu chigaŵa cha Kahramanmaraş. Ŵanthu ŵanandi ŵakakomeka. Chindindindi cha M 7.8 ndicho chikaŵa chankhongono chomene mu Turkey kufuma apo chikachitikira ku Erzincan mu 1939 ndipo chikaŵa chakukhora chomene. Cikaŵa cinyake mwa vindindindi vikuru comene ivyo vikacitikapo mu vyaru vya ku Levant. Likapulikikwa m'paka ku Eguputo, Israyeli, Palestina, Lebanoni, Kipro, na mumphepete mwa Nyanja Yiswesi ku Turkey. Mu masabata ghatatu ghakulondezgapo, kukachitika vindindindi vinyake vyakujumpha 10,000. Vinthu ivi vikacitika cifukwa ca kuzgoka kwa maji. Vinthu vikaparanyika chomene pa malo ghakujumpha 350,000 km2 (pafupifupi malo ghakukwana maulendo 12 kufuma ku Belgium). Ŵanthu pafupifupi 14 miliyoni, panji kuti 16 peresenti ya ŵanthu wose ŵa ku Turkey, ŵakakhwaskika. Ŵanthu awo ŵakumanya vya vinthu vya ku caru ca United Nations ŵakati ŵanthu pafupifupi 1.5 miliyoni ŵakasoŵa pakukhala. Pa 1 Malichi 2023, ŵanthu ŵakujumpha 51,800 ŵakafwa: ŵanthu ŵakujumpha 45,000 ku Turkey, ndipo ŵakujumpha 6,700 ku Syria. Ni cindindindi ico cikakoma ŵanthu ŵanandi comene mu Turkey kwambira mu 526 apo kukacitika cindindindi ca ku Antiyoke, kweniso ico cikakoma ŵanthu ŵanandi comene mu Syria kwambira mu 1822 apo kukacitika cindindi ca ku Aleppo. Chikaŵa chankhongono chomene pa charu chose kufuma apo kukachitika chindindindi cha ku Haiti mu 2010, ndipo chikaŵa cha nambara 5 pa chindindindi chikuru chomene cha m'ma 2000. Vinthu vyose ivyo vikaparanyika pa chindindindi ichi vikakwana madola 84.1 biliyoni. Iyi ni soka likuru comene kuluska masoka ghose ghacilengiwa agho ghali kucitika mu Turkey. Misewu iyo yikanangika, chimphepo cha mu nyengo ya chiwuvi, na kutondeka kwendera lumoza, vikapangiska kuti mulimo wa kuponoska na kovwira awo ŵakakhwaskika na masoka wa AFAD uleke kwenda makora. Ku Turkey, ŵanthu ŵakujumpha 141,000 ŵakufuma mu vyaru 94 ŵakawovwirapo. == Vinthu vya mu charu == === Vya pa charu === [[File:Anatolian_Plate_Vectoral.svg|link=https://en.wikipedia.org/wiki/File:Anatolian_Plate_Vectoral.svg?lang=en|lang=en|thumb|300x300px|Mapu gha Anatolian Plate, agho ghakulongora chigaŵa cha East Anatolian Fault]] Chindindindi ichi chikachitika pafupi na malo agho ghakukolerana pakati pa Anatolia, Arabia, na Africa. Malo na nthowa iyo chindindindi ichi chikachitikira vikukolerana na malo agho chikachitikira. Chigaŵa cha East Anatolian Fault chikovwira kuti charu cha Turkey chijumphe kumanjiliro gha dazi na kunjira mu Nyanja ya Aegean, apo chigaŵa cha Dead Sea Transform chikovwira kuti chigaŵa cha Arabia chijumphe kumpoto. Chigaŵa chakumafumiro gha dazi kwa Anatolia ni chigaŵa chakumafumiro gha dazi na kumwera kwa kumanjiliro gha dazi uko kuli mphaka pakati pa Anatolia na Arabia. Ku chigaŵa cha kumafumiro gha dazi, chigaŵa ichi chikuchepa pa 10 mm (0.39 inchi) pa chaka. Mu 1789 (M 7.2), 1795 (M 7.0), 1872 (M 7.2), 1874 (M 7.1), 1875 (M 6.7), 1893 (M 7.1), na 2020 (Template:M 6.8) kukaŵa vindindindi vikuru. Vipasi ivi vikaphulika mu vigaŵa vyakupambanapambana. Ku chigaŵa cha kumafumiro gha dazi kwa charu ichi kuli chindindindi cha Palu na Pütürge. Ku chigaŵa cha Pazarcık na Amanos kumanjiliro gha dazi kuli vindindindi vya vyaka 237 na 772 kweniso vyaka 414 na 917. Malo agha ndigho ghakwimira malo ghaŵiri ghakuru chomene ku Turkey. Mwakupambana na chigaŵa cha North Anatolian Fault icho chikachitika na vindindindi vikuruvikuru 11 mu vyaka vya m'ma 1900, chigaŵa cha East Anatolian Fault chikaŵa chamtende. Vipinda vya Palu-Sincik na Çelikhan-Türkoglu vikaŵa na mphepo. Kufuma apo chindindindi chikuru chikachitikira, maji ghakukwera kufika pa mamita 1.5 na mamita 5.2. Vinthu ivi vyawunjika nkhongono zinandi mwakuti vingapangiska vindindindi. Chigaŵa cha Palu ̇Sincik chili na makilomita 135, ndipo chili na chigaŵa cha Palu ̇Sivrice (50 km (31 mi)) na Sivrice ̇Sincik (85 km (53 mi)). Mu 1874 na 1875, kukachitika vindindindi mu chigaŵa cha Palu-Sincik. Chigaŵa cha Çelikhan-Türkoglu chili na utali wa makilomita 140. Chindindindi chikuru chaumaliro icho chikachitika pa chigaŵa cha Çelikhan-Türkoglu chikachitika mu 1513. Chigaŵa cha East Anatolian chikukumana na chigaŵa cha North Anatolian ku Karlıova Triple Junction mu chigaŵa cha Karlıova mu chigaŵa cha Bingöl. Pafupifupi 60 km (37 mi) kumwera kwa kumanjiliro gha dazi kukaŵa malo agho kukachitika chindindindi cha Bingöl mu 2003. Chinthu ichi chikachitika yayi pa East Anatolian Fault. Chindindindi cha magnitude 7.1 chikachitika kumpoto cha kumafumiro gha dazi kwa Bingöl mu 1971. Chigaŵa cha Nyanja Yakufwa chikwenda kumpoto na kumwera kufuma ku Nyanja Yiswesi m'paka ku Marash Triple Junction, uko chikukumana na East Anatolian Fault. Ku chigaŵa cha kumpoto kwa chigaŵa icho chili kumwera kwa Turkey, kukachitika vindindindi vikuruvikuru 14. Sonosono apa, kukachitika vindindindi vikuruvikuru viŵiri mu 1822 na 1872. Chindindindi cha mu 1872 chikakoma ŵanthu pafupifupi 1,800. Vindindindindi ivyo vikachitika mu 115, 526, 587, 1170 na 1822 vikakoma ŵanthu ŵanandi. === Vinthu vyakofya === Malo agho kukachitika chindindindi pa Febuluwale 6 ghakukhala waka chete. Kufuma waka mu 1905, kukachitika vindindindi vinkhondi pera (1905, 1945, 1986, 1998) ivyo vikaŵa vikuru chomene. Chindindindi chikuru chomene icho chikachitika pa Janyuwale 24, 2020, chikaŵa chakumpoto cha kumafumiro gha dazi kwa chindindindi icho chikachitika pa Febuluwale 6. Vinthu vyose ivi vikachitika kufupi na East Anatolian Fault. Nangauli chivomezi cha Febuluwale 6 chikachitika mu chigaŵa icho chikaŵa pakatikati pa charu, kweni kumwera kwa Turkey na kumpoto kwa Syria kukachitika kale vindindindi vikuru. Aleppo, msumba ukuru comene waciŵiri mu Syria, ukaparanyika kanandi waka na vindindindi vikuru, nangauli malo na ukuru wa vindindindi ivi tingamanya waka. Mu 1138 ku Aleppo kukachitika chindindindi chikuru icho chikaŵa na nkhongono ya 7.1 ndipo mu 1822 chikaŵa na nkhongono ya 7.0. Ŵanthu ŵakukwana 60,000 ŵakafwa pa chindindindi cha mu 1822. Mu 1114, mu msumba wa Marash mukachitika chindindindi icho chikakoma ŵanthu 40,000. Vindindindindi vikuru ivyo vikachitika ku Middle East mu 856, 1033 na 1754 vikakoma ŵanthu 200,000, 70,000 na 40,000. <ref>{{cite news|last1=Uddin|first1=R.|title=Five deadly earthquakes in the Middle East through history|url=https://www.middleeasteye.net/news/five-deadly-earthquakes-middle-east-history-turkey-syria|access-date=7 February 2023|agency=[[Middle East Eye]]|date=6 February 2023|archive-date=6 February 2023|archive-url=https://web.archive.org/web/20230206194124/https://www.middleeasteye.net/news/five-deadly-earthquakes-middle-east-history-turkey-syria|url-status=live}}</ref> == Vindindindi == [[File:2023_Gaziantep-Marash_Earthquakes.svg|link=https://en.wikipedia.org/wiki/File:2023_Gaziantep-Marash_Earthquakes.svg|thumb|405x405px|Malo agho kukachitika chindindindi chakwamba na chachiŵiri]] === Seismogram === Cindindindindi cikuru cakwamba cikacitika pa 01:17 UTC. United States Geological Survey (USGS) na Global Centroid Moment Tensor (GCMT) ŵakayipima pa magnitude Template:M7.8 na Template:M7.8. GEOSCOPE yikalembapo kuti mapulaneti agha ghakaŵa na ukuru wa M8.0 ndipo Kandilli Observatory (KOERI) yikalembapo kuti mapulaneti agha ghakaŵa na ukuru wa M7.7 na M7.4. Chindindindi ichi chikaŵa pa 37°09′58′′N 37°01′55′′E / 37.166°N 37.032°E, 34 km (21 mi) kumanjiliro gha dazi kwa Gaziantep mu chigaŵa cha Gaziantep, icho chili pafupi na mphaka na Syria. Malo agho kukachitika chindindindi ghakaŵa pasi pa mtunda wa makilomita 10.0 kuyana na USGS na makilomita 5 kuyana na KOERI. Cinthu ico cikapangiska kuti munthu watenthemere cikaŵa cinthu cambura kusunkhunyika. Ŵakaŵa pa malo agho ghakaŵa pafupi na malo ghakupambanapambana. Chindindindi ichi chikaŵa chankhongono chomene kuluska vyose ivyo vikachitikapo mu Turkey. Chivomezi ichi chikachitika mu chaka cha 1668 ku North Anatolia, ndipo pa charu chose chapasi chikaŵa chankhongono chomene kufuma mu Ogasiti 2021. Seismogram Pa 10:24 UTC, chindindindi icho chikapima Template:M7.5 kuyana na USGS, Template:M7.6 kuyana na KOERI, panji Template:M7.7 kuyana na Geoscope na GCMT. Kuyana na Geoscope, yikaŵa yakuzika makilomita 13, ndipo KOERI yikaŵa yakuzika makilomita 5. Chindindindi ichi chikaŵa pa 38°04′54′′N 37°10′38′′E / 38.0818°N 37.1773°E kuyana na KOERI na 38°01′26′′N 37°12′11′′E / 38.024°N 37.203°E kuyana na USGS. Likaphulika pa malo ghakupambanapambana gha kumpoto na kumwera. Kufuma apo, kukachitika chindindindi chinyake. Chindindindi chachiŵiri chikalutilira pa Febuluwale 9. == Kuzgoka == Mu maora 24 kufuma apo chindindindi ichi chikachitikira, pakachitika vibingu vinyake vyakujumpha 570. Chindindindi cha M 7.7 chikapangiska kuti paŵe chindindindi. Nkhwantha iyi yikati yafika pa malo agha, yikapulika chimphepo chikuru. Mu maora 6 kufuma apo chindindindi chikuru chikachitikira, kukachitika vindindindi vikuruvikuru 25. Pakati pajumpha maora ghakujumpha 12, USGS yikati pakaŵa vindindindi 54 vya ukuru wa 4.3 panji kujumpha apa, apo wupu wa Turkey Disaster and Emergency Management Presidency (AFAD) ukati pakaŵa vindindindi vyakujumpha 120. Chindindindi cha M6.3 chikachitika kufupi na Uzunbağ mu chigaŵa cha Hatay pa Febuluwale 20. Wasayansi munyake wa pa Seismology Research Centre ku Australia wakati vindindindi vikuru vizamulutilira kwa chaka chimoza. Ndipouli, para kwachitika chindindindi chikuru, chindindindi ichi chikulutilira mazuŵa panji masabata ghanandi. {{maplink|frame=yes|frame-align=|frame-width=450|frame-height=300|from=2023 Turkey–Syria earthquake.map|frame-latitude=37.2|frame-longitude=37|zoom=7|text=Map of mainshock and aftershocks – Mw  4.0 or greater}} === Seismology === {{multiple image|direction=vertical|header={{M|w}}7.8 finite fault|width=250px|image1=Central Turkey M7.8 finite fault.png|alt1=|caption1=Distribution of slip across the rupture|image2=Central Turkey M7.8 finite fault surface projection.png|alt2=|caption2=Surface projection of finite fault model}} {{multiple image|direction=vertical|header={{M|w}}7.7 finite fault|width=250px|image1=Central Turkey M7.5 finite fault.png|alt1=|caption1=Distribution of slip across the rupture|image2=Central Turkey M7.5 finite fault surface projection.png|alt2=|caption2=Surface projection of finite fault model}} Harold Tobin, mulara wa Pacific Northwest Seismic Network ndiposo pulofesa wa pa Yunivesite ya Washington, wakati East Anatolian Fault yili na mbiri yakale ya vindindindi ndipo yikumanyikwa kuti ni malo ghakofya chomene. Kwamba kale, pa malo agha palije chindindindi chikuru kuluska 7.0. Kweni kale kukaŵa vindindindi vikuruvikuru ivyo vikaŵa na nkhongono ya 7.4. Tobin wakati vindindindi ivyo vikacitika pa Febuluwale 6 vikaŵa "vikuru comene kuluska umo tikaghanaghaniranga". Wakasazgirapo kuti ni viŵi yayi kuti para munthu wapwetekeka pa malo ghanyake wapwetekeso ghanyake. Vinthu ivyo vikapangiska kuti ku [[California]] kuŵe vindindindi vikamba chifukwa cha kupasuka kwa malo ghaŵiri. Mtundu wakupangika na USGS ukulongora kuti chindindindi cha M7.8 chikaphulika vigaŵa vitatu vya mphinjika na utali wakukwana 40 km (25 mi) × 30 km (19 mi) (Chigaŵa 1), >175 km (109 mi) × 30 km (19 mi) (Chigaŵa 2) na >160 km (99 mi) × 20 km (12 mi) (Chigaŵa 3). Kuphulika uku kukufuma mu chigaŵa 1 ndipo kukufuma mu chigaŵa 2. Likamba kuphulika kumpoto ca kumafumiro gha dazi mumphepete mwa Cigaŵa ca 2 na kumwera ca kumanjiliro gha dazi mumphepete mwa Cigaŵa ca 3. Chindindindi ichi chikapangiska kuti maji ghasolere mtunda wa mamita 11.2 (37 ft) mu chigaŵa cha 2, kusi kwa Sakarya mu chigaŵa cha Kahramanmaraş, kumpoto kwa kumafumiro gha dazi kwa malo agho ghakusanganako na chigaŵa cha 1. Chigaŵa chinyake icho chikaŵa pa mtunda wa mamita 4.96 chikaŵa kumpoto cha kumafumiro gha dazi, kumpoto cha kumanjiliro gha dazi kwa Adıyaman. Chindindindi icho chikachitika pakati pajumpha maora ghankhondi na ghatatu, chikaphulika. Kuphulika uku kukamba mu cigaŵa ca 1 ndipo kukafika pa cigaŵa ca 3 kumafumiro gha dazi na cigaŵa ca 2 kumanjiliro gha dazi. Chigaŵa cha 1 ni mphinjika ya kumafumiro gha dazi na kumanjiliro gha dazi iyo yili na utali × usani wa makilomita 70 × makilomita 20. Cigaŵa caciŵiri cikulimbana na kumafumiro gha dazi, kumpoto ca kumafumiro gha dazi, kumanjiliro gha dazi na kumwera ca kumanjiliro gha dazi, ndipo cacitatu cikulimbana na kumpoto ca kumafumiro gha dazi na kumanjiliro gha dazi. Chigaŵa cha 2 na cha 3 vili na utali × ufupi wa makilomita >40 (25 mi) × > makilomita 20 (12 mi) na ~80 km (50 mi) × > makilomita 20 (12 mi), mwakulondezgana. Pa chigaŵa cha 1 pakaŵa mtunda wa mamita 11.4. Vyakwananga Wasayansi munyake wa vyapasi wa ku Middle East Technical University wakati chindindindi chakwamba cha M>7 chikwenera kuti chikaphulika mu vigaŵa vinandi mumphepete mwa East Anatolian Fault. Malo agha ndigho ghali kumpoto comene kwa Nyanja Yakufwa. Chivundikirochi chikupita ku East Anatolian Fault; chimafalikira kumwera chakumadzulo kudutsa Amanos ndi kumpoto chakum'mawa kudutsa magawo a Pazarcık-Erkenek. Ŵasayansi ŵa pa Yunivesite ya Istanbul ŵakati mu nyengo ya chindindindi chakwamba, pakaŵa mabowo ghankhondi. Pulofesa munyake wa pa yunivesite iyi wakati nangauli East Anatolian Fault ndiyo yikaŵa yikuru chomene, kweni pakaŵaso vinyake ivyo vikabwangasuka. Wasayansi munyake wa pa California Institute of Technology wakati chigaŵa cha East Anatolian Fault icho chili pa mtunda wa makilomita 55 pakati pa 2023 na 2020 chikaŵa kuti chindapwetekeke. Chimphepo cha M 6.8 icho chikachitika maminiti 11 pamanyuma ndipo kumanjiliro gha dazi kwa malo ghakwambilira gha M>7 chikwenera kuti chikaphulika mumphepete mwa Salçagöz Fault. Chindindindi chachiŵiri cha M>7 chikamba pa malo ghanyake agho ghakumanyikwa kuti Çardak'Sürgü Fault Zone. Chinthu ichi ntchigaŵa cha East Anatolian Fault yayi, kweni ntchigaŵa chinyake cha kumanjiliro gha dazi. Chivundikirocho chinafalikira kum'mawa kwa Malatya kudutsa kumpoto chakum'mawa kwa Doğanşehir Fault Zone. Kweniso chivundungwele chikafika kumwera ku chigaŵa cha kumanjiliro gha dazi kwa Çardak-Sürgü Fault Zone. Utali wose wa malo agha ukaŵa makilomita 160. Wasayansi munyake zina lake Ross Stein wakati chindindindi ichi chikaŵa "chinthu chambura kunozgekera". Chindindindi chakwamba chikati chachitika, chivundikiro cha Sürgü na Çardak chikamara..<ref name="Toda1">{{cite web |last1=Toda |first1=Shinji |last2=Stein |first2=Ross S. |last3=Özbakir |first3=Ali Deger |last4=Gonzalez-Huizar |first4=Hector |last5=Sevilgen |first5=Volkan |last6=Lotto |first6=Gabriel |last7=Sevilgen |first7=Serkan |date=8 February 2023 |title=Stress change calculations provide clues to aftershocks in 2023 Türkiye earthquakes |url=https://temblor.net/earthquake-insights/stress-calculation-clues-aftershocks-turkey-earthquakes-2023-14952/ |access-date=13 February 2023 |publisher=Temblor, Inc.}}</ref> === Surface rupture === [[File:2023_Turkey–Syria_earthquake_surface_rupture.png|link=https://en.wikipedia.org/wiki/File:2023_Turkey%E2%80%93Syria_earthquake_surface_rupture.png|right|thumb|250x250px|Map of surface rupture; blue indicates surface rupture mapped using satellite imagery; red indicates rupture inferred from [[:en:Sentinel-1|Sentinel-1]] pixel matching]] Vithuzithuzi ivyo Sentinel-1 yikajambura pambere chindindindi chindachitike na pamanyuma pake, vikulongora kuti pakaŵa malo ghaŵiri agho ghakapasuka. Chivomezi chakwamba chikaŵa na mtunda wa makilomita 300, ndipo chachiŵiri chikaŵa na mtunda wa makilomita 125. Ku chigaŵa cha East Anatolian Fault kukaŵa chivundungwele. Kuyana na AFAD, malo agha ghakaŵa ghakutali pafupifupi makilomita 400. Likamba kumpoto kwa Antakya, chigaŵa cha Hatay kulazga ku Pazarcık, chigaŵa cha Kahramanmaraş na Gölbaşı, chigaŵa cha Adıyaman. Ku mpoto kwa matawuni agha, maji ghakalutilira kuphulika. Mu chigodobu cha Amik mukaŵa maji ghanandi. Chigaŵa chakumanjiliro gha dazi kwa chiŵanja cha ndege cha Hatay chikapwetekeka chifukwa cha kuphulika kwa malo. Mlonga ukuru ukaparanyika ndipo ukayambiska maji ghanandi mu chigaŵa cha Amik Valley icho kale chikaŵa Nyanja ya Amik. Kuwona ivyo vikucitika mu malo agha, kukulongora kuti malo agho ghakukhalako ghakukwana mamita 7.3. Ŵasayansi ŵakamanya kuti pa malo agha pakaŵa chivundungwele cha makilomita 15 icho chikaŵa kumwera kwa Pazarcik. Kufuma ku Golbasi kuya ku Nurdağı, malo ghakaŵa gha mamita 5. Chivundungwele ichi nchimoza mwa vivundungwele vikuru comene pa caru cose, ndipo nchakuyanako na cindindindi ca mu 1906 ico cikacitika mu San Francisco. Pulofesa munyake wa [[sayansi]] ya charu ku King Abdullah University of Science and Technology ku Saudi Arabia wakati chindindindi ichi chikwenera kuti chikachitika pa mtunda wa makilomita 300. Ŵanthu ŵakughanaghana kuti maji agha ghakaphulika kufuma ku East Anatolian Fault na ku Dead Sea Transform. Shinji Toda, uyo wakusanda vya vindindindi pa Yunivesite ya Tohoku, wakati ni "chitenthe chankhongono comene" ca mu vyaka ivi. Kale kukaŵa vindindindi vikuru ivyo vikachitikanga mu vigaŵa vya mukati mwa charu. Mu 1905, vindindindi viŵiri vya mu charu cha Mongolia vikachitika. Ungano uwu ukamba na chindindindi cha ku Tsetserleg. Chindindindi cha Bulnay, icho chikachitika mazuŵa 14 pamanyuma, chikapangiska kuti chivundungwele chakumafumiro gha dazi na kumanjiliro gha dazi. Mu 2002, mu Alaska mukachitika chindindindi chakuchemeka Template:M7.9. Chindindindi ichi chikaphulika mu Denali na Totschunda, ndipo chikapangiska kuti pa vigaŵa vyose viŵiri ivi paŵe chivundungwele cha mtunda wa makilomita 340. Mu 1976, chindindindi cha M7.5 chikaphulika pa mtunda wa makilomita 250 (160 mi) kufuma ku Motagua Fault ku [[Guatemala]].<ref name="Matumoto1976">{{cite journal|last1=Matumoto|first1=Tosimatu|last2=Latham|first2=Gary V.|title=Aftershocks of the Guatemalan Earthquake of February 4, 1976|url=https://archive.org/details/geophysical-research-letters_1976-10_3_10/page/599|journal=Geophysical Research Letters|year=1976|volume=3|issue=10|pages=599–602|doi=10.1029/GL003i010p00599|bibcode=1976GeoRL...3..599M}}</ref> == Kusuntha kwa nthaka == Vinthu ivyo vikupangiska chindindindi ichi kuŵa chikuru chomene ni chindindindi icho chili na nkhongono ya 11. Vinthu vinyake ivyo vikachitika pafupi na malo agha vikaŵa vyakukwera chomene. Maofesi ghatatu gha USGS, ghaŵiri ku Antakya na limoza ku Hassa, ghakawona kuti charu chikusunkhunyika chomene. Mu tawuni ya Hassa ŵakalembapo 0.9082 g pa malo gha pasi (pga) na 215.34 cm/s pa malo gha pasi. Mauthenga gha pa siteshoni iyi ghakakolerana na nkhongono ya Mercalli ya X (Extreme). Pa malo agha pakaŵa malo ghakuchemeka Fevzipaşa. == Ukaboni == l8blayovujd8kmx0elpivffw402hp2c 10 18405 122226 121947 2026-09-22T03:24:56Z Viyowoyero-vya-Malaŵi 11606 122226 wikitext text/x-wiki {| align=center class=toccolours width=100% |<div class="center">[[File:Greek Roman Laurel wreath with branches vector.svg|40px]] <big>'''Tamupokelelani pa Wikipediya ya ChiTumbuka, {{PAGENAME}}!''' [[File:Greek Roman Laurel wreath with branches vector.svg|40px]]</big></div> Tikutemwa kuŵa na ŵanthu ŵaphya awo ŵakovwira pa Wikipediya. Chonde masukani pala pali fumbo lililose, panji pala chilipo icho mukukhumba kumanya. Tikugomezga kuti mukondwenge na malo agha. Yewo chomene. <br> <div style="font-weight:bold; color:blue;"><small>"I don't know Tumbuka Language, I speak English or other but I want to contribute here. What should I do?" Please click [[Wikipedia:Embassy|here]] and select your Embassy in your language. If there is no Embassy of your language, please request it so that we create it.</small></div> <nowiki>~~</nowiki><!-- --><nowiki>~~</nowiki>. |}<noinclude> </noinclude> bmw1rvdlk7hstmv0jw2108imatlist2 0 35996 122214 119335 2026-09-22T00:30:00Z InternetArchiveBot 6449 Add 2 books for [[en:Wikipedia:Verifiability|verifiability]] (20260921sim)) #IABot (v2.0.9.6) ([[User:GreenC bot|GreenC bot]] 122214 wikitext text/x-wiki {{Short description|Mlimo wakulondezga ndondomeko pakusanga umanyi}} {{pp-semi-indef}} {{pp-move}} {{For-multi|the journal|Science (journal){{!}}''Science'' (journal)|a topical guide|Outline of science|other uses}} {{Use British English|date=December 2024}} {{Use dmy dates|date=February 2025}} {{Sidebar | name = Usanthuro | pretitle = Part of [[Portal:Science|a series]] on | title = [[Usanthuro]] | image = [[File:Stylised atom with three Bohr model orbits and stylised nucleus.svg|100px]] | contentclass = hlist | heading1 = Usanisani | content1 = * [[Mbiri ya Usanthuro|Mbiri]] * [[vyakulemba vya Usanthuro|Vyakulemba]] * [[Ndondomeko ya Usanthuro|Ndondomeko]] * [[Kusanda umanyi mwa usanthuro|Kusanda-Umanyi]] | heading2 = Nthavi | content2 = * [[usanthuro wa malango ghakunyoloka|Vya malango ghakunyoloka]] * [[Usanthuro chilengiwa chose|Vya chilengiwa chose]] ** [[Usanthuro wa vya mvimba|Vya mvimba]] ** [[Usanthuro wa vya moyo|Vya moyo]] * [[Usanthuro wa ŵanthu|Vya ŵanthu]] ** [[Usanthuro wa nkharo za ŵanthu|Vya nkharo za ŵanthu]] ** [[Usanthuro wa vya zeru|Vya zeru]] * [[Usanthuro wa kukhazikiskika|wa Kukhazikiskika]] | heading3 = Mu Vikaya | content3 = * [[Kudumbiskana kwa vya usanthuro|Kudumbiskana]] * [[Ŵasanthuri|Ŵasanthuri]] * [[Masambiro gha sayansi|Masambiro]] * [[Kufighilira ndalama za usanthuro|Kufighilira ndalama]] * [[Malango gha usanthuro|Malango]] * [[Ma usanthuro gha yautesi]] * [[Msanthura]] | below = * [[File:Nuvola apps kcmsystem.png|15px|link=Portal:Science]] [[Portal:Science|Science portal]] * [[Outline of science|Outline]] * [[:Category:Science|Category]] * [[Index of science articles|Article indexes]] * [[Glossary of scientific terms|Glossaries]] }} '''Usanthuro''' ni nthowa yakulongosoka ya masambiro iyo yikuzenga na kunozga umanyi kwizira mu [[maghanoghano|maghanoghano gha kusachizga]] agho ghangapimika na [[ivyo vikusololeka|vyakuloskeka]] vya chilengiwa chose.<ref>{{Cite book |last=Wilson |first=E. O. |url=https://archive.org/details/consilienceunity00wils_135 |title=Consilience: The Unity of Knowledge |publisher=Vintage |year=1999 |isbn=978-0-679-76867-8 |edition=Reprint |location=New York |pages=[https://archive.org/details/consilienceunity00wils_135/page/n55 49]–71 |chapter=The natural sciences |url-access=limited}}</ref><ref name="Heilbron2003">{{cite book |last=Heilbron |first=J. L. |author-link=J. L. Heilbron |title=The Oxford Companion to the History of Modern Science |url=https://archive.org/details/oxfordcompaniont0000unse_q5e5 |publisher=Oxford University Press |year=2003 |isbn=978-0-19-511229-0 |location=New York |pages=vii–x |chapter=Preface |quote=...modern science is a discovery as well as an invention. It was a discovery that nature generally acts regularly enough to be described by laws and even by mathematics; and required invention to devise the techniques, abstractions, apparatus, and organization for exhibiting the regularities and securing their law-like descriptions. |display-authors=etal}}</ref> Usanthuro wa mu nyengo yasono kanandi yikugaŵika mu vipaturo vikuru viŵiri{{snd}}panji vitatu{{snd}}vikuru:<ref name="Cohen2021">{{cite book |last=Cohen |first=Eliel |url=https://www.routledge.com/The-University-and-its-Boundaries-Thriving-or-Surviving-in-the-21st-Century/Cohen/p/book/9780367562984 |title=The University and its Boundaries: Thriving or Surviving in the 21st Century |publisher=Routledge |year=2021 |isbn=978-0-367-56298-4 |location=New York |pages=14–41 |chapter=The boundary lens: theorising academic activity |access-date=4 May 2021 |archive-date=5 May 2021 |archive-url=https://web.archive.org/web/20210505045450/https://www.routledge.com/The-University-and-its-Boundaries-Thriving-or-Surviving-in-the-21st-Century/Cohen/p/book/9780367562984 |url-status=live}}</ref> [[vipaturo vya kusanda vinthu vya chilengiwa]], ivyo vikusanda [[charu chakukhwaskika na vyakuwoneka|vya mvimba]], na [[vipaturo vya kusanda makhaliro gha ŵanthu|mausanthuro gha kusanda makhaliro gha ŵanthu]], agho ghakusanda munthu payekha na kakhaliro ka ŵanthu mu vikaya na misumba.<ref name="Colander2019">{{cite book |last1=Colander |first1=David C. |title=Social Science: An Introduction to the Study of Society |last2=Hunt |first2=Elgin F. |year=2019 |publisher=Routledge |edition=17th |location=New York |pages=1–22 |chapter=Social science and its methods}}</ref><ref name="Nisbet2020">{{cite encyclopedia |title=Social Science |encyclopedia=Encyclopædia Britannica |url=https://www.britannica.com/topic/social-science |access-date=9 May 2021 |date=16 October 2020 |archive-url=https://web.archive.org/web/20220202193947/https://www.britannica.com/topic/social-science |archive-date=2 February 2022 |last2=Greenfeld |first2=Liah |last1=Nisbet |first1=Robert A. |url-status=live}}</ref> Nangauli ghakuchemeka [[masambiro gha malango ghakunyoloka|mausanthuro gha malango ghakunyoloka]], masambiro gha [[kaghanaghaniro kanyoloka|kaghanaghaniro kakunyoloka]], [[kusanda kwa manambala|kusanda kwa kupenda]], na [[kaghanaghaniro ka makina ghakupenda|usanthuro wa fundo za makina gha kurangura]] kanandi ghakuwoneka kuti ngapadera chifukwa ghakuthemba pa [[nthowa yakulongosolera kufuma ku malango ghakumanyikwa kale]] m'malo mwa [[nthowa ya kusanda vinthu pakuyezgelera|nthowa ya kusanthura]] kuŵa nthowa yawo yikuru ya kachitiro ka milimo.<ref name="Kluwer">{{cite book |last1=Bishop |first1=Alan |title=Mathematical Enculturation: A Cultural Perspective on Mathematics Education |publisher=Kluwer |year=1991 |isbn=978-0-7923-1270-3 |location=Norwell, MA |pages=20–59 |chapter=Environmental activities and mathematical culture |access-date=24 March 2018 |chapter-url=https://books.google.com/books?id=9AgrBgAAQBAJ&pg=PA54}}</ref><ref>{{cite book |last1=Bunge |first1=Mario |title=Philosophy of Science: Volume 1, From Problem to Theory |publisher=Routledge |year=1998 |isbn=978-0-7658-0413-6 |edition=revised |volume=1 |location=New York |pages=3–50 |chapter=The Scientific Approach}}</ref><ref name="Fetzer2013">{{cite book |last1=Fetzer |first1=James H. |title=Computers and Cognition: Why Minds are not Machines |publisher=Kluwer |year=2013 |isbn=978-1-4438-1946-6 |location=Newcastle, United Kingdom |pages=271–308 |chapter=Computer reliability and public policy: Limits of knowledge of computer-based systems}}</ref><ref>{{cite book |last1=Nickles |first1=Thomas |title=Philosophy of Pseudoscience: Reconsidering the Demarcation Problem |publisher=The University of Chicago Press |year=2013 |page=104 |chapter=The Problem of Demarcation}}</ref> Panyengo yeneyiyo, [[masambiro ghakuŵika kumanya pa milimo|mausanthuro ghakuŵika kumanya pa milimo]] ni masambiro agho ghakugwiliskira ntchito kumanya kwa usanthuro pa milimo yakukhwaskika, nga ni luso la kupanga-mwaufundi na luso la munkhwara.<ref>{{Cite journal |last1=Fischer |first1=M. R. |last2=Fabry |first2=G |year=2014 |title=Thinking and acting scientifically: Indispensable basis of medical education |journal=GMS Zeitschrift für Medizinische Ausbildung |volume=31 |issue=2 |pages=Doc24 |doi=10.3205/zma000916 |pmc=4027809 |pmid=24872859}}</ref><ref>{{Cite journal |last=Sinclair |first=Marius |year=1993 |title=On the Differences between the Engineering and Scientific Methods |url=https://www.ijee.ie/contents/c090593.html |url-status=live |journal=The International Journal of Engineering Education |archive-url=https://web.archive.org/web/20171115220102/https://www.ijee.ie/contents/c090593.html |archive-date=15 November 2017 |access-date=7 September 2018}}</ref><ref name="Bunge1966">{{Cite book |last=Bunge |first=M. |title=Contributions to a Philosophy of Technology |publisher=Springer |year=1966 |isbn=978-94-010-2184-5 |editor-last=Rapp |editor-first=F. |location=Dordrecht |pages=19–39 |chapter=Technology as Applied Science |doi=10.1007/978-94-010-2182-1_2 |s2cid=110332727}}</ref> [[Mbiri ya kusanda kwa ndondomeko|Mbiri ya usanthuro]] yikutandazgika mu vyaka vinandi ivyo vili kulembeka kale, apo masambiro ghakwambilira agho ghakatovwira kufika pa masambiro gha mazuŵa ghano ghakamba mu [[Nyengo ya Chikuŵa]] ku [[Eguputo wa kale|Eguputo]] na [[Mesopotamiya]] ({{circa|3000–1200 BC}}). Kutovwira kwawo pa masambiro gha manambala, [[kusanda nyenyezi]], na [[luso la kurapa]] kukasolora na kuozga [[mahala gha chilengedwe]] gha Chigiriki gha [[nyengo yakale chomene]] ndipo pamanyuma masambiro gha mu [[Medieval renaissances|nyengo ya kuwuka kwa masambiro ya mu pakati]], apo pakaŵa kuyezgelera kwa ndondomeko kuti paŵe kulongosola vinthu ivyo vikuchitika mu [[charu chakukhwaskika na vyakuwoneka]] kwizira mu vifukwa vya chilengedwe; apo kukulira kunyake, kusazgapo kwizika kwa [[nthowa ya manambala ya ku Indiya na Chiarabu]], kukachitika mu [[Golden Age of India#Gupta Empire|Nyengo ya Ukuru ya Indiya]] na [[Islamic Golden Age|Nyengo ya Ukuru ya Chisilamu]].<ref name="Lindberg2007">{{Cite book |last=Lindberg |first=David C. |title=The beginnings of Western science: the European Scientific tradition in philosophical, religious, and institutional context |url=https://archive.org/details/beginningsofwest0000lind_d9a5 |publisher=University of Chicago Press |year=2007 |isbn=978-0-226-48205-7 |edition=2nd}}</ref><ref name="Grant2007a"> {{cite book |last=Grant |first=Edward |title=A History of Natural Philosophy: From the Ancient World to the Nineteenth Century |url=https://archive.org/details/historyofnatural0000gran |publisher=Cambridge University Press |year=2007 |isbn=978-0-521-68957-1 |location=New York }}</ref><ref>[https://books.google.com/books?id=rMAaBgAAQBAJ Building Bridges Among the BRICs] {{Webarchive|url=https://web.archive.org/web/20230418081025/https://books.google.com/books?id=rMAaBgAAQBAJ |date=18 April 2023 }}, p. 125, Robert Crane, Springer, 2014</ref><ref>{{Cite book |last=Keay |first=John |url=https://archive.org/details/indiahistory00keay/page/132 |title=India: A history |publisher=Atlantic Monthly Press |year=2000 |isbn=978-0-87113-800-2 |page=[https://archive.org/details/indiahistory00keay/page/132 132] |quote=The great era of all that is deemed classical in Indian literature, art and science was now dawning. It was this crescendo of creativity and scholarship, as much as ... political achievements of the Guptas, which would make their age so golden. |author-link=John Keay}}</ref><ref name="Lindberg2007" /> Kusangika so na kusazgika kwa [[Ancient Greek literature|mabuku gha Chigiriki]] na [[Science in the medieval Islamic world|mafumbo gha Chisilamu]] mu kumanjiliro gha dazi kwa Yuropu mu nyengo ya [[Renaissance|Kuwuka kukhuru kwa masambiro]] kukawuska so mahala gha chilengedwe,<ref name="Lindberg2007" />{{rp|pp=193–224, 225–253}}<ref>Sease, Virginia; Schmidt-Brabant, Manfrid. Thinkers, Saints, Heretics: Spiritual Paths of the Middle Ages. 2007. [https://books.google.com/books?id=8Lkzp-StZGUC&dq=%22Everything+we+would+today+call+science+came+through+Islam%22&pg=PA80 Pages 80–81] {{Webarchive|url=https://web.archive.org/web/20240827070053/https://books.google.com/books?id=8Lkzp-StZGUC&dq=%22Everything%20we%20would%20today%20call%20science%20came%20through%20Islam%22&pg=PA80 |date=27 August 2024 }}. Retrieved 6 October 2023</ref> ilo pamanyuma likasinthika na [[Scientific Revolution|Kusintha kukhuru kwa nthowa zakusandira vinthu]] uko kukamba mu vyaka vya m'ma 1500<ref>{{cite book |last=Principe |first=Lawrence M. |title=Scientific Revolution: A Very Short Introduction |url=https://archive.org/details/scientificrevolu0000prin |publisher=Oxford University Press |year=2011 |isbn=978-0-19-956741-6 |location=New York |pages=[https://archive.org/details/scientificrevolu0000prin/page/1 1]–3 |chapter=Introduction}}</ref> apo maghanoghano na visangwa viphya vikapatukana na kaghanaghaniro na maluso gha kale gha Chigiriki.<ref name="Lindberg2007" /><ref name="Grant2007a" /> [[nthowa ya kusanda vinthu pakuyezgelera]] mwaluŵiro yikamba kuchita ntchito yikuru pa kusanga kumanya, ndipo mu [[19th century in science|vyaka vya m'ma 1800]], vinandi mwa kakhaliro ka [[Institutionalisation|nyumba za masambiro]] na [[Professionalization|luso la pa ntchito]] la kusanda kwa ndondomeko vikamba kuoneka,<ref>{{cite book |title=From Natural Philosophy to the Sciences: Writing the History of Nineteenth-Century Science |url=https://archive.org/details/fromnaturalphilo0000unse |year=2003 |publisher=University of Chicago Press |isbn=978-0-226-08928-7 |editor1-last=Cahan |editor1-first=David}}</ref><ref>{{cite book |last1=Lightman |first1=Bernard |title=Wrestling with Nature: From Omens to Science |url=https://archive.org/details/isbn_9780226317830 |year=2011 |publisher=University of Chicago Press |isbn=978-0-226-31783-0 |editor1-last=Shank |editor1-first=Michael |page=[https://archive.org/details/isbn_9780226317830/page/367 367] |chapter=13. Science and the Public |editor2-last=Numbers |editor2-first=Ronald |editor3-last=Harrison |editor3-first=Peter}}</ref> pamoza na kusintha kwa "mahala gha chilengedwe" kuŵa "vipaturo vya kusanda vinthu vya chilengedwe".<ref>{{cite book |last1=Harrison |first1=Peter |title=The Territories of Science and Religion |year=2015 |publisher=University of Chicago Press |isbn=978-0-226-18451-7 |pages=164–165 |quote=The changing character of those engaged in scientific endeavors was matched by a new nomenclature for their endeavors. The most conspicuous marker of this change was the replacement of "natural philosophy" by "natural science". In 1800 few had spoken of the "natural sciences" but by 1880 this expression had overtaken the traditional label "natural philosophy". The persistence of "natural philosophy" in the twentieth century is owing largely to historical references to a past practice (see figure 11). As should now be apparent, this was not simply the substitution of one term by another, but involved the jettisoning of a range of personal qualities relating to the conduct of philosophy and the living of the philosophical life. |author-link1=Peter Harrison (historian)}}</ref> Kumanya kupya mu kusanda kwa ndondomeko kukukulira chifukwa cha kusanda kwa ŵasandi awo ŵali na khumbo la kumanya vinandi vya charu na khumbo la kumazga masuzgo.<ref>{{cite book |last=MacRitchie |first=Finlay |url=https://www.routledge.com/Scientific-Research-as-a-Career/MacRitchie/p/book/9781439869659 |title=Scientific Research as a Career |publisher=Routledge |year=2011 |isbn=978-1-4398-6965-9 |location=New York |pages=1–6 |chapter=Introduction |access-date=5 May 2021 |archive-date=5 May 2021 |archive-url=https://web.archive.org/web/20210505074020/https://www.routledge.com/Scientific-Research-as-a-Career/MacRitchie/p/book/9781439869659 |url-status=live}}</ref><ref>{{cite book |last=Marder |first=Michael P. |url=https://www.cambridge.org/core/books/research-methods-for-science/1C04E5D747781B68C52A79EE86BF584B |title=Research Methods for Science |publisher=Cambridge University Press |year=2011 |isbn=978-0-521-14584-8 |location=New York |pages=1–17 |chapter=Curiosity and research |access-date=5 May 2021 |archive-date=5 May 2021 |archive-url=https://web.archive.org/web/20210505001547/https://www.cambridge.org/core/books/research-methods-for-science/1C04E5D747781B68C52A79EE86BF584B |url-status=live}}</ref> Kusanda kwa ndondomeko kwa mazuŵa ghano kanandi nkhwa kugwilira ntchito pamoza kwa magulu mu [[nyumba za masambiro na zakusandiramo vinthu]], maofesi gha boma,<ref name="Lindberg2007" /> na magulu gha malonda.<ref>{{cite book |last=Szycher |first=Michael |url=https://www.routledge.com/Commercialization-Secrets-for-Scientists-and-Engineers/Szycher/p/book/9781498730600 |title=Commercialization Secrets for Scientists and Engineers |publisher=Routledge |year=2016 |isbn=978-1-138-40741-1 |location=New York |pages=159–176 |chapter=Establishing your dream team |access-date=5 May 2021 |archive-date=18 August 2021 |archive-url=https://web.archive.org/web/20210818032914/https://www.routledge.com/Commercialization-Secrets-for-Scientists-and-Engineers/Szycher/p/book/9781498730600 |url-status=live}}</ref> Pa nyengo yeneyiyo, visangwa vinandi vikuru—makamaka mu [[kusanda vinthu pafupifupi na mizu yawo]]—vafuma ku ŵasandi payekha ndipo vikumanyikwa chomene kwizira mu [[chawanangwa]] chikuru cha pa charu chose nga ni [[Nobel Prize|Chawanangwa cha Nobelo]]. Vyandulo vyakukhwaskika vya ntchito ya kusanda vinthu vyapangiska kuti kuŵe [[Science policy|ndondomeko za boma pa vya kusanda vinthu]] izo zikupenja kuŵika pakwamba [[Responsible Research and Innovation|kukuzga mwakuchita makora]] kwa vinthu vya malonda, chisamaliro cha umoyo, nthowa za kwendera na kukhala kwa ŵanthu, [[environmental protection|kuvikilira chilengedwe]], na mphanvu za kuvikilira charu. == Kujima lizgu == Mazgu ghakuti ''science (usanthuro)'' ghayamba kale kugwiliskirika ntchito mu Chingelezi kufuma mu vyaka vya m'ma 1300 ([[Middle English|Chingelezi cha mu vyaka vya pakati]]) mu kakhaliro kakuti "kuŵa na kumanya". Mazgu agha ghakatoleka kufuma ku [[Anglo-Norman language|chiyowoyero cha Anglo-Norman]] nga ni chivizizgo cha {{lang|xno|-cience}}, icho chikachita kutoleka kufuma ku mazgu gha [[Latin|Chilatini]] gha {{lang|la|[[wikt:scientia|scientia]]}}, kung'anamura {{gloss|kumanya, kuŵa maso, kupulikiska}}, [[Morphological derivation|mazgu ghakufuma]] ku {{lang|la|[[wikt:sciens|sciens]]}} kung'anamura {{gloss|kumanya}}, ilo pakulokha ni kanyake ka mazgu ghakuchita ka {{wikt-lang|la|sciō}} {{gloss|kumanya}}.<ref>{{cite dictionary |title=Science |encyclopedia=Merriam-Webster Online Dictionary |url=http://www.merriam-webster.com/dictionary/science |access-date=16 October 2011 |archive-url=https://web.archive.org/web/20190901035713/https://www.merriam-webster.com/dictionary/science |archive-date=1 September 2019 |url-status=live}}</ref> Paliso maghanoghano ghanandi ghakuyezgelereka pa nkhani ya uko mazgu ghakuti ''science'' ghakafuma na kukhazikika. Kuyana na [[Michiel de Vaan]], wakumanya vya viyowoyero wa ku Netherlands ndipo [[Indo-Europeanist|wakumanya viyowoyero vya ku Indiya na Yuropu]], {{lang|la|sciō}} lingaŵa kuti lina mafumiro ghake mu [[Proto-Italic language|chiyowoyero chakwambilira cha Chitaliya]] nga ni {{lang|itc-x-proto|*skije-}} panji {{lang|itc-x-proto|*skijo-}} kung'anamura {{gloss|kumanya}}, icho lingaŵa kuti lina mafumiro kufuma mu [[Proto-Indo-European language|chiyowoyero chakwambilira cha ku Indiya na Yuropu]] nga ni {{lang|ine-x-proto|skh₁-ie}}, {{lang|ine-x-proto|skh₁-io}} kung'anamura {{gloss|kuŵatula}}. Buku la ''[[Lexikon der indogermanischen Verben]]'' likati {{lang|la|sciō}} ni [[back-formation|mazgu ghakupangika kufuma]] ku {{lang|la|[[wikt:nescire|nescīre]]}}, kung'anamura {{gloss|kuleka kumanya, kuleka kuŵa na chizambizambi}}, icho lingafuma ku Proto-Indo-European ''{{lang|ine-x-proto|[[wikt:Reconstruction:Proto-Indo-European/sek-|sekH-]]}}'' mu Chilatini ni {{lang|la|[[wikt:secare|secāre]]}}, panji {{lang|ine-x-proto|skh₂-}} kufuma ku {{lang|ine-x-proto|sḱʰeh2(i)-}} kung'anamura {{gloss|kudumura}}.<ref>{{Cite dictionary |year=2008 |title=sciō |dictionary=Etymological Dictionary of Latin and the other Italic Languages |url=https://archive.org/details/m-de-vaan-2008-etymological-dictionary-of-latin-and-the-other-italic-languages/page/544/ |last=Vaan |first=Michiel de |author-link=Michiel de Vaan |series=[[Indo-European Etymological Dictionary]] |page=545 |isbn=978-90-04-16797-1}}</ref> Mu nyengo zakale, kusanda kwa ndondomeko yikaŵa chinthu chimoza na "kumanya" panji "kusambira," mwakukolerana na mafumiro ghake gha Chilatini. Munthu uyo wakachitanga kafukufuku wa kusanda kwa ndondomeko wakachemekanga "[[natural philosopher|wamahara wa vinthu vya chilengedwe]]" panji "munthu wa masambiro gha kusanda."<ref>{{Cite book |last=Cahan |first=David |title=From natural philosophy to the sciences: writing the history of nineteenth-century science |url=https://archive.org/details/fromnaturalphilo0000unse |year=2003 |publisher=University of Chicago Press |isbn=0-226-08927-4 |pages=[https://archive.org/details/fromnaturalphilo0000unse/page/3 3]–15}}</ref> Mu chaka cha 1834, [[William Whewell]] wakazika mazgu ghakuti ''scientist'' (wakumanya vya kusanda kwa ndondomeko) mu kuwunika kwake kwa buku la [[Mary Somerville]] lakuti ''[[On the Connexion of the Physical Sciences]]'',<ref>{{Cite journal |last=Ross |first=Sydney |year=1962 |title=Scientist: The story of a word |journal=[[Annals of Science]] |volume=18 |issue=2 |pages=65–85 |doi=10.1080/00033796200202722 |doi-access=free}}</ref> apo wakapeleka ulemu wa kupangika kwa mazgu agha kwa "mwanalume munyake wamahara" (panyake wakaŵa iyeyu mwaŵene).<ref>{{cite OED|scientist}}</ref> == Mbiri == {{Main|Mbiri ya usanthuro}} === Mbiri yakwambilira === {{Main|Usanthuro mu charu cha mchiyamwaka}} [[File:Megaliths Aswan Nubia museum.JPG|left|thumb|Malibwe ghakuru kufuma ku [[Nabta Playa]], ghakazengeka na ŵanthu ŵa mu [[Neolithic|nyengo ya mawe ghasono]] kuti ŵalongozge kawonero ka vinthu vya mu mlengalenga, ghakusangika mu [[Aswan]], [[Upper Egypt|Kuchanya kwa Eguputo]].<ref>{{cite book |last1=Ehret |first1=Christopher |url=https://books.google.com/books?id=Q5KjEAAAQBAJ |title=Ancient Africa: A Global History, to 300 CE |date=20 June 2023 |publisher=Princeton University Press |isbn=978-0-691-24409-9 |page=107 |language=en}}</ref>]] [[File:Plimpton 322.jpg|thumb|Lupapati la dongo la [[Plimpton 322]] cha ŵanthu ŵa ku [[Babylonia]] chikulemba [[Pythagorean triple|vigaŵa vitatu vya Pythagoras]], chikulembeka {{circa|1800 BCE}}|alt=Clay tablet with markings, three columns for numbers and one for ordinals]] Kusanda kwa ndondomeko kulije mafumiro ghamoza pera. M'malo mwake, kaghanaghaniro ka kusanda kanyumba kano kakamba kuoneka pachoko na pachoko mu vyaka vinkhaniro vinandi,<ref>{{Citation |last=Carruthers |first=Peter |title=The roots of scientific reasoning: infancy, modularity and the art of tracking |date=2 May 2002 |work=The Cognitive Basis of Science |pages=73–96 |editor-last=Carruthers |editor-first=Peter |publisher=Cambridge University Press |doi=10.1017/cbo9780511613517.005 |isbn=978-0-521-81229-0 |editor2-last=Stich |editor2-first=Stephen |editor3-last=Siegal |editor3-first=Michael}}</ref><ref>{{Cite journal |last1=Lombard |first1=Marlize |last2=Gärdenfors |first2=Peter |year=2017 |title=Tracking the Evolution of Causal Cognition in Humans |journal=Journal of Anthropological Sciences |volume=95 |issue=95 |pages=219–234 |doi=10.4436/JASS.95006 |pmid=28489015 |issn=1827-4765}}</ref> pakutora kakhaliro kantu kakupambanapambana pa charu chose, ndipo vigaŵa vichoko pera ndivyo vikumanyikwa pa nkhani ya kukuzga kwakwambilira chomene. [[Women in science|Ŵanakazi]] ŵakaŵa na ntchito yikuru chomene mu kusanda kwa ndondomeko mu nyengo zakuzizwa pambere mbiri yindakhalikike,<ref>{{cite book |last1=Graeber |first1=David |last2=Wengrow |first2=David |author-link1=David Graeber |author-link2=David Wengrow |year=2021 |title=The Dawn of Everything |title-link=The Dawn of Everything |page=[https://archive.org/details/dawnofeverything0000grae/page/248 248]}}</ref> nga ni umo vikaŵira na [[Ritual#Religious perspectives|maluso gha chisopa]].<ref>{{cite journal |title=The Faerie Smith Meets the Bronze Industry: Magic Versus Science in the Interpretation of Prehistoric Metal-Making |jstor=124782 |last1=Budd |first1=Paul |last2=Taylor |first2=Timothy |journal=World Archaeology |year=1995 |volume=27 |issue=1 |pages=133–143 |doi=10.1080/00438243.1995.9980297 |bibcode=1995WoArc..27..133B }}</ref> Ŵamahara ŵanyake ŵakugwiliskira ntchito mazgu ghakuti "[[protoscience|masambiro ghakuyana na kusanda]]" pakuyowoya vya milimo ya mu nyengo yakale iyo yikuyana na kusanda kwa mazuŵa ghano mu vigaŵa vinyake kweni mu vyose yayi;<ref>{{cite book |last=Tuomela |first=Raimo |year=1987 |chapter=Science, Protoscience, and Pseudoscience |editor-last1=Pitt |editor-first1=J. C. |editor-last2=Pera |editor-first2=M. |title=Rational Changes in Science |series=Boston Studies in the Philosophy of Science |volume=98 |pages=83–101 |publisher=Springer |location=Dordrecht |doi=10.1007/978-94-009-3779-6_4 |isbn=978-94-010-8181-8}}</ref><ref>{{cite journal |doi=10.1086/599864 |first=Pamela H. |last=Smith |title=Science on the Move: Recent Trends in the History of Early Modern Science |url=https://archive.org/details/sim_renaissance-quarterly_summer-2009_62_2/page/345 |journal=Renaissance Quarterly |volume=62 |number=2 |year=2009 |pages=345–375 |pmid=19750597 |s2cid=43643053}}</ref><ref>{{Cite journal |last=Fleck |first=Robert |date=March 2021 |title=Fundamental Themes in Physics from the History of Art |journal=Physics in Perspective |volume=23 |issue=1 |pages=25–48 |doi=10.1007/s00016-020-00269-7 |bibcode=2021PhP....23...25F |s2cid=253597172 |issn=1422-6944 |doi-access=free}}</ref> kweni, mazgu agha ghakususulika kuti ghakuyuyura, panji ghakuŵika mtima chomene pa [[Presentism (historical analysis)|kawonero ka mazuŵa ghano]], pakughanaghanira milimo iyo mwakukolerana pera na vigaŵa vya mazuŵa ghano.<ref>{{cite journal |doi=10.1177/007327531205000203 |first=Peter |last=Dear |title=Historiography of Not-So-Recent Science |journal=History of Science |volume=50 |number=2 |year=2012 |pages=197–211 |s2cid=141599452}}</ref> Ukaboni wakudunjika wa nthowa za kusanda kwa ndondomeko ukumanyikwa makora chomene pamanyuma pa kwizika kwa [[writing systems|nthowa za kulembera]] mu [[Bronze Age|nyengo ya chikuŵa]] mu vyaka vya m'ma civilisations gha [[Ancient Egypt|Eguputo wa kale]] na [[Mesopotamia|Mesopotamiya]] ({{circa|3000–1200 BCE}}), kupanga maliboti ghakwambilira gha kulembeka mu [[history of science|mbiri ya kusanda kwa ndondomeko]].<ref name="Lindberg2007" /><ref name="Grant2007a" /> Nangauli mazgu na maghanoghano gha "kusanda kwa ndondomeko" na "chilengedwe" ghakaŵa mu maghanoghano gha ŵanthu panyengo iyo yayi, ŵanthu ŵa ku Eguputo ŵakale na Mesopotamiya ŵakaŵa na vyakusanguluska ivyo pamanyuma vikaŵa na malo mu kusanda kwa Chigiriki na kwa mu nyengo ya pakati: masambiro gha manambala, kusanda nyenyezi, na luso la kurapa.<ref>{{cite book |last1=Rochberg |first1=Francesca |author-link=Francesca Rochberg |editor1-last=Shank |editor1-first=Michael |editor2-last=Numbers |editor2-first=Ronald |editor3-last=Harrison |editor3-first=Peter |title=Wrestling with Nature: From Omens to Science |url=https://archive.org/details/isbn_9780226317830 |year=2011 |publisher=University of Chicago Press |isbn=978-0-226-31783-0 |page=[https://archive.org/details/isbn_9780226317830/page/9 9] |chapter=Ch.1 Natural Knowledge in Ancient Mesopotamia}}</ref><ref name="Lindberg2007" /> Kufuma mu vyaka vya m'ma 3000 BCE, ŵanthu ŵa ku Eguputo ŵakale ŵakazenga [[Decimal#Origin|nthowa ya kupenda ya nambala khumi]] iyo njakuzengeka pa kakhaliro ka manambala yayi,<ref>{{Cite book |last=Krebs |first=Robert E. |title=Groundbreaking Scientific Experiments, Inventions, and Discoveries of the Middle Ages and the Renaissance |url=https://archive.org/details/groundbreakingsc0000kreb_p4w4 |publisher=[[Greenwood Publishing Group]] |year=2004 |isbn=978-0-313-32433-8 |page=[https://archive.org/details/groundbreakingsc0000kreb_p4w4/page/127 127]}}</ref> ŵakamazgo masuzgo gha pa mlima kwizira mu [[geometry|masambiro gha mikhaliro ya malo na vigaŵa]],<ref>{{cite book |last1=Erlich |first1=Ḥaggai |author-link=Haggai Erlich |url=https://books.google.com/books?id=LcsJosc239YC&q=egyptian%20geometry%20Nile&pg=PA80 |title=The Nile: Histories, Cultures, Myths |last2=Gershoni |first2=Israel |year=2000 |publisher=Lynne Rienner |isbn=978-1-55587-672-2 |pages=80–81 |quote=The Nile occupied an important position in Egyptian culture; it influenced the development of mathematics, geography, and the calendar; Egyptian geometry advanced due to the practice of land measurement "because the overflow of the Nile caused the boundary of each person's land to disappear." |access-date=9 January 2020}}</ref> ndipo ŵakapanga [[Egyptian calendar|ndondomeko ya kalendala]].<ref>{{Cite web |title=Telling Time in Ancient Egypt |url=https://www.metmuseum.org/toah/hd/tell/hd_tell.htm |access-date=27 May 2022 |website=The Met's Heilbrunn Timeline of Art History |date=February 2017 |archive-date=3 March 2022 |archive-url=https://web.archive.org/web/20220303133140/https://www.metmuseum.org/toah/hd/tell/hd_tell.htm |url-status=live}}</ref> Nthowa zawo za kuraŵa zikasazgapo matupi gha munkhwala na milimo yakuzizwa, nga ni malurombo, [[incantation|mashontho]], na maluso gha kachitiro.<ref name="Lindberg2007" /> Ŵanthu ŵa ku [[Nubians|Nubiya]] ŵakale ŵakaŵa na nthowa yakwambilira ya [[antibiotics|minkhwala yakukoma tushilingini mu thupi]] ndipo ŵakakhazikiska nthowa ya [[geometrics|masambiro gha mikhaliro ya malo]] iyo yikawovwira pa [[sundials|maworoghe gha dazi]] ghakwambilira. Ŵanthu ŵa ku Nubiya ŵakagwiliskirangaso ntchito nthowa ya [[Trigonometry|masambiro gha makona gha vigaŵa vitatu]] yakuyanako na ŵanyawo ŵa ku Eguputo.<ref>{{Cite journal |author=Armelagos, George |date=2000 |title=Take Two Beers and Call Me in 1,600 Years: Use of Tetracycline by Nubians and Ancient Egyptians |url=https://digitallibrary.amnh.org/items/482bd90a-de71-49b3-9bbc-d8ff0ab974b3 |journal=Natural History |volume=109 |issue=5 |pages=50–3 |s2cid=89542474}}</ref><ref>{{Cite journal|title=Gnomons at Meroë and Early Trigonometry|first=Leo|last=Depuydt|date=1 January 1998|journal=The Journal of Egyptian Archaeology|volume=84|pages=171–180|doi=10.2307/3822211|jstor=3822211}}</ref><ref>{{Cite web|url=http://www.archaeology.org/online/news/nubia.html|title=Neolithic Skywatchers|date=27 May 1998|first=Andrew|last=Slayman|website=Archaeology Magazine Archive|access-date=17 April 2011|archive-url=https://web.archive.org/web/20110605234044/http://www.archaeology.org/online/news/nubia.html|archive-date=5 June 2011|url-status=live}}</ref><ref>{{Cite book|url=https://books.google.com/books?id=vO5FCVIxz2YC&q=nubia&pg=PA744|title=A History of Ancient Mathematical Astronomy|last=Neugebauer|first=O.|date=2004-09-17|publisher=Springer Science & Business Media|isbn=978-3-540-06995-9|language=en}}</ref> Ŵanthu ŵa ku [[Mesopotamia|Mesopotamiya]] ŵakale ŵakagwiliskira ntchito kumanya kwa makhaliro gha vinthu vyakupambanapambana vya chilengedwe pakupanga [[pottery|viŵiya vya dongo]], [[faience|vinthu vya dongo vyakuŵala]], gilasi, sopo, visulo, [[lime plaster|malasitara gha njala]], na nthowa za kukanizga maji kunjira.<ref name="McIntosh2005">{{cite book |last1=McIntosh |first1=Jane R. |author-link=Jane McIntosh |title=Ancient Mesopotamia: New Perspectives |year=2005 |publisher=ABC-CLIO |location=Santa Barbara, CA |isbn=978-1-57607-966-9 |pages=273–276 |url=https://books.google.com/books?id=9veK7E2JwkUC&q=science+in+ancient+Mesopotamia |access-date=20 October 2020}}</ref> Ŵakasambira vya [[animal physiology|kakhaliro ka matupi gha vinyama]], [[anatomy|makhaliro gha mukati mwa thupi]], [[animal behavior|makhaliro gha vinyama]], na [[astrology|kusambira nyenyezi]] chifukwa cha [[divinatory|milimo ya kuombeza]].<ref>{{Cite journal |title=Scientific Astronomy in Antiquity |last=Aaboe |first=Asger |author-link=Asger Aaboe |journal=[[Philosophical Transactions of the Royal Society]] |volume=276 |issue=1257 |date=2 May 1974 |pages=21–42 |doi=10.1098/rsta.1974.0007 |bibcode=1974RSPTA.276...21A |jstor=74272 |s2cid=122508567}}</ref> Ŵanthu ŵa ku Mesopotamiya ŵakaŵa na [[Babylonian medicine|khumbo likuru mu luso la kurapa]] ndipo [[medical prescription|machira gha minkhwala]] ghakwambilira ghakaoneka mu [[Sumerian language|chiyowoyero cha Chisumeriya]] mu nyengo ya [[Third Dynasty of Ur|Ufumu wachitatu wa Ur]].<ref name="McIntosh2005" /><ref>{{cite journal |title=Medicine, Surgery, and Public Health in Ancient Mesopotamia |first=R. D. |last=Biggs |journal=Journal of Assyrian Academic Studies |volume=19 |number=1 |year=2005 |pages=7–18}}</ref> Vikulongora kuti ŵakasambiranga vinthu vya kusanda ivyo vikaŵa na ntchito ya pa mlima panji ya chisopa ndipo ŵakaŵa na khumbo lichoko chomene la kumanya vinthu chifukwa cha khumbo lakukhorweska waka fumbo la mu mtima.<ref name="McIntosh2005" /> === Nyengo yakale ya mahara === {{Main|Science in classical antiquity}} [[File:MANNapoli 124545 plato's academy mosaic.jpg|left|thumb|[[Plato's Academy mosaic]], yakupangika pakati pa 100 BC na 79 AD, yikulongora ŵavinjeru ŵanandi na ŵakusambira ŵa Chigiriki.|alt=Chithuzi cha ŵavinjeru ŵakuwungana na kudumbiskana]] Mu [[classical antiquity|nyengo yakale ya mahara]], mukaŵavyepi munthu uyo tingamuyana na munasayansi wa mazuŵa ghano. M'malo mwake, ŵanalume ŵakusambira, awo kanandi ŵakaŵa ŵakusampha, ŵakachitanga kafukufuku wakupambanapambana mu vyaka vya chilengiwa pa nyengo iyo ŵakaŵira na mpata.<ref>{{cite book |last1=Lehoux |first1=Daryn |editor1-last=Shank |editor1-first=Michael |editor2-last=Numbers |editor2-first=Ronald |editor3-last=Harrison |editor3-first=Peter |title=Wrestling with Nature: From Omens to Science |url=https://archive.org/details/isbn_9780226317830 |year=2011 |publisher=University of Chicago Press |isbn=978-0-226-31783-0 |page=[https://archive.org/details/isbn_9780226317830/page/39 39] |chapter=2. Natural Knowledge in the Classical World}}</ref> Pambere fundo ya [[concept|chilengiwa]] panji kuti ''[[phusis]]'' yindasandulike na [[pre-Socratic philosopher|ŵavinjeru ŵakwambilira ŵa Chigiriki]], mazgu ghamoza ghakagwiliskirikanga ntchito pakulongosora "nthowa" iyo khuni likukulira,<ref>An account of the pre-Socratic use of the concept of φύσις may be found in {{cite book |last=Naddaf |first=Gerard |year=2006 |title=The Greek Concept of Nature |publisher=SUNY Press |postscript=,}} and in {{cite journal |last1=Ducarme |first1=Frédéric |last2=Couvet |first2=Denis |year=2020 |title=What does 'nature' mean? |journal=[[Palgrave Communications]] |volume=6 |issue=14 |article-number=14 |publisher=[[Springer Nature]] |doi=10.1057/s41599-020-0390-y |doi-access=free |url=https://hal.science/hal-02554932/file/s41599-020-0390-y.pdf |access-date=16 August 2023 |archive-date=16 August 2023 |archive-url=https://web.archive.org/web/20230816053756/https://hal.science/hal-02554932/file/s41599-020-0390-y.pdf |url-status=live}} The word φύσις, while first used in connection with a plant in Homer, occurs early in Greek philosophy, and in several senses. Generally, these senses match rather well the current senses in which the English word ''nature'' is used, as confirmed by {{cite book |last=Guthrie |first=W. K. C. |title=Presocratic Tradition from Parmenides to Democritus |postscript=none}} (volume 2 of his ''History of Greek Philosophy''), Cambridge University Press, 1965.</ref> kweniso "nthowa" iyo fuko linyake likusopera chiuta wawo. Pa chifukwa ichi, chikuyowoyeka kuti ŵanthu aŵa ŵakaŵa ŵavinjeru ŵakwamba panji kuti ŵafilozofwa ŵeneko, kweniso ŵakwamba kupatula pakati pa "chilengiwa" na "maluso gha ŵanthu".<ref>{{Cite book |last1=Strauss |first1=Leo |url=https://books.google.com/books?id=cpx2j0TumyIC |title=An Introduction to Political Philosophy: Ten Essays by Leo Strauss |last2=Gildin |first2=Hilail |publisher=[[Wayne State University Press]] |isbn=978-0-8143-1902-4 |chapter=Progress or Return? The Contemporary Crisis in Western Education |year=1989 |access-date=30 May 2022 |page=209}}</ref> Ŵavinjeru ŵakwambilira ŵa [[Greek philosophers|Chigiriki]] ŵa ku sukulu ya ku Mileto, iyo yikambika na [[Thales of Miletus|Thales]] ndipo panyuma yikalutilizgika na [[Anaximander]] ndipo pamanyuma [[Anaximenes of Miletus|Anaximenes]], ŵakaŵa ŵakwamba kuyezga kulongosora [[natural phenomena|vinthu vyakuzizwiska vya chilengiwa]] kwambura kuthemba pa [[supernatural|nkhongono za mizimu]].<ref>{{cite book |last1=O'Grady |first1=Patricia F. |author-link=Patricia O'Grady |title=Thales of Miletus: The Beginnings of Western Science and Philosophy |year=2016 |publisher=Routledge |location=New York |isbn=978-0-7546-0533-1 |page=245 |url=https://books.google.com/books?id=ZTUlDwAAQBAJ&q=Thales+of+Miletus+first+scientist&pg=PA245 |access-date=20 October 2020}}</ref> Ŵa [[Pythagoreans|pizagoliyasi]] ŵakapanga mahara ghakusuzga ghakukhwaskana na manambara<ref name="Burkert1972">{{cite book |last=Burkert |first=Walter |author-link=Walter Burkert |date=1 June 1972 |title=Lore and Science in Ancient Pythagoreanism |url=https://books.google.com/books?id=0qqp4Vk1zG0C&q=Pythagoreanism |location=Cambridge, MA |publisher=Harvard University Press |isbn=978-0-674-53918-1}}</ref>{{rp|467–468}} ndipo ŵakawovwira chomene pakukuzga mahara gha kupenda na kulinganya.<ref name="Burkert1972" />{{rp|465}} Fundo ya [[atomism|tizidutswa tuchoko-tuchoko]] yikapangika na mwanamahara wa ku Giriki [[Leucippus]] na msambiri wake [[Democritus]].<ref>{{Cite book |last1=Pullman |first1=Bernard |title=The Atom in the History of Human Thought |year=1998 |isbn=978-0-19-515040-7 |pages=31–33 |publisher=Oxford University Press |url=https://books.google.com/books?id=IQs5hur-BpgC&q=Leucippus+Democritus+atom&pg=PA56 |bibcode=1998ahht.book.....P |access-date=20 October 2020}}</ref><ref>{{cite book |editor1-last=Cohen |editor1-first=Henri |editor2-last=Lefebvre |editor2-first=Claire |title=Handbook of Categorization in Cognitive Science |year=2017 |publisher=Elsevier |location=Amsterdam |isbn=978-0-08-101107-2 |page=427 |edition=2nd |url=https://books.google.com/books?id=zIrCDQAAQBAJ&q=Leucippus+Democritus+atom&pg=PA427 |access-date=20 October 2020}}</ref> Pamanyuma, [[Epicurus]] wakazenga fundo yakunonoka ya makhaliro gha chilengiwa yakujintha pa tizidutswa utu, ndipo wakambiska "ndondomeko" iyo yikaŵika vipimo vya unenesko wa sayansi. <ref>[[Lucretius]] ({{floruit}}1st century BCE) {{lang|la|[[De rerum natura]]}}</ref> Dokotala wa ku Giriki [[Hippocrates]] wakambiska ndondomeko ya masambiro gha munkhwala na wovwiri wa thupi<ref>{{cite book |last=Margotta |first=Roberto |year=1968 |title=The Story of Medicine |url=https://books.google.com/books?id=vFZrAAAAMAAJ |location=New York |publisher=[[Golden Press]] |access-date=18 November 2020}}</ref><ref>{{cite book |last1=Touwaide |first1=Alain |title=Medieval Science, Technology, and Medicine: An Encyclopedia |year=2005 |editor1-last=Glick |editor1-first=Thomas F. |editor2-last=Livesey |editor2-first=Steven |editor3-last=Wallis |editor3-first=Faith |publisher=Routledge |location=New York |isbn=978-0-415-96930-7 |page=224 |url=https://books.google.com/books?id=77y2AgAAQBAJ&q=Hippocrates+medical+science&pg=PA224 |access-date=20 October 2020}}</ref> ndipo wakumanyikwa kuti "[[List of persons considered father or mother of a scientific field#Medicine and physiology|Wiske wa Munkhwala]]".<ref>{{cite book |last1=Leff |first1=Samuel |last2=Leff |first2=Vera |year=1956 |title=From Witchcraft to World Health |url=https://books.google.com/books?id=HjNrAAAAMAAJ |location=London |publisher=Macmillan |access-date=23 August 2020}}</ref> Kusinthika kukuru mu mdauko wa vinjeru vya chilengiwa kukawoneka pa chiyelezgero cha [[Socrates]] uyo wakagwiliskira ntchito mahara pakusambira vya makhaliro gha ŵanthu, makhaliro gha magulu gha ndale, na kumanya kwa munthu mwenecho. [[Socratic method|Ndondomeko ya Socrates]] umo yikulembekera mu mabuluku gha [[Plato]] ni nthowa ya kudumbiskana m’paka kusanga unenesko: fundo ziwemi zikusangika mwa kuwunguzga na kuseka zila izo zikupereka kususukana. Nthowa iyi yikupenja unenesko uwo ŵanthu ŵanandi ŵali nawo uwo ukulongozga vigomezgo vyawo na kuviwunguzga kuti viwoneke usange ni vyaunenesko.<ref>{{cite web |url=https://www.perseus.tufts.edu/hopper/text?doc=Perseus%3Atext%3A1999.01.0170%3Atext%3DApol.%3Apage%3D17 |title=Plato, Apology |page=17 |access-date=1 November 2017 |url-status=live |archive-url=https://web.archive.org/web/20180129145253/http://www.perseus.tufts.edu/hopper/text?doc=Perseus%3Atext%3A1999.01.0170%3Atext%3DApol.%3Apage%3D17 |archive-date=29 January 2018}}</ref> Socrates wakasuska masambiro gha kale gha sayansi ya vinthu (physics) chifukwa wakati ghakaŵa gha maghanoghano waka kwambura kujiwunguzga dankha.<ref>{{cite web |url=https://www.perseus.tufts.edu/hopper/text?doc=Perseus%3Atext%3A1999.01.0170%3Atext%3DApol.%3Apage%3D27 |title=Plato, Apology |page=27 |access-date=1 November 2017 |url-status=live |archive-url=https://web.archive.org/web/20180129145253/http://www.perseus.tufts.edu/hopper/text?doc=Perseus%3Atext%3A1999.01.0170%3Atext%3DApol.%3Apage%3D27 |archive-date=29 January 2018}}</ref> Mu vyaka vya m'ma 300 BCE, [[Aristotle]] wakambiska ndondomeko yakunozgeka makora ya vinjeru vya [[teleological|chilato cha chilengiwa]].<ref>{{cite book |author1=Aristotle |title=Nicomachean Ethics |edition=H. Rackham |url=https://www.perseus.tufts.edu/hopper/text?doc=Perseus%3Atext%3A1999.01.0054%3Abekker%20page%3D1139b |url-status=live |archive-url=https://web.archive.org/web/20120317140402/http://www.perseus.tufts.edu/hopper/text?doc= |archive-date=17 March 2012 |access-date=22 September 2010 |at=1139b}}</ref> Mu vyaka vya m'ma 200 BCE, munthu wakusambira vya nyenyezi wa ku Giriki [[Aristarchus of Samos]] wakaŵa wakwamba kuyowoya kuti [[heliocentric model|dazi lili pakati pa chilengiwa]], ndipo mapulaneti ghose ghakuchizungulira.<ref name="McClellan2015">{{cite book |last1=McClellan |first1=James E. III |last2=Dorn |first2=Harold |title=Science and Technology in World History: An Introduction |year=2015 |publisher=Johns Hopkins University Press |location=Baltimore |isbn=978-1-4214-1776-9 |pages=99–100 |url=https://books.google.com/books?id=ah1ECwAAQBAJ&q=Aristarchus+heliocentrism&pg=PA99 |access-date=20 October 2020}}</ref> Fundo ya Aristarchus yikakanika na ŵanthu ŵanandi chifukwa ŵakawonanga kuti yikususkana na malango gha sayansi ya vinthu,<ref name="McClellan2015" /> ndipo m'malo mwake buku la Ptolemy la ''[[Almagest]]'', lilo likuti charu chapasi ndicho chili pakati pa [[Solar System|ndondomeko ya dazi]], likapokelereka m’paka mu nyengo ya Renaissance.<ref>{{Cite book |last=Graßhoff |first=Gerd |title=The History of Ptolemy's Star Catalogue |year=1990 |publisher=Springer |isbn=978-1-4612-8788-9 |series=Studies in the History of Mathematics and Physical Sciences |volume=14 |location=New York |doi=10.1007/978-1-4612-4468-4}}</ref><ref>{{Cite book |last=Hoffmann |first=Susanne M. |title=Hipparchs Himmelsglobus |year=2017 |publisher=Springer Fachmedien Wiesbaden |isbn=978-3-658-18682-1 |location=Wiesbaden |language=de |doi=10.1007/978-3-658-18683-8 |bibcode=2017hihi.book.....H}}</ref> Munthu wakupanga vinthu na kusambira manambara [[Archimedes of Syracuse]] wakachita vintu vikuru pakwambiska masambiro gha [[calculus|masamu ghakusuzga]].<ref>{{cite book |last1=Edwards |first1=C. H. Jr. |title=The Historical Development of the Calculus |year=1979 |publisher=Springer |location=New York |isbn=978-0-387-94313-8 |page=75 |url=https://books.google.com/books?id=ilrlBwAAQBAJ&q=Archimedes+calculus&pg=PA75 |access-date=20 October 2020}}</ref> [[Pliny the Elder]] wakaŵa mulembi wa Chiroma uyo wakamanyanga vinthu vinandi, ndipo wakalemba buku likuru lakuti ''[[Natural History (Pliny)|Natural History]]''.<ref>{{cite book |last1=Lawson |first1=Russell m. |title=Science in the Ancient World: An Encyclopedia |year=2004 |publisher=ABC-CLIO |location=Santa Barbara, CA |isbn=978-1-85109-539-1 |pages=190–191 |url=https://books.google.com/books?id=1AY1ALzh9V0C&q=Pliny+the+Elder+encyclopedia&pg=PA190 |access-date=20 October 2020}}</ref><ref>{{cite book |last1=Murphy |first1=Trevor Morgan |title=Pliny the Elder's Natural History: The Empire in the Encyclopedia |year=2004 |publisher=Oxford University Press |isbn=978-0-19-926288-5 |page=1 |url=https://books.google.com/books?id=6NC_T_tG9lQC&q=Pliny+the+Elder+encyclopedia |access-date=20 October 2020}}</ref><ref>{{cite book |last1=Doody |first1=Aude |title=Pliny's Encyclopedia: The Reception of the Natural History |year=2010 |publisher=Cambridge University Press |isbn=978-1-139-48453-4 |page=1 |url=https://books.google.com/books?id=YoEhAwAAQBAJ&q=Pliny+the+Elder+encyclopedia |access-date=20 October 2020}}</ref> [[Positional notation|Nthowa yakulembera manambara kuyana na malo ghawo]] yikulongora kuti yikawoneka pakati pa vyaka vya m'ma 200 na 400 CE mu nthowa za malonda za ku Indiya. Ndondomeko ya manambara iyi yikapangitsa kuti [[arithmetic|kupenda manambara]] kuŵe kwambura kusuzga ndipo pamanyuma yikazakaŵa nthowa yakuzirwa ya masamu pa charu chose.<ref>{{Cite book |last=Conner |first=Clifford D. |title=A People's History of Science: Miners, Midwives, and "Low Mechanicks" |url=https://archive.org/details/peopleshistoryof0000conn_v0x0 |year=2005 |publisher=Nation Books |isbn=1-56025-748-2 |location=New York |pages=[https://archive.org/details/peopleshistoryof0000conn_v0x0/page/72 72]–74}}</ref> === Vyaka vya Pakati === {{Main|History of science#Middle Ages}} [[File:ViennaDioscoridesEndpaperPeacock.jpg|thumb|Pa peji lakwamba la [[Vienna Dioscurides]] pali chithuzi cha [[peacock|nkhwali]], icho chikalembeka mu vyaka vya m’ma 500.|alt=Picture of a peacock on very old paper]] Chifukwa cha [[collapse of the Western Roman Empire|kubwanganduka kwa Ufumu wa Roma wa Kumanjiliro gha Dazi]], mu vyaka vya m’ma 400 vinjeru vikakhira chomene, ndipo kamanidwe ka vinjeru vya Ŵagriki ŵakale pakuyowoya vya chilengiwa kakamba kumala mu Ulaya wa Kumanjiliro gha Dazi.<ref name="Lindberg2007" />{{rp|p=194}} Ŵasungiri ŵa vinjeru mu viyowoyero vya Chilatini mu nyengo iyi, nga ni [[Isidore of Seville]], ŵakasungilira vinjeru vinandi vya kale.<ref>{{cite book |last1=Grant |first1=Edward |url=https://books.google.com/books?id=YyvmEyX6rZgC |title=The Foundations of Modern Science in the Middle Ages: Their Religious, Institutional and Intellectual Contexts |publisher=Cambridge University Press |year=1996 |isbn=978-0-521-56762-6 |series=Cambridge Studies in the History of Science |pages=7–17 |access-date=9 November 2018}}</ref> Kweni mwakupambana na ichi, chifukwa chakuti [[Byzantine Empire|Ufumu wa Bizantini]] ukatonda nkhondo za ŵalwani, ukaŵa na nkhongono yakusungilira na kunozga vinjeru ivyo vikaŵako kale.<ref name="Lindberg2007" />{{rp|p=159}} [[John Philoponus]], nkhwantha ya ku Bizantini mu vyaka vya m’ma 500, wakamba kususkana na masambiro gha Aristotelu pa nkhani ya malango gha chilengiwa, ndipo wakambiska [[theory of impetus|chigomezgo cha nkhongono ya kachidukulu]].<ref name="Lindberg2007" />{{rp|pp=307, 311, 363, 402}} Kususkana kwake kukawovwira nkhwantha za mu vyaka vya pakati na Galileo Galilei, uyo wakazunura chomene mabuku ghake pakati pajumpha vyaka chikwi chimoza.<ref name="Lindberg2007" />{{rp|pp=307–308}}<ref>{{cite encyclopedia |title=Philoponus |url=https://plato.stanford.edu/archives/spr2016/entries/philoponus/ |encyclopedia=Stanford Encyclopedia of Philosophy |first=Christian |last=Wildberg |editor-first=Edward N. |editor-last=Zalta |date=1 May 2018 |publisher=Metaphysics Research Lab, Stanford University |access-date=1 May 2018 |archive-date=22 August 2019 |archive-url=https://web.archive.org/web/20190822110331/https://plato.stanford.edu/archives/spr2016/entries/philoponus/ |url-status=live}}</ref> Mu nyengo ya [[late antiquity|kunthazi ya usambazi wakale]] na [[Early Middle Ages|Vyaka vya Pakati vya Pakwamba]], vinjeru vya chilengiwa vikapimikanga chomene kwizira mu kandiro ka Aristotelu. Kandiro aka kakuŵa na [[four causes|vifukwa vinayi]] vya Aristotelu: chifukwa cha chinthu icho chapangika, kawonekelo kake, icho chikuchichititiska kwenda, na chilato chake chaumaliro.<ref>{{Cite encyclopedia |title=Aristotle on Causality |last=Falcon |first=Andrea |editor-last=Zalta |year=2019 |editor-first=Edward |encyclopedia=Stanford Encyclopedia of Philosophy |edition=Spring 2019 |publisher=Metaphysics Research Lab, Stanford University |url=https://plato.stanford.edu/archives/spr2019/entries/aristotle-causality/#FouCau |access-date=3 October 2020 |archive-date=9 October 2020 |archive-url=https://web.archive.org/web/20201009032459/https://plato.stanford.edu/archives/spr2019/entries/aristotle-causality/#FouCau |url-status=live}}</ref> Malemba manandi gha Ŵagriki ŵakale yakasungika na [[Byzantine Empire|Ufumu wa Bizantini]] ndipo yakang’anamulika mu [[Arabic|Chiarabu]] na Ŵakhristu, chomenechomene ŵa [[Nestorian schism|Chinesitoli]] na ŵa [[Miaphysites|Chimiyafiziti]]. Mu muwuso wa Ŵaabasi, mang’anamuliro agha ghakanozgeka na kukuzgika na nkhwantha za Chiarabu.<ref name="Grant2007a"/>{{rp|pp=62-67}} Mu vyaka vya m’ma 500 na 600, [[Sasanian Empire|Ufumu wa Sasani]] uwo ukaŵa pafupi ukakhazikiska sukulu ya un’anga ya [[Academy of Gondishapur]], iyo yikawonekanga na madokotala gha Chigriki, Chisiriya, na Chipereziya kuŵa malo ghakuzirwa chomene gha munkhwala mu charu cha kale.<ref>{{Cite book |title=The Cambridge history of Iran |url=https://archive.org/details/cambridgehistory0007unse_b4w5 |date=1968–1991 |publisher=Cambridge University Press |last=Fisher |first=W. B. |isbn=978-0-521-20093-6}}</ref> Kusanda kwa Chisilamu pa vya [[Aristotelianism#Islamic world|Masambiro gha Aristotelu]] kukakura chomene mu [[House of Wisdom|Nyumba ya Vinjeru]] iyo yikakhazikiskika mu msumba wa [[Baghdad]], Iraq<ref>{{cite encyclopedia |url=https://www.britannica.com/place/Bayt-al-Hikmah |title=Bayt al-Hikmah |encyclopedia=Encyclopædia Britannica |access-date=3 November 2016 |url-status=live |archive-url=https://web.archive.org/web/20161104043313/https://www.britannica.com/place/Bayt-al-Hikmah |archive-date=4 November 2016}}</ref> ndipo kukalutilira<ref>{{Cite book |editor-last=Hossein Nasr |editor-first=Seyyed |title=History of Islamic Philosophy |title-link=History of Islamic Philosophy |editor-last2=Leaman |editor-first2=Oliver |publisher=Routledge |year=2001 |isbn=978-0-415-25934-7 |pages=165–167 |editor-link=Seyyed Hossein Nasr}}</ref> m’paka mu nyengo ya [[Mongol invasions|kuwukira kwa Ŵamongoli]] mu vyaka vya m’ma 1200. [[Ibn al-Haytham]], uyo wakumanyikwa na zina lakuti Alhazen, wakachita magesi ghakupimika mu kusanda kwake kwa mboniwoni.{{efn|name=doubtPtolemy|1= Buku la Ibn al-Haytham la ''[[Book of Optics|Mboniwoni]]'' likasuskana na chigomezgo cha Claudius Ptolemy chakuti mboniwoni yikufuma mu maso kuluta ku chinthu: "Ntheura, kufuma kwa minziro ya mboniwoni nkhwakusazgirapo waka ndipo kulije ntchito". Wonani kung’anamulika kwa A. Mark Smith kufuma mu Chilatini,<ref name="Smith2001" /> Buku I, [6.54], pp. 372, 408. }}<ref>{{cite journal |jstor=228328 |last1=Toomer |first1=G. J. |title=Reviewed work: Ibn al-Haythams Weg zur Physik, Matthias Schramm |journal=Isis |volume=55 |issue=4 |pages=463–465 |year=1964 |doi=10.1086/349914}} Wonani p. 464: "Schramm wakulongosora ivyo [Ibn Al-Haytham] wafiska pa nkhani ya kukuzga nthowa ya vinjeru.", p. 465: "Schramm walongora .. kwambura kukana kulikose kuti Ibn al-Haytham ni munthu wakuzirwa mu luso la vinjeru vya Chisilamu, chomenechomene pa nkhani ya kulenga nthowa zakuyezgelera." p. 465: "pekha pala muwuso wa Ibn al-Haytham na ŵanyake pa malemba gha chilengiwa gha mu vyaka vya pakati wasandika mwakupwelelera ndipo apo chigomezgo cha Schramm chakuti Ibn al-Haytham ndiyo wakaŵa muvumbuzi wanadi wa vinjeru vya mazuŵa gano gha chilengiwa chingapimika."</ref><ref>{{cite book |last1=Cohen |first1=H. Floris |author-link=Floris Cohen |chapter=Greek nature knowledge transplanted: The Islamic world |title=How modern science came into the world. Four civilizations, one 17th-century breakthrough |year=2010 |pages=99–156 |publisher=Amsterdam University Press |isbn=978-90-8964-239-4 |edition=2nd}}</ref> Kudandawula kwa [[Avicenna]] mu buku la ''[[The Canon of Medicine|Dango la Un’anga]]'', ilo ni buku likuru la usambazi wa munkhwala, kukuwoneka kuŵa limoza mwa mabuku ghakuzirwa chomene mu un’anga ndipo likagwiriskikanga ntchito m’paka mu vyaka vya m’ma 1700.<ref>{{Cite book |title=Encyclopaedia of the History of Science, Technology, and Medicine in Non-Western Cultures |url=https://archive.org/details/encyclopaediahis00seli |url-access=limited |year=2006 |pages=[https://archive.org/details/encyclopaediahis00seli/page/n168 155]–156 |publisher=Springer |bibcode=2008ehst.book.....S |isbn=978-1-4020-4559-2 |editor-last1=Selin |editor-first1=Helaine |editor-link=Helaine Selin}}</ref> Pofika mu vyaka vya m’ma 1000, vigaŵa vinandi vya Ulaya vikaŵa vya Chikhristu,<ref name="Lindberg2007" />{{rp|p=204}} ndipo mu 1088, [[University of Bologna|Sukulu Yikuru ya Bologna]] ikawoneka kuŵa sukulu yikuru yakwamba mu Ulaya.<ref>{{Cite journal |last=Russell |first=Josiah C. |year=1959 |title=Gratian, Irnerius, and the Early Schools of Bologna |url=https://archive.org/details/sim_mississippi-quarterly_fall-1959_12_4/page/168 |journal=[[The Mississippi Quarterly]] |volume=12 |issue=4 |pages=168–188 |jstor=26473232 |quote=Panji ntheura kale chomene mu 1088 (nyengo iyo yikapangika mwadango yakukhazikiskika kwa Sukulu Yikuru)}}</ref> Chifukwa cha ichi, khumbiro la kung’anamulira malemba gha kale na gha vinjeru mu Chilatini likakura,<ref name="Lindberg2007" />{{rp|p=204}} icho chikaŵa chifukwa chikuru cha [[Renaissance of the 12th century|Kuŵajikaso kwa Vinjeru kwa mu vyaka vya m’ma 1100]]. Masambiro gha ku sukulu mu Ulaya wa kumanjiliro gha dazi yakakura, ndipo magesi ghakachitikanga mu nthowa ya kulaŵiska, kulongosora, na kupanga magulu gha vinthu vya m’chilengiwa.<ref>{{cite encyclopedia |url=https://www.britannica.com/biography/Saint-Albertus-Magnus |title=St. Albertus Magnus |encyclopedia=Encyclopædia Britannica |access-date=27 October 2017 |url-status=live |archive-url=https://web.archive.org/web/20171028045424/https://www.britannica.com/biography/Saint-Albertus-Magnus |archive-date=28 October 2017}}</ref> Mu vyaka vya m’ma 1200, ŵasambi na ŵasambizgi ŵa un’anga ku Bologna ŵakamba kujula mathupi gha ŵanthu, icho chikapangiska kuti paŵe buku lakwamba la kamanidwe ka thupi lakuzingatira pa kujula thupi la munthu ilo likalembeka na [[Mondino de Luzzi]].<ref>{{cite book |last=Numbers |first=Ronald |url=http://www.hup.harvard.edu/catalog.php?isbn=9780674057418 |title=Galileo Goes to Jail and Other Myths about Science and Religion |publisher=Harvard University Press |year=2009 |isbn=978-0-674-03327-6 |page=45 |access-date=27 March 2018 |archive-date=20 January 2021 |archive-url=https://web.archive.org/web/20210120190509/https://www.hup.harvard.edu/catalog.php?isbn=9780674057418 |url-status=live}}</ref> === Kuŵajikaso kwa Vinjeru === {{Main|Science in the Renaissance|Copernican heliocentrism}} [[File:De Revolutionibus manuscript p9b.jpg|thumb|Chithuzi cha nthowa ya kuzingulira kwa dazi nga umo vikasachizgika na Copernicus mu buku lake la {{lang|la|[[De revolutionibus orbium coelestium]]}}alt=Drawing of planets' orbit around the Sun]] Vinthu viphanya ivyo vikavumbulika pa nkhani ya mboniwoni vikawovwira pakwamba kwa [[Renaissance|Kuŵajikaso kwa Vinjeru]], mwa kususkana na maghanoghano gha kale gha [[metaphysical|vinjeru vya kuseri kwa chilengiwa]] pa nkhani ya umo munthu wakuwonera vinthu, kweniso mwa kuwovwira pa kunozga na kukuzga maluso gha mazuŵa gano nga ni [[camera obscura]] na [[telescope|galasi lakulaŵiskira vyakumaso]]. Pakuyamba kwa Kuŵajikaso kwa Vinjeru, [[Roger Bacon]], [[Vitello]], na [[John Peckham]] waliyose wakazenga usambazi wa [[ontology|masambiro gha umo vinthu viliri]] pa nkhani ya kudura kwa vinthu kwambira na kupulika, kuwona, na paumaliro [[apperception|kumanya chomene]] kwa kawonekelo ka munthu payekha na ka chilengiwa chose ka Aristotelu.<ref name="Smith2001">{{cite book |last=Smith |first=A. Mark |title=Alhacen's Theory of Visual Perception: A Critical Edition, with English Translation and Commentary, of the First Three Books of Alhacen's ''De Aspectibus'', the Medieval Latin Version of Ibn al-Haytham's ''Kitāb al-Manāẓir'': Volume Two |title-link=De Aspectibus |publisher=[[American Philosophical Society]] |year=2001 |isbn=978-0-87169-914-5 |series=Transactions of the American Philosophical Society |volume=91, parts 4 & 5 |location=Philadelphia }}</ref>{{rp|Book I}} Nthowa ya mboniwoni iyo pambere yikamanyikwanga kuti [[perspectivism|nthowa ya kawonekelo]] [[One-point perspective|yikagwiriskikanga ntchito na kusambirika]] na ŵaluso ŵa vyakujambula ŵa mu nyengo ya Kuŵajikaso kwa Vinjeru. Chigomezgo ichi chikugwiriskira ntchito vifukwa vitatu pera pa vifukwa vinayi vya Aristotelu: kawonekelo, chinthu icho chapangika, na chilato chaumaliro.<ref name="Smith1981">{{Cite journal |jstor=231249 |doi=10.1086/352843 |pmid=7040292 |title=Getting the Big Picture in Perspectivist Optics |journal=Isis |volume=72 |issue=4 |pages=568–589 |last1=Smith |first1=A. Mark |year=1981 |s2cid=27806323}}</ref> Mu vyaka vya m’ma 1500, [[Nicolaus Copernicus]] wakapanga [[Copernican_heliocentrism|nthowa yakuti dazi ndilo liri pakati]] pa nthandala ya vyakuzingulira, uku Dazi lili pafupi na pakati pa chilengiwa chose,<ref>"Munthu uyo wakawuskapo charu pa malo ghake ghakunotha pakuŵa pakati pa chilengiwa ndipo wakamanya kuti nkhachimoza waka mwa vyakuzingulira vinyake, wakawona kuti nkhwakukhumbikwa kuchipha malo ghapadera mu nthowa yake yiphanya. Nangauli wakati 'pakati pa vyose pali dazi,' mu vigomezgo vyake vya vyakuzingulira wakayezgerera kuti pakati pa mayendero ghose pakaŵa pakati pa nthandala ya charu, apo dazi pakaŵavye." Dreyer, J.L.E. ''A History of Astronomy from Thales to Kepler,'' (Dover Publications, 1953). p.343. {{ISBN|9780486600796}}</ref><ref>"...chikaŵa chakuwonekerathu kwa Copernicus...kuti charu chingenda mwakuyana yanyi yayi mu nkhulungulu uku dazi lili pakati. Ntheura Copernicus wakaŵika dazi pakati pa nthandala ya charu yayi, kweni patali kachoko. Pakati pa nthandala ya vyakuzingulira, na pa chilengiwa chose, mu nthowa ya Copernicus ni dazi yayi, kweni ni 'dazi la pakati,' la pakati pa nthandala ya charu. Ntheura, nkhunozga chomene kuchema nthowa ya Copernicus kuŵa nthowa yakukhazikika ya dazi kuluska nthowa yakuti dazi liri pakati." [[I. Bernard Cohen|Cohen, I. Bernard]]. ''The Birth of a New Physics (Revised and Updated)'' (W.W. Norton & Company, 1985). p.44. {{ISBN|0-393-01994-2}}</ref> kwambura kwenda, uku Charu na vyakuzingulira vinyake vikuchizungulira mu mayendero gha nkhulungulu,<ref>"Mayendero ghose mukati mwake (kuwaro kwa pafupi na Charu) yakutolezga dango lakuti mayendero gha kuchanya nga nkhulungulu ndipo ntheura ghakusintha yayi. Ptolemy, Copernicus wakaghanaghana, wakapambana na dango ili...mwa kusazgirapo tumikhulungulu tuchoko pa mayendero ghakuru kuti walongosore chifukwa chake vyakuzingulira nyengo zinyake vikuwoneka nga vikufuma kunyuma mu mlengalenga, kweni mwa kwambiska [[equant]] kuti wachitiske mayendero agha kwenda luŵiro panji kukhira." [[David_Wootton_(historian)|Wootton, David]]. ''The Invention of Science: A New History of the Scientific Revolution'' (Penguin, 2015). p.152. {{ISBN|0-06-175952-X}}</ref> ghakosoleka na [[epicycle|tumikhulungulu]], kweniso pa maluwiro ghakuyana. Nthowa ya Copernicus ikasuskana na [[Geocentrism#Ptolemaic_model|nthowa yakuti charu chili pakati]] ya [[Ptolemy]], iyo yikaŵika Charu pakati pa chilengiwa chose. Ŵasanda-nyenyezi ŵa m’ma 1500 ŵakagomezganga kuti kufumyapo kwa Copernicus kwa [[equant]] ndiko kukaŵa kufiska kwake kukuru<ref>"Kupenda kwane kwa Copernicus paumaliro kukawovwira kukhazikiska kuti unandi wa ŵasanda-nyenyezi ŵa m’ma 1500 ŵakaghanaghananga kuti kufumyapo kwa [[equant]] ndiko kukaŵa kufiska kukuru kwa Copernicus, chifukwa chikakhorweska dango la kale la kawonekelo kakutowa lakuti mayendero ghamuyirayira gha kuchanya yakaŵenge ghakuyana na gha nkhulungulu..." Gingerich, Owen. ''The Book Nobody Read'' (Walker & Company, 2004).p.55. {{ISBN|0-8027-1415-3}}</ref> kweni nthowa yake yikapoka malo gha Ptolemy yayi, iyo yikaluŵika pakati pajumpha vyaka 70 kufuma apo [[Galileo_Galilei#Phases_of_Venus|Galileo wakawonera na galasi lakulaŵiskira mu 1610]].<ref>"Nkhupusu kulongora kuti usambazi wa Ptolemy ukaŵa wakukula m’paka 1610 [apo Galileo wakawona masinthiro gha Venus na galasi] ndipo ukathera nyengo yichoko waka panyuma...Ukaboni ngwakupanikizga: [[Geocentrism#Ptolemaic_model|usambazi wa Ptolemy]] ukayambukirika na Copernicus yayi; ukasuzgika kachoko waka na [[SN 1572|nyenyezi yiphanya ya 1572]], kweni pofika kuumaliro wa vyaka vya m’ma 1500 ukaŵa kuti waŵajikaso. Galasi lakulaŵiskira, ku kanyake, likapangiska kubwanganduka kwake kwa luŵiro na kwambura kuwelera." [[David_Wootton_(historian)|Wootton, David]]. ''The Invention of Science: A New History of the Scientific Revolution'' (Penguin, 2015). p.152. {{ISBN|0-06-175952-X}}</ref> === Kusintha Kukuru kwa Vinjeru vya Chilengiwa === {{Main|Scientific Revolution}} [[Johannes Kepler]] na ŵanyake ŵakasuskana na maghanoghano ghakuti ntchito yimoza pera ya jiso nkhuwona, ndipo ŵakasuntha khumbo likuru mu masambiro gha mboniwoni kufuma ku jiso kuya ku umo ungweru ukuyendera.<ref name="Smith1981" /><ref>{{cite book |last1=Cohen |first1=H. Floris |author-link=Floris Cohen |chapter=Greek nature knowledge transplanted and more: Renaissance Europe |title=How modern science came into the world. Four civilizations, one 17th-century breakthrough |year=2010 |pages=99–156 |publisher=Amsterdam University Press |isbn=978-90-8964-239-4 |edition=2nd}}</ref> Kweni Kepler wakumanyikwa chomene chifukwa cha kusanga kwa [[Kepler's laws of planetary motion|malango gha Kepler gha mayendero gha vyakuzingulira]]. Kepler wakakana yayi vinjeru vya kuseri kwa chilengiwa vya Aristotelu ndipo wakalongosora ntchito yake nga nkhupenja [[Harmony of the Spheres|Kuyana kwa Vyakuchanya]].<ref>{{Cite book |last=Koestler |first=Arthur |url=https://archive.org/details/sleepwalkershist00koes_0/page/1 |title=The Sleepwalkers: A History of Man's Changing Vision of the Universe |publisher=Penguin |year=1990 |isbn=0-14-019246-8 |location=London |page=[https://archive.org/details/sleepwalkershist00koes_0/page/1 1] |author-link=Arthur Koestler |orig-date=1959}}</ref> [[Galileo]] wakachita vintu vyakuzirwa chomene mu usambazi wa nyenyezi, malango gha chilengiwa, na vyakupangapanga. Kweni, wakamba kutambuzgika panyuma pakuti Papa Urban VIII wamupaka mulandu chifukwa cha kulemba vya nthowa yakuti dazi ndilo liri pakati.<ref>{{cite web |url=http://galileo.rice.edu/gal/urban.html |title=Pope Urban VIII |last=van Helden |first=Al |year=1995 |website=The Galileo Project |access-date=3 November 2016 |url-status=live |archive-url=https://web.archive.org/web/20161111033150/http://galileo.rice.edu/gal/urban.html |archive-date=11 November 2016}}</ref> [[printing press|Chakuponderezgera malemba]] chikagwiriskikanga ntchito chomene pakupharazga maghanoghano gha nkhwantha, kusazgapo ghanyake agho yakasuskana chomene na maghanoghano gha mu nyengo iyo pa vya chilengiwa.<ref>{{cite journal |last=Gingerich |first=Owen |title=Copernicus and the Impact of Printing |journal=Vistas in Astronomy |volume=17 |year=1975 |issue=1 |pages=201–218 |doi=10.1016/0083-6656(75)90061-6 |bibcode=1975VA.....17..201G}}</ref> [[Francis Bacon]] na [[René Descartes]] ŵakafumiska maghanoghano gha vinjeru pakuvikilira mtundu uphanya wa vinjeru vya chilengiwa uwo ukaŵa wa Aristotelu yayi. Bacon wakadidimizga pa kuzirwa kwa kuyezgelera kuluska kulanguruka waka, wakasuskana na vifukwa vya Aristotelu vya kawonekelo na chilato chaumaliro, ndipo wakachiska fundo yakuti vinjeru vya chilengiwa visambirenge [[Physical law|malango gha chilengiwa]] na kunozga kwa umoyo wa ŵanthu wose.<ref>{{Cite book |last=Zagorin |first=Perez |title=Francis Bacon |url=https://archive.org/details/francisbacon0000zago |page=[https://archive.org/details/francisbacon0000zago/page/84 84] |year=1998 |publisher=Princeton University Press |isbn=978-0-691-00966-7}}</ref> Descartes wakadidimizga pa kaghanaghaniro ka munthu payekha ndipo wakayowoya kuti masambiro gha manambala m’malo mwa masambiro gha mapangikiro gha vinthu ndigho ghagwiriskikenge ntchito pa kusanda chilengiwa.<ref>{{cite book |last1=Davis |first1=Philip J. |last2=Hersh |first2=Reuben |year=1986 |title=Descartes' Dream: The World According to Mathematics |url=https://archive.org/details/descartesdreamwo0000davi |location=Cambridge, MA |publisher=[[Harcourt Brace Jovanovich]]}}</ref> Gemini said === Nyengo ya Kungweluka kwa Vinjeru === {{Main|Science in the Age of Enlightenment}} [[File:Newton's Principia title page.png|thumb|upright|Pa peji lakwamba la buku lakwamba la mu 1687 la {{lang|la|[[Philosophiæ Naturalis Principia Mathematica]]}} lakulembeka na Isaac Newton]] Kuyamba kwa [[Age of Enlightenment|Nyengo ya Kung’weluka kwa Vinjeru]], [[Isaac Newton]] wakakhazikiska fumbiro la [[classical mechanics|malango gha kanyamazira na kachidukulu]] kwizira mu buku lake la {{lang|la|[[Philosophiæ Naturalis Principia Mathematica]]}} ilo likawovwira chomene nkhwantha za vinjeru vya chilengiwa zanthazi.<ref>{{cite book |last=Gribbin |first=John |title=Science: A History 1543–2001 |url=https://archive.org/details/sciencehistory150000grib |year=2002 |page=[https://archive.org/details/sciencehistory150000grib/page/241 241] |publisher=Allen Lane |isbn=978-0-7139-9503-9 |quote=Nangauli chikaŵa chimoza mwa vinthu vinandi mu Nyengo ya Kung'weluka, kutonda kwa malango gha Newton pa nkhani ya kupereka ndondomeko ya manambala ya charu chakunozgeka kukachita chigaŵa chikuru mu kukura kwa kayendero aka mu vyaka vya m'ma 1700}}</ref> [[Gottfried Wilhelm Leibniz]] wakasazgira mazgu ghakufuma mu [[Aristotelian physics|vinjeru vya chilengiwa vya Aristotelu]], agho panyengo iyi ghakagwiriskikanga ntchito mu nthowa yiphanya [[teleological|yambura kulinga pa chilato chakubabika nacho]]. Ichi chikang’anamuranga kusintha kwa umo vinthu vikuwonekerwa: vinthu vikamba kuwoneka kuŵa vyambura vilato vya m’kati. Leibniz wakagomezganga kuti mitundu yakupambanapambana ya vinthu yose yikugwira ntchito kuyana na malango ghakuyana gha chilengiwa, kwambura vifukwa vyapadera vya kawonekelo panji vya chilato chaumaliro.<ref>{{Cite web |url=https://mathshistory.st-andrews.ac.uk/Biographies/Leibniz/ |title=Gottfried Leibniz – Biography |website=Maths History |access-date=2 March 2021 |archive-date=11 July 2017 |archive-url=https://web.archive.org/web/20170711221621/http://www-groups.dcs.st-and.ac.uk/~history/Biographies/Leibniz.html |url-status=live}}</ref> Mu nyengo iyi, chilato na kuzirwa kwa vinjeru vya chilengiwa kukazgoka kupanga usambazi na vyakupangapanga ivyo vinganozga umoyo wa ŵanthu, mu nthowa ya [[Economic materialism|khumbiro la vyakuthupi]] ya kuŵa na vyakurya vinandi, vyakuvwala, na vinthu vinyake. Mu [[Novum Organum|mazgu gha Bacon]], "chilato cheneko na chakuzomerezgeka cha vinjeru {{em|nkhupereka mwaŵi ku umoyo wa munthu na vyakupangapanga viphanya na usambazi}}", ndipo wakachiska nkhwantha kuti zileke kulondezga maghanoghano gha kuseri kwa chilengiwa panji gha vyauzimu, agho wakagomezganga kuti ghakovwira pachoko chomene ku chimwemwe cha munthu kuluska "utunthi wa maghanoghano ghakusuzga panji ghakukondweska waka".<ref>{{Cite book |url=https://books.google.com/books?id=PgmbZIybuRoC&pg=PA162 |title=The Social and Economic Roots of the Scientific Revolution: Texts by Boris Hessen and Henryk Grossmann |last1=Freudenthal |first1=Gideon |last2=McLaughlin |first2=Peter |date=20 May 2009 |publisher=Springer |isbn=978-1-4020-9604-4 |access-date=25 July 2018}}</ref> Vinjeru vya chilengiwa mu nyengo ya Kung’weluka vikalongozgekanga na [[scientific societies|mabungwe gha nkhwantha]] na masukulu ghakuya,<ref>{{Cite book |editor-last1=Goddard Bergin |editor-first1=Thomas |editor1-link=Thomas G. Bergin |url=https://archive.org/details/encyclopediaofre0000unse_d0p5 |title=Encyclopedia of the Renaissance |editor-last2=Speake |editor-first2=Jennifer |editor2-link=Jennifer Speake |year=1987 |publisher=Facts on File |isbn=978-0-8160-1315-9}}</ref> agho panyengo iyi yakatora malo gha masukulu ghachanya pakuŵa malo ghakusandira na kukuzgyira vinjeru. Mabungwe na masukulu agha yikaŵa fumbiro la kukura kwa ntchito ya unkhwantha wa vinjeru vya chilengiwa. Chinthu chinyake chakuzirwa chikaŵa [[popular culture|kuthandazgika kwa vinjeru]] pakati pa ŵanthu awo ŵakambanga kumanya chomene kuŵazga na kulemba.<ref>{{Cite book |last=van Horn Melton |first=James |url=https://www.cambridge.org/core/books/rise-of-the-public-in-enlightenment-europe/BA532085A260114CD430D9A059BD96EF |title=The Rise of the Public in Enlightenment Europe |publisher=Cambridge University Press |year=2001 |isbn=978-0-511-81942-1 |doi=10.1017/CBO9780511819421 |access-date=27 May 2022 |url-access=subscription |pages=82–83 |archive-date=20 January 2022 |archive-url=https://web.archive.org/web/20220120143805/https://www.cambridge.org/core/books/rise-of-the-public-in-enlightenment-europe/BA532085A260114CD430D9A059BD96EF |url-status=live}}</ref> Nkhwantha za vinjeru za mu nyengo ya Kung’weluka zikaŵazganga ntchito za ŵakale ŵawo—chomenechomene [[Galileo]], [[Kepler]], [[Robert Boyle|Boyle]], na Newton—pakuŵa ŵalongozgi mu vigaŵa vyose vya vyakuthupi na vya kukhaliro kwa ŵanthu vya mazuŵa gano.<ref>{{Cite web |title=The Scientific Revolution and the Enlightenment (1500–1780) |url=https://www.tamaqua.k12.pa.us/cms/lib07/PA01000119/Centricity/Domain/119/TheScientificRevolution.pdf |access-date=29 January 2024 |archive-date=14 January 2024 |archive-url=https://web.archive.org/web/20240114191547/https://www.tamaqua.k12.pa.us/cms/lib07/PA01000119/Centricity/Domain/119/TheScientificRevolution.pdf |url-status=live}}</ref><ref>{{Cite encyclopedia |title=Scientific Revolution |url=https://www.britannica.com/science/Scientific-Revolution |access-date=29 January 2024 |encyclopedia=Encyclopædia Britannica |archive-date=18 May 2019 |archive-url=https://web.archive.org/web/20190518105004/https://www.britannica.com/science/Scientific-Revolution |url-status=live}}</ref> Mu vyaka vya m’ma 1700 kukawoneka kukura kukuru mu kachitidwe ka un’anga<ref>{{cite book |title=Brock Biology of Microorganisms |url=https://archive.org/details/brockbiologyofmi0011madi |publisher=Prentice Hall |year=2006 |isbn=978-0-13-144329-7 |editor-last=Madigan |editor-first=M. |editor-last2=Martinko |editor-first2=J. |edition=11th}}</ref> na vinjeru vya chilengiwa;<ref>{{cite book |last=Guicciardini |first=N. |url=https://archive.org/details/readingprincipia0000guic |title=Reading the Principia: The Debate on Newton's Methods for Natural Philosophy from 1687 to 1736 |publisher=Cambridge University Press |year=1999 |isbn=978-0-521-64066-4 |location=New York |url-access=registration}}</ref> kukuzgyika kwa [[Taxonomy (biology)|ndondomeko ya magulu gha vyamoyo]] na [[Carl Linnaeus]];<ref>{{cite journal |author1-link=Charles Calisher |last1=Calisher |first1=CH |year=2007 |title=Taxonomy: what's in a name? Doesn't a rose by any other name smell as sweet? |journal=Croatian Medical Journal |volume=48 |issue=2 |pages=268–270 |pmc=2080517 |pmid=17436393}}</ref> kapulikisko kaphanya ka [[magnetism|nkhongono yakuguza]] na mphenzi; <ref>{{cite book |last1=Darrigol |first1=Olivier |url=https://archive.org/details/electrodynamicsf0000darr |title=Electrodynamics from Ampère to Einstein |year=2000 |publisher=Oxford University Press |isbn=0-19-850594-9 |location=New York |url-access=registration}}</ref> ndipo kukura kwa vinjeru vya [[chemistry|kapangikiro ka vinthu]] pakuŵa chigaŵa chakujiyimira pa chekha.<ref>{{cite book |last1=Olby |first1=R. C. |last2=Cantor |first2=G. N. |last3=Christie |first3=J. R. R. |last4=Hodge |first4=M. J. S. |year=1990 |title=Companion to the History of Modern Science |location=London |publisher=Routledge |page=265}}</ref> Maghanoghano pa nkhani ya mukhaliro wa munthu, chalo, na usambazi yakasinthaso mu nyengo ya Kung’weluka. Hume na nkhwantha zinyake za ku Scotland ŵakapanga buku la ''[[A Treatise of Human Nature|Muwonekelo wa Mukhaliro wa Munthu]]'', ilo likalongosoreka mu nthowa ya mbiri mu malemba gha ŵalembi nga ni [[James Burnett, Lord Monboddo|James Burnett]], [[Adam Ferguson]], [[John Millar (philosopher)|John Millar]] na [[William Robertson (historian)|William Robertson]], ŵose awo ŵakasazga kusanda kwa unkhwantha kwa umo ŵanthu ŵakachitiranga mu nyengo za kale na mu mitheto yakwamba, uku ŵakumanya chomene nkhongono izo zikupanga [[modernity|mukhaliro wa mazuŵa gano]].<ref>{{Cite web |last=Magnusson |first=Magnus |date=10 November 2003 |title=Review of James Buchan, ''Capital of the Mind: how Edinburgh Changed the World'' |url=http://www.newstatesman.com/200311100040 |archive-url=https://web.archive.org/web/20110606015918/http://www.newstatesman.com/200311100040 |archive-date=6 June 2011 |access-date=27 April 2014 |work=New Statesman}}</ref> Masambiro gha mazuŵa gano gha mukhaliro wa ŵanthu mu chalo yakambira mu nthandala iyi.<ref>{{Cite journal |jstor=588406 |title=Origins of Sociology: The Case of the Scottish Enlightenment |url=https://archive.org/details/sim_british-journal-of-sociology_1970-06_21_2/page/164 |journal=The British Journal of Sociology |volume=21 |issue=2 |pages=164–180 |last1=Swingewood |first1=Alan |year=1970 |doi=10.2307/588406}}</ref> Mu 1776, [[Adam Smith]] wakafumiska buku la ''[[The Wealth of Nations|Usambazi wa Mabuku]]'', ilo kanandi likuwoneka kuŵa ntchito yakwamba ya masambiro gha mazuŵa gano gha usambazi.<ref>{{Cite book |last=Fry |first=Michael |url=https://archive.org/details/adamsmithslegacy0000unse |title=Adam Smith's Legacy: His Place in the Development of Modern Economics |publisher=[[Routledge]] |others=[[Paul Samuelson]], [[Lawrence Klein]], [[Franco Modigliani]], [[James M. Buchanan]], [[Maurice Allais]], [[Theodore Schultz]], [[Richard Stone]], [[James Tobin]], [[Wassily Leontief]], [[Jan Tinbergen]] |year=1992 |isbn=978-0-415-06164-3 |url-access=registration}}</ref> === Vyaka vya m’ma 1800 === {{Main|19th century in science}} [[File:Darwin Tree 1837.png|thumb|upright|Chithuzi chakwamba cha [[Phylogenetic tree|khuni la kusanduka kwa vyamoyo]] chakupangika na [[Charles Darwin]] mu 1837|alt=Sketch of a map with captions]] Mu vyaka vya m’ma 1800, vinthu vinandi ivyo vikumanyikwitsa vinjeru vya chilengiwa vya mazuŵa gano vikamba kuŵako. Ivi vikasazgapo kusanduka kwa masambiro gha vyamoyo na vyakuthupi; kugwiriskira ntchito chomene vipimiro vyakugomezgeka; kuŵako kwa mazgu nga ni "wasanda-vyamoyo", "wasanda-vyakuthupi", na "wasanda-vinjeru vya chilengiwa"; kukura kwa ntchito ya kusanda chilengiwa; nkhwantha za vinjeru kusanga mazaza gha mitheto pa vigaŵa vinandi vya ŵanthu; kukhazikiskika kwa mafakitale mu vyaru vinandi; kuthandazgika kwa malemba gha vinjeru vya chilengiwa pakati pa ŵanthu; na kuŵako kwa mabuku gha nkhwantha.<ref>{{cite book |last1=Lightman |first1=Bernard |editor1-last=Shank |editor1-first=Michael |editor2-last=Numbers |editor2-first=Ronald |editor3-last=Harrison |editor3-first=Peter |title=Wrestling with Nature: From Omens to Science |url=https://archive.org/details/isbn_9780226317830 |year=2011 |publisher=University of Chicago Press |isbn=978-0-226-31783-0 |page=[https://archive.org/details/isbn_9780226317830/page/367 367] |chapter=13. Science and the Public}}</ref> Mu vyaka vya m’ma 1800, masambiro gha makhaliro gha maghanoghano yakafumamo mu masambiro gha vinjeru vya umoyo apo [[Wilhelm Wundt]] wakakhazikiskika malo ghakwamba ghakusandira makhaliro gha maghanoghano mu 1879.<ref>{{cite book |last=Leahey |first=Thomas Hardy |title=A History of Psychology: From Antiquity to Modernity |url=https://archive.org/details/historyofpsychol0000thom |year=2018 |publisher=Routledge |isbn=978-1-138-65242-2 |edition=8th |location=New York |pages=[https://archive.org/details/historyofpsychol0000thom/page/219 219]–253 |chapter=The psychology of consciousness}}</ref> Pakati pa vyaka vya m’ma 1800, [[Charles Darwin]] na [[Alfred Russel Wallace]] waliyose payekha wakasachizga chigomezgo cha kusanduka kwa vyamoyo kwizira mu [[natural selection|kusankhika na chilengiwa]] mu 1858, icho chikulongosora umo vyakumera na vinyama vyakupambanapambana vikayambira na kusanduka. Chigomezgo chawo chikayowoyeka mwakudidimizga mu buku la Darwin la ''[[On the Origin of Species|Pa Chiyambi cha Mitundu ya Vyamoyo]]'', ilo likafumiskika mu 1859.<ref>{{cite journal |last=Padian |first=Kevin |title=Darwin's enduring legacy |url=https://archive.org/details/sim_nature-uk_2008-02-07_451_7179/page/632 |journal=Nature |volume=451 |issue=7179 |pages=632–634 |year=2008 |doi=10.1038/451632a |pmid=18256649 |bibcode=2008Natur.451..632P |doi-access=free}}</ref> Kwakujiyimira pa yekha, [[Gregor Mendel]] wakapereka lipoti lake, "[[Experiments on Plant Hybridisation|Kuyezgelera pa Kusazga Vyakumera]]" mu 1865,<ref>{{Cite book |last=Henig |first=Robin Marantz |author-link=Robin Marantz Henig |url=https://archive.org/details/monkingardenlost00heni |title=The monk in the garden: the lost and found genius of Gregor Mendel, the father of genetics |year=2000 |pages=134–138}}</ref> ilo likalongosora malango gha chiharo cha m’thupi, icho chikachita pakuŵa fumbiro la vinjeru vya mazuŵa gano vya chiharo.<ref>{{cite journal |last=Miko |first=Ilona |title=Gregor Mendel's principles of inheritance form the cornerstone of modern genetics. So just what are they? |journal=Nature Education |volume=1 |issue=1 |page=134 |year=2008 |url=https://www.nature.com/scitable/topicpage/gregor-mendel-and-the-principles-of-inheritance-593/ |access-date=9 May 2021 |archive-date=19 July 2019 |archive-url=https://web.archive.org/web/20190719224056/http://www.nature.com/scitable/topicpage/gregor-mendel-and-the-principles-of-inheritance-593 |url-status=live}}</ref> Kuyamba kwa vyaka vya m’ma 1800 [[John Dalton]] wakasachizga [[atomic theory|chigomezgo cha mazuŵa gano cha kachidutswa kambura kugaŵika]], chakuzingatira pa ghanoghano la Democritus la tuchidutswa tuchoko chomene twambura kugaŵika uto tikuchemeka ''atoms''.<ref>{{cite journal |last1=Rocke |first1=Alan J. |year=2005 |title=In Search of El Dorado: John Dalton and the Origins of the Atomic Theory |url=https://archive.org/details/sim_social-research_spring-2005_72_1/page/125 |journal=Social Research |volume=72 |issue=1 |pages=125–158 |doi=10.1353/sor.2005.0003 |jstor=40972005 |s2cid=141350239}}</ref> Malango gha [[conservation of energy|kusungilira nkhongono]], [[conservation of momentum|kusungilira kanyamazira]] na [[conservation of mass|kusungilira unandi wa chinthu]] yakalongora chilengiwa chakukhalira apo pangaŵa kutayika pachoko kwa vinthu. Kweni, chifukwa cha kwiza kwa [[steam engine|injini ya nthuzi]] na [[Industrial Revolution|Kusintha Kukuru kwa Mafakitale]] pakaŵa kapulikisko kakuru kakuti ni mitundu yose ya nkhongono yayi iyo yili na mukhaliro wakuyana, mwa kupusu kusandulika kuŵa [[Work (thermodynamics)|ntchito]] yakuzirwa panji kuŵa nkhongono yinyake.<ref name="Reichl1980" /> Kumanya ichi kukapangiska kukuzga kwa malango gha [[thermodynamics|vinjeru vya nkhongono ya chithukuzi]], mwa icho nkhongono yakuzirwa ya chilengiwa yikuwoneka kuŵa yakukhira nyengo zose: [[entropy|kubwanganduka]] kwa chilengiwa chakuzingika kukuluta panthazi m’paka muyirayira.{{efn|name= HelmholtzGibbsGuthLinde|1= Usange chilengiwa chili chakuzingika panji chakujulika, panji [[shape of the universe|kawonekelo ka chilengiwa]], ni fumbo lambura kumanyikwa. Dango lachiŵiri la vinjeru vya nkhongono ya chithukuzi,<ref name="Reichl1980">{{cite book |last=Reichl |first=Linda |author-link=Linda Reichl |year=1980 |title=A Modern Course in Statistical Physics |url= |location= |publisher=Edward Arnold |isbn=0-7131-2789-9}}</ref>{{rp|9}}<ref>{{cite book |last=Rao |first=Y. V. C. |title=Chemical Engineering Thermodynamics |publisher=Universities Press |isbn=978-81-7371-048-3 |year=1997 |page=158}}</ref> na dango lachitatu la vinjeru vya nkhongono ya chithukuzi<ref>{{cite journal |doi=10.1016/j.aop.2016.07.031 |title=Bounded energy exchange as an alternative to the third law of thermodynamics |year=2016 |last1=Heidrich |first1=M. |journal=Annals of Physics |volume=373 |pages=665–681 |bibcode=2016AnPhy.373..665H}}</ref> ghakulongora [[heat death of the universe|nyifwa ya chithukuzi ya chilengiwa]] usange chilengiwa chili nthandala yakuzingika, kweni ni ntheura yayi kwa chilengiwa icho chikukulirako.}} [[electromagnetic theory|Chigomezgo cha nkhongono ya mphenzi na kuguza]] chikakhazikiskika mu vyaka vya m’ma 1800 na ntchito za [[Hans Christian Ørsted]], [[André-Marie Ampère]], [[Michael Faraday]], [[James Clerk Maxwell]], [[Oliver Heaviside]], na [[Heinrich Hertz]]. Chigomezgo chiphanya ichi chikawuska mafumbo agho yakaŵa ghakusuzga kuzgoreka kwizira mu ndondomeko ya Newton. Kusangika kwa [[X-ray|minziro ya X]] kukachiska kusangika kwa [[radioactivity|ungweru wakofya wa malibwe]] na [[Henri Becquerel]] na [[Marie Curie]] mu 1896,<ref>{{cite book |last=Mould |first=Richard F. |title=A century of X-rays and radioactivity in medicine: with emphasis on photographic records of the early years |year=1995 |publisher=Inst. of Physics Publ. |isbn=978-0-7503-0224-1 |edition=Reprint. with minor corr |location=Bristol |page=12}}</ref> Marie Curie panyuma wakazgoka munthu wakwamba kutonda viphale viŵiri vya Nobel.<ref name="Estreicher1938">{{cite book |last=Estreicher |first=Tadeusz |title=Polski słownik biograficzny, vol. 4 |title-link=Polski słownik biograficzny |year=1938 |page=113 |language=pl |chapter=Curie, Maria ze Skłodowskich |author-link=Tadeusz Estreicher}}</ref> Mu chaka chakulondezgapo kukasangika kachidutswa kakwamba kam’kati ka atomu, kano kakuchemeka [[electron]].<ref>{{cite journal |last=Thomson |first=J. J. |year=1897 |title=Cathode Rays |journal=[[Philosophical Magazine]] |volume=44 |issue=269 |pages=293–316 |doi=10.1080/14786449708621070 |bibcode=1897LEDPM..44..293T }}</ref> === Vyaka chitanda cha 20 === {{Main|20th century in science}} [[File:Carte trou ozone Antarctique.jpg|alt=Chithuzi chikulongora kuchepa kwa nkhongono ya mlengalenga ku Mpoto kwa charu|thumb|Chithuzi cha pakompyuta cha [[dindi la mlengalenga]] icho chikachitika mu chaka cha 1987 pakugwiliskira ntchito uthenga wa telesikopu ya ku mlengalenga]] Mu chigaŵa chakwamba cha chaka chitanda ichi, kupangika kwa [[munkhwala wakukoma tumpoyo]] na [[mufundo wakupangika na mawoko]] kukawovya chomene umoyo wa ŵanthu pa charu chose.<ref>{{Cite journal |last=Goyotte |first=Dolores |year=2017 |title=The Surgical Legacy of World War II. Part II: The age of antibiotics |url=https://www.ast.org/ceonline/articles/402/files/assets/common/downloads/publication.pdf |url-status=live |journal=The Surgical Technologist |volume=109 |pages=257–264 |archive-url=https://web.archive.org/web/20210505180530/https://www.ast.org/ceonline/articles/402/files/assets/common/downloads/publication.pdf |archive-date=5 May 2021 |access-date=8 January 2021}}</ref><ref>{{cite journal |last1=Erisman |first1=Jan Willem |first2=M. A. |last2=Sutton |first3=J. |last3=Galloway |first4=Z. |last4=Klimont |first5=W. |last5=Winiwarter |date=October 2008 |title=How a century of ammonia synthesis changed the world |url=http://www.physics.ohio-state.edu/~wilkins/energy/Resources/Essays/ngeo325.pdf.xpdf |journal=[[Nature Geoscience]] |volume=1 |issue=10 |pages=636–639 |bibcode=2008NatGe...1..636E |doi=10.1038/ngeo325 |s2cid=94880859 |archive-url=https://web.archive.org/web/20100723223052/http://www.physics.ohio-state.edu/~wilkins/energy/Resources/Essays/ngeo325.pdf.xpdf |archive-date=23 July 2010 |access-date=22 October 2010}}</ref> Masuzgo ghakofya gha [[vyakuzingilizga]] nga ni [[kumalika kwa mlengalenga]], [[kununkhira kwa nyanja]], [[kuzara kwa vyakumera mu maji]], na [[kusintha kwa kanyengo]] kukamba kumanyikwa na ŵanthu ndipo kukambiska [[masambiro gha vyakuzingilizga]].<ref>{{cite journal |editor-last1=Emmett |editor-first1=Rob |editor-last2=Zelko |editor-first2=Frank |url=http://www.environmentandsociety.org/perspectives/2014/2/minding-gap-working-across-disciplines-environmental-studies |title=Minding the Gap: Working Across Disciplines in Environmental Studies |archive-url=https://web.archive.org/web/20220121054306/https://www.environmentandsociety.org/perspectives/2014/2/minding-gap-working-across-disciplines-environmental-studies |archive-date=21 January 2022 |series=RCC Perspectives no. 2 |year=2014 |doi=10.5282/rcc/6313 |last1=Emmett |first1=Robert |last2=Zelko |first2=Frank |journal=Environment & Society Portal}}</ref> Mu nyengo iyi, kuyezgelera kwa vya umanyi kukakula chomene ndipo kukamba kupenja [[Umanyi ukuru|ndalama zinandi na nthowa zikuru]].<ref>{{Cite journal |last=Furner |first=Jonathan |date=1 June 2003 |title=Little Book, Big Book: Before and After Little Science, Big Science: A Review Article, Part I |url=https://archive.org/details/journal-of-librarianship-and-information-science_2003-06_35_2/page/115 |journal=Journal of Librarianship and Information Science |volume=35 |issue=2 |pages=115–125 |doi=10.1177/0961000603352006 |s2cid=34844169}}</ref> Kusintha kukuru kwa luso chifukwa cha [[Nkhondo Yakwamba ya pa Charu Chose]], [[Nkhondo Yachiŵiri ya pa Charu Chose]], na [[Nkhondo ya Mazgu]] kukambiska chiphalizgano pakati pa [[Mautongi ghankhongono|mautongi ghakurughakuru gha charu]], nga ni [[Chiphalizgano cha ku Mlengalenga]] na [[chiphalizgano cha vilwero vyakofya]].<ref>{{cite book |last1=Kraft |first1=Chris |url=https://archive.org/details/flight00chri |title=Flight: My Life in Mission Control |first2=James |last2=Schefter |publisher=Dutton |year=2001 |isbn=0-525-94571-7 |location=New York |author-link1=Christopher C. Kraft, Jr. |pages=3–5}}</ref><ref>{{cite book |last=Kahn |first=Herman |author-link=Herman Kahn |year=1962 |title=Thinking about the Unthinkable |url=https://archive.org/details/thinkingaboutunt0000kahn |publisher=Horizon}}</ref> Kukawa so kukolerana kukuru pakati pa vyaru, nangauli pakaŵa nkhondo.<ref>{{Cite book |last=Shrum |first=Wesley |title=Structures of scientific collaboration |url=https://archive.org/details/structuresofscie0000shru |year=2007 |publisher=MIT Press |others=Joel Genuth, Ivan Chompalov |isbn=978-0-262-28358-8 |location=Cambridge, MA}}</ref> Kukumpoto kwa vyaka chitanda cha 20, kukoleka kwa ŵanakazi na kuwuskapo kwa [[kusankhulana chifukwa cha kwanakazi]] kukapangiska kuti ŵanakazi ŵanandi ŵaje ŵasanduzi ŵa umanyi, kweni kupambana kukuru pakati pa ŵanalume na ŵanakazi kukhalilira mu vigaŵa vinyake.<ref>{{cite book |last=Rosser |first=Sue V. |title=Breaking into the Lab: Engineering Progress for Women in Science |url=https://archive.org/details/breakingintolabe0000ross |date=12 March 2012 |publisher=New York University Press |isbn=978-0-8147-7645-2 |page=[https://archive.org/details/breakingintolabe0000ross/page/7 7]}}</ref> Kusangika kwa [[kungweruka kwa mlengalenga]] mu chaka cha 1964<ref>{{cite journal |last=Penzias |first=A. A. |year=2006 |title=The origin of elements |url=http://nobelprize.org/nobel_prizes/physics/laureates/1978/penzias-lecture.pdf |journal=Science |publisher=[[Nobel Foundation]] |volume=205 |issue=4406 |pages=549–554 |doi=10.1126/science.205.4406.549 |pmid=17729659 |access-date=4 October 2006 |archive-date=17 January 2011 |archive-url=https://web.archive.org/web/20110117225210/http://nobelprize.org/nobel_prizes/physics/laureates/1978/penzias-lecture.pdf |url-status=live}}</ref> kukapangiska kukana [[fundo ya chilengiwa chakukhazikika]] na kupokelera fundo ya [[Big Bang]] ya [[Georges Lemaître]].<ref>{{cite book |last=Weinberg |first=S. |url=https://archive.org/details/gravitationcosmo00stev_0/page/495 |title=Gravitation and Cosmology |publisher=John Whitney & Sons |year=1972 |isbn=978-0-471-92567-5 |pages=[https://archive.org/details/gravitationcosmo00stev_0/page/495 464–495] |url-access=registration}}</ref> Chaka chitanda ichi chikawona kusintha kukuru mu vigaŵa vya umanyi. Kusintha kwa vyamoyo kukazgoka fundo yimoza mu vyaka vyakwamba vya 1900 apo [[Kukolerana kwa mazuŵa gano (chaka chitanda cha 20)|kukolerana kwa mazuŵa gano]] kukasazga fundo ya kusintha kwa vyamoyo ya Darwin na [[masambiro gha mazuŵa ghano gha ndonda za umoyo]].<ref>{{Cite book |last1=Futuyma |first1=Douglas J. |title=Evolution |url=https://archive.org/details/evolution0000futu_j9h3 |last2=Kirkpatrick |first2=Mark |year=2017 |isbn=978-1-60535-605-1 |edition=4th |pages=[https://archive.org/details/evolution0000futu_j9h3/page/n26 3]–26 |chapter=Chapter 1: Evolutionary Biology |publisher=Sinauer}}</ref> [[Albert Einstein]] na [[fundo yake ya unandi wa vinthu]] kweniso kukura kwa [[umanyi wa tinthu tuchoko chomene]] kukasazgirapo pa umanyi wakale wa kanyengo na [[nkhongono yakuguzira]].<ref>{{Cite book |last=Miller |first=Arthur I. |title=Albert Einstein's special theory of relativity. Emergence (1905) and early interpretation (1905–1911) |year=1981 |location=Reading |publisher=Addison–Wesley |isbn=978-0-201-04679-3}}</ref><ref>{{cite book |last=ter Haar |first=D. |url=https://archive.org/details/oldquantumtheory0000haar |title=The Old Quantum Theory |publisher=Pergamon |year=1967 |isbn=978-0-08-012101-7 |pages=[https://archive.org/details/oldquantumtheory0000haar/page/206 206] |url-access=registration}}</ref> Kugwiliskira ntchito chomene [[nthambo zakukolerana za magesi]] mu vigaŵa vyaumaliro vya chaka chitanda cha 20, pamoza na [[pachanya pa mlengalenga vyakuperekera uthenga]], kukambiska kusintha kukuru mu luso lwa uthenga na kukura kwa nthambo ya charu chose ya uthenga na [[vipangizgo vyakuyendayenda]], kusazgapo [[foni zamazuŵa gano]]. Kukhumbikwa kwa ndondomeko ya vinthu vinandi vyakukolerana kukapangiska kukura kwa [[fundo ya ndondomeko]] na [[kapangiro ka vinthu pakugwiliskira ntchito kompyuta]].<ref>{{cite journal |last1=von Bertalanffy |first1=Ludwig |year=1972 |title=The History and Status of General Systems Theory |url=https://archive.org/details/sim_academy-of-management-journal_1972-12_15_4/page/407 |journal=The Academy of Management Journal |volume=15 |issue=4 |pages=407–426 |jstor=255139 |bibcode=1972AManJ..15..407V }}</ref> === Vyaka chitanda cha 21 === {{Main|21st century#Science and technology}} [[Ndondomeko ya ndonda za umoyo wa muntu]] ikamalizgika mu chaka cha 2003 pakumanya na kuŵika mapu gha ndonda zose za [[ndonda za muntu]].<ref>{{Cite journal |last1=Naidoo |first1=Nasheen |last2=Pawitan |first2=Yudi |last3=Soong |first3=Richie |last4=Cooper |first4=David N. |last5=Ku |first5=Chee-Seng |date=October 2011 |title=Human genetics and genomics a decade after the release of the draft sequence of the human genome |journal=Human Genomics |volume=5 |issue=6 |pages=577–622 |doi=10.1186/1479-7364-5-6-577 |pmc=3525251 |pmid=22155605 |doi-access=free}}</ref> Maselo ghakwamba gha [[Maselo ghakuyana na gha mwana uyo wandababike]] ghakapangika mu chaka cha 2006, icho chikazomerezga maselo gha ŵanthu ŵakuru kuzgoka [[maselo ghakwamba]] na kuŵa selo lililose ilo likusangika mu thupi.<ref>{{Cite journal |last1=Rashid |first1=S. Tamir |last2=Alexander |first2=Graeme J. M. |date=March 2013 |title=Induced pluripotent stem cells: from Nobel Prizes to clinical applications |journal=Journal of Hepatology |volume=58 |issue=3 |pages=625–629 |doi=10.1016/j.jhep.2012.10.026 |issn=1600-0641 |pmid=23131523 |doi-access=free}}</ref> Pakusimikizga kusangika kwa [[Higgs boson]] mu chaka cha 2013, kantu kaumaliro ako kakayowoyekerathu na [[Ndondomeko ya Umanyi]] ya umanyi wa tinthu tuchoko chomene kakasangika.<ref>{{cite press release |last=O'Luanaigh |first=C. |date=14 March 2013 |title=New results indicate that new particle is a Higgs boson |publisher=[[CERN]] |url=http://home.web.cern.ch/about/updates/2013/03/new-results-indicate-new-particle-higgs-boson |access-date=9 October 2013 |url-status=live |archive-url=https://web.archive.org/web/20151020000722/http://home.web.cern.ch/about/updates/2013/03/new-results-indicate-new-particle-higgs-boson |archive-date=20 October 2015}}</ref> Mu chaka cha 2015, [[mafumbi gha nkhongono yakuguzira]], agho ghakayowoyekerathu na [[fundo ya unandi wa vinthu]] chaka chitanda chimoza kumasinda, [[Kuwoneka kwakwamba kwa mafumbi gha nkhongono yakuguzira|ghakawoneka kakwamba]].<ref>{{Cite journal |doi=10.3847/2041-8213/aa91c9 |title=Multi-messenger Observations of a Binary Neutron Star Merger |journal=The Astrophysical Journal |volume=848 |issue=2 |page=L12 |year=2017 |last1=Abbott |first1=B. P. |last2=Abbott |first2=R. |last3=Abbott |first3=T. D. |last4=Acernese |first4=F. |last5=Ackley |first5=K. |last6=Adams |first6=C. |last7=Adams |first7=T. |last8=Addesso |first8=P. |last9=Adhikari |first9=R. X.|last10 = Adya|first10 = V. B. |last11=Affeldt |first11=C. |last12=Afrough |first12=M. |last13=Agarwal |first13=B. |last14=Agathos |first14=M. |last15=Agatsuma |first15=K. |last16=Aggarwal |first16=N. |last17=Aguiar |first17=O. D. |last18=Aiello |first18=L. |last19=Ain |first19=A.|last20 = Ajith|first20 = P. |last21=Allen |first21=B. |last22=Allen |first22=G. |last23=Allocca |first23=A. |last24=Altin |first24=P. A. |last25=Amato |first25=A. |last26=Ananyeva |first26=A. |last27=Anderson |first27=S. B. |last28=Anderson |first28=W. G. |last29=Angelova |first29=S. V.|last30 = Antier|first30 = S. |display-authors=29 |bibcode=2017ApJ...848L..12A |arxiv=1710.05833 |s2cid=217162243 |doi-access=free}}</ref><ref>{{cite journal |doi=10.1126/science.aar2149 |title=Merging neutron stars generate gravitational waves and a celestial light show |journal=Science |year=2017 |last1=Cho |first1=Adrian}}</ref> Mu chaka cha 2019, kukolerana kwa charu chose kwa [[Telesikopu ya m'mbali mwa dindi]] kukalongora chithuzi chakwamba cha [[chizongwe chafifi]].<ref>{{Cite web |date=20 April 2019 |title=Media Advisory: First Results from the Event Horizon Telescope to be Presented on April 10th |publisher=Event Horizon Telescope |url=https://eventhorizontelescope.org/blog/media-advisory-first-results-event-horizon-telescope-be-presented-april-10th |archive-url=https://web.archive.org/web/20190420135254/https://eventhorizontelescope.org/blog/media-advisory-first-results-event-horizon-telescope-be-presented-april-10th |archive-date=20 April 2019 |access-date=21 September 2021}}</ref> == Mirazi == {{Main|Branches of science}} Umanyi wa mazuŵa gano ukugaŵika mu [[Mirazi ya umanyi|mirazi]] yikuru yitatu: [[umanyi wa chilengiwa]], [[umanyi wa kakhaliro ka ŵanthu]], na [[umanyi wa ndondomeko]].<ref name="Cohen2021" /> Chigaŵa chilichose mwa vigaŵa ivi chili na masambiro ghake agho nyengo zinyake ghakusazgikana ndipo ghali na [[maina gha luso]] na umanyi wake.<ref>{{cite magazine |url=http://seedmagazine.com/content/article/scientific_method_relationships_among_scientific_paradigms/ |title=Scientific Method: Relationships Among Scientific Paradigms |date=7 March 2007 |magazine=Seed Magazine |access-date=4 November 2016 |archive-url=https://web.archive.org/web/20161101001155/http://seedmagazine.com/content/article/scientific_method_relationships_among_scientific_paradigms/ |archive-date=1 November 2016}}</ref> Umanyi wa chilengiwa na wa kakhaliro ka ŵanthu ghose ni [[umanyi wa kuyezgelera]],<ref>{{cite book |title=Philosophy of Science: From Problem to Theory |url=https://archive.org/details/philosophyofscie0001bung |last=Bunge |first=Mario Augusto |year=1998 |publisher=Transaction |isbn=978-0-7658-0413-6 |page=[https://archive.org/details/philosophyofscie0001bung/page/24 24]}}</ref> pakuti umanyi wawo wukuzikira pa [[ukaboni wa maso]] ndipo ungayezgeka na ŵasanduzi ŵanyake awo ŵakugwira ntchito mu mikhalidwe yakuyana.<ref name="Popper2002">{{cite book |last=Popper |first=Karl R. |year=2002a |chapter=A survey of some fundamental problems |title=The Logic of Scientific Discovery |url=https://archive.org/details/logicscientificd00popp_574 |url-access=limited |orig-date=1959 |pages=[https://archive.org/details/logicscientificd00popp_574/page/n133 3]–26 |publisher=Routledge |location=New York |isbn=978-0-415-27844-7}}</ref>{{rp|pp=3-26}} === Chilengiwa === [[Natural science|Umanyi wa chilengiwa]] ni kusambira vya charu icho tikuwona. Ukugaŵika mu vigaŵa viŵiri: [[umanyi wa vyamoyo]] na [[umanyi wa vinthu vyambura umoyo]]. Mirazi iyi yingasazgirika mu vigaŵa vinyake vya luso. Chiyelezgero, umanyi wa vinthu vyambura umoyo ungagaŵika mu physics, [[chemistry]], [[umanyi wa mlengalenga]], na [[umanyi wa charu pasi]]. Umanyi wa chilengiwa wa mazuŵa gano uli kufuma ku [[fundo za chilengiwa]] izo zikambira ku [[Greece yakale]]. [[Galileo]], [[Descartes]], [[Francis Bacon|Bacon]], na [[Isaac Newton|Newton]] ŵakadumbiskananga uwemi wa kugwiliskira ntchito nthowa za [[physics wa masamu]] na kuyezgelera mu nthowa yakudunjika. Kweni, kaghanaliro ka vinthu na [[maghanoghano gha mu mutu]] vikuŵa vyakukhumbikwa ni m'paka lero mu umanyi wa chilengiwa.<ref>{{cite book |last=Gauch |first=Hugh G. Jr. |chapter=Science in perspective |title=Scientific Method in Practice |publisher=Cambridge University Press |chapter-url=https://books.google.com/books?id=iVkugqNG9dAC&pg=PA71 |pages=21–73 |isbn=978-0-521-01708-4 |year=2003 |access-date=3 September 2018}}</ref> Kusonkhanitsa uthenga mu nthowa yakukhazikika kukatora malo gha [[mbiri ya chilengiwa]], iyo ikawoneka mu vyaka vya m'ma 1500 pakulongosora na kugaŵa vyakumera, vinyama, malibwe, na vinthu vinyake vyamoyo.<ref>{{cite book |last=Oglivie |first=Brian W. |year=2008 |chapter=Introduction |title=The Science of Describing: Natural History in Renaissance Europe |url=https://archive.org/details/scienceofdescrib0000ogil |pages=[https://archive.org/details/scienceofdescrib0000ogil/page/1 1]–24 |edition=Paperback |publisher=University of Chicago Press |isbn=978-0-226-62088-6}}</ref> Lero, "mbiri ya chilengiwa" yikuyowoya chomene za malongosolero gha vinthu ivyo vikuwoneka na maso ku ŵanthu bweka.<ref>{{cite dictionary |title=Natural History |url=http://wordnetweb.princeton.edu/perl/webwn?s=natural+history |dictionary=Princeton University WordNet |access-date=21 October 2012 |url-status=live |archive-url=https://web.archive.org/web/20120303173506/http://wordnetweb.princeton.edu/perl/webwn?s=natural+history |archive-date=3 March 2012}}</ref> === Kakhaliro ka ŵanthu === [[File:Supply-demand-equilibrium.svg|thumb|[[Kuguliska na kukhumba]] mu vyachuma, kukumana pa malo ghawemi|alt=Mizere yiŵiri yakusatuka, kupanga chizindikiro cha X]] [[Social science|Umanyi wa kakhaliro ka ŵanthu]] ni kusambira kakhaliro ka ŵanthu na umo magulu gha ŵanthu ghakwendera.<ref name="Colander2019" /><ref name="Nisbet2020" /> Uli na masambiro ghanandi nga ni [[anthropoloji]], vyachuma, mbiri, [[geografe ya ŵanthu]], [[umanyi wa ndyali]], sayikoloji, na sosiyoloji.<ref name="Colander2019" /> Mu umanyi wa kakhaliro ka ŵanthu, muli maghanoghano ghanandi ghakupambana agho ghakusazgirika mu [[mapulogilamu gha kafukufuku]] ghakupambana.<ref name="Colander2019" /> Chifukwa cha kusuzga kuchita kuyezgelera kwa ŵanthu ŵanandi panji pa nkhani zakusuzga, ŵasanduzi ŵa kakhaliro ka ŵanthu ŵangagwiliskira ntchito nthowa zinyake nga ni [[nthowa ya mbiri]], [[kusambira chinthu chimoza]], na [[kusambira mitheto yakupambana]]. Kweniso, usange uthenga wa manambala ulipo, ŵasanduzi ŵangagwiliskira ntchito nthowa za masamu kuti ŵapulikiske makora kakhaliro na mendero gha ŵanthu.<ref name="Colander2019" /> === Ndondomeko === [[Formal science|Umanyi wa ndondomeko]] ni chigaŵa cha masambiro icho chikupanga umanyi pakugwiliskira ntchito [[ndondomeko zakukhazikika]].<ref>{{cite web |url=https://my.wlu.edu/the-sciences-at-wandl/formal-sciences |title=Formal Sciences: Washington and Lee University |website=Washington and Lee University |access-date=14 May 2021 |quote=A "formal science" is an area of study that uses formal systems to generate knowledge such as in Mathematics and Computer Science. Formal sciences are important subjects because all of quantitative science depends on them. |archive-date=14 May 2021 |archive-url=https://web.archive.org/web/20210514125428/https://my.wlu.edu/the-sciences-at-wandl/formal-sciences |url-status=live}}</ref><ref name="Löwe2002">{{cite journal |last=Löwe |first=Benedikt |author-link=Benedikt Löwe |year=2002 |title=The formal sciences: their scope, their foundations, and their unity |journal=Synthese |volume=133 |issue=1/2 |pages=5–11 |doi=10.1023/A:1020887832028 |issn=0039-7857 |s2cid=9272212}}</ref><ref name="Rucker2019">{{cite book |last=Rucker |first=Rudy |author-link=Rudy Rucker |url=http://www.rudyrucker.com/infinityandthemind/#calibre_link-328 |title=Infinity and the Mind: The Science and Philosophy of the Infinite |publisher=Princeton University Press |year=2019 |isbn=978-0-691-19138-6 |edition=Reprint |pages=157–188 |chapter=Robots and souls |access-date=11 May 2021 |archive-url=https://web.archive.org/web/20210226212447/http://www.rudyrucker.com/infinityandthemind/#calibre_link-328 |archive-date=26 February 2021 |url-status=live}}</ref> Ndondomeko yakukhazikika ni [[kakhaliro ka vinthu mu mutu]] ako kakugwiliskira ntchito [[fundo zakusimikizga]] kufuma pa [[fundo zakwamba]] kuyana na malango. Ukusazgapo masamu,<ref>{{cite book |last=Tomalin |first=Marcus |year=2006 |title=Linguistics and the Formal Sciences}}</ref><ref>{{Cite journal |title=The Formal Sciences: Their Scope, Their Foundations, and Their Unity |journal=Synthese |volume=133 |pages=5–11 |doi=10.1023/a:1020887832028 |year=2002 |last1=Löwe |first1=Benedikt |issue=1/2 |s2cid=9272212}}</ref> [[fundo ya ndondomeko]], na [[umanyi wa kompyuta]]. Umanyi wa ndondomeko wuli na kukozgana na mirazi yinyake yiŵiri pakugomezga kusambira vinthu mu nthowa yakudunjika na yakutowa. Kweni upambana na umanyi wa kuyezgelera chifukwa ukugomezga chomene kaghanaliro ka mu mutu kwambura kukhumbikwa kwa ukaboni wa maso kuti usimikizge vinthu.<ref name="Fetzer2013" /><ref>{{cite book |first=Thompson |last=Bill |title=The Nature of Statistical Evidence |chapter=2.4 Formal Science and Applied Mathematics |publisher=Springer |series=Lecture Notes in Statistics |volume=189 |year=2007 |page=15}}</ref><ref name="Popper2002" /> Pa chifukwa ichi, pali kupambana maghanoghano usange umanyi uwu ni umanyi nadi.<ref name="Kluwer" /><ref>{{cite book |last1=Bunge |first1=Mario |title=Philosophy of Science: Volume 1, From Problem to Theory |year=1998 |publisher=Routledge |isbn=978-0-7658-0413-6 |edition=revised |volume=1 |location=New York |pages=3–50 |chapter=The Scientific Approach}}</ref> Ndipouli, umanyi wa ndondomeko uli na ntchito yikuru mu umanyi wa kuyezgelera. Chiyelezgero, [[Calculus]] wakambiska kuti munthu apulikiske [[mendero]] mu physics.<ref>{{Cite book |last1=Mujumdar |first1=Anshu Gupta |last2=Singh |first2=Tejinder |year=2016 |chapter=Cognitive science and the connection between physics and mathematics |title=Trick or Truth?: The Mysterious Connection Between Physics and Mathematics |url=https://archive.org/details/trickortruthmyst0000unse |editor-first1=Anthony |editor-last1=Aguirre |editor-first2=Brendan |editor-last2=Foster |series=The Frontiers Collection |pages=[https://archive.org/details/trickortruthmyst0000unse/page/201 201]–218 |location=Switzerland |publisher=Springer |isbn=978-3-319-27494-2}}</ref> Umanyi wa chilengiwa na wa kakhaliro ka ŵanthu uwo ukugomezga chomene masamu ukusazgapo [[physics wa masamu]],<ref>{{cite web |title=About the Journal |url=http://jmp.aip.org/jmp/staff.jsp |archive-url=https://web.archive.org/web/20061003233339/http://jmp.aip.org/jmp/staff.jsp |archive-date=3 October 2006 |access-date=3 October 2006 |website=[[Journal of Mathematical Physics]]}}</ref> [[chemistry wa masamu]],<ref>{{cite book |last=Restrepo |first=G. |chapter=Mathematical chemistry, a new discipline |title=Essays in the philosophy of chemistry |editor-last1=Scerri |editor-first1=E. |editor-last2=Fisher |editor-first2=G. |publisher=Oxford University Press |location=New York |year=2016 |pages=332–351 |isbn=978-0-19-049459-9 |url=https://global.oup.com/academic/product/essays-in-the-philosophy-of-chemistry-9780190494599?cc=de&lang=en& |archive-date=10 June 2021 |access-date=31 May 2022 |archive-url=https://web.archive.org/web/20210610130352/https://global.oup.com/academic/product/essays-in-the-philosophy-of-chemistry-9780190494599?cc=de&lang=en& |url-status=live}}</ref> [[bioloji wa masamu]],<ref>{{Cite web |title=What is mathematical biology |publisher=Centre for Mathematical Biology, University of Bath |url=http://www.bath.ac.uk/cmb/mathBiology/ |archive-url=https://web.archive.org/web/20180923070442/http://www.bath.ac.uk/cmb/mathBiology/ |archive-date=23 September 2018 |access-date=7 June 2018}}</ref> [[vyachuma vya masamu]],<ref>{{cite magazine |last=Johnson |first=Tim |date=1 September 2009 |title=What is financial mathematics? |url=https://plus.maths.org/content/what-financial-mathematics |access-date=1 March 2021 |magazine=+Plus Magazine |archive-date=8 April 2022 |archive-url=https://web.archive.org/web/20220408231344/https://plus.maths.org/content/what-financial-mathematics |url-status=live}}</ref> na [[ekonomiki ya masamu]].<ref>{{cite book |last=Varian |first=Hal |author-link=Hal Varian |year=1997 |chapter=What Use Is Economic Theory? |editor-last1=D'Autume |editor-first1=A. |editor-last2=Cartelier |editor-first2=J. |title=Is Economics Becoming a Hard Science? |publisher=Edward Elgar}} [https://web.archive.org/web/20060625062619/http://www.sims.berkeley.edu/~hal/Papers/theory.pdf Pre-publication]. {{Webarchive|url=https://web.archive.org/web/20060625062619/http://www.sims.berkeley.edu/~hal/Papers/theory.pdf |date=25 June 2006 }}. Retrieved 1 April 2008.</ref> === Kugwiliskira Ntchito === [[Applied science|Umanyi wakugwiliskira ntchito]] ni kukhazikika kwa [[nthowa za umanyi]] na kumanya vinthu kuti ufikepo pa ivyo ukukhumba mu umoyo wa zuŵa na zuŵa, ndipo ukusazgapo vigaŵa nga ni unjinariya na munkhwala.<ref>{{Cite journal |last=Abraham |first=Reem Rachel |year=2004 |title=Clinically oriented physiology teaching: strategy for developing critical-thinking skills in undergraduate medical students |journal=Advances in Physiology Education |volume=28 |issue=3 |pages=102–104 |doi=10.1152/advan.00001.2004 |pmid=15319191 |s2cid=21610124}}</ref><ref name="Bunge1966" /> Unjinariya ni kugwiliskira ntchito fundo za umanyi pakupanga, kuzenga mashini, na luso linyake.<ref>{{cite dictionary |url=https://dictionary.cambridge.org/dictionary/english/engineering |title=Engineering |dictionary=Cambridge Dictionary |publisher=Cambridge University Press |access-date=25 March 2021 |archive-date=19 August 2019 |archive-url=https://web.archive.org/web/20190819030859/https://dictionary.cambridge.org/dictionary/english/engineering |url-status=live}}</ref> Umanyi ungawovya pakupanga luso liphya.<ref>{{Cite journal |last=Brooks |first=Harvey |date=1 September 1994 |title=The relationship between science and technology |url=https://www.belfercenter.org/sites/default/files/files/publication/sciencetechnology.pdf |journal=Research Policy |series=Special Issue in Honor of Nathan Rosenberg |volume=23 |issue=5 |pages=477–486 |doi=10.1016/0048-7333(94)01001-3 |issn=0048-7333 |access-date=14 October 2022 |archive-date=30 December 2022 |archive-url=https://web.archive.org/web/20221230224402/https://www.belfercenter.org/sites/default/files/files/publication/sciencetechnology.pdf |url-status=live}}</ref> Munkhwala ni ntchito ya kupwelelerera ŵalwari mwa kusunga na kuwezgerapo umoyo kwizira mu [[kuvilekeska (munkhwala)|kuvilekeska]], [[kumanya nthenda]], na [[chovwiro|kuchizga]] nthenda panji kupwetekeka.<ref>{{cite book |last=Firth |first=John |title=Oxford textbook of medicine |publisher=Oxford University Press |year=2020 |isbn=978-0-19-874669-0 |chapter=Science in medicine: when, how, and what}}</ref><ref>{{cite journal |last=Saunders |first=J. |date=June 2000 |title=The practice of clinical medicine as an art and as a science |journal=Med Humanit |volume=26 |issue=1 |pages=18–22 |doi=10.1136/mh.26.1.18 |pmid=12484313 |doi-access=free |s2cid=73306806 |pmc=1071282}}</ref> === Yakwamba === Umanyi wakugwiliskira ntchito kanandi ukupambaniskika na [[umanyi wakwamba]], uwo ukulaŵiska chomene pa kusazgirako fundo na malango gha umanyi agho ghakulongosora na kuyowoyerathu ivyo vikuchitika mu chilengiwa.<ref>{{cite journal |last1=Davis |first1=Bernard D. |date=March 2000 |title=Limited scope of science |journal=Microbiology and Molecular Biology Reviews |volume=64 |issue=1 |pages=1–12 |doi=10.1128/MMBR.64.1.1-12.2000 |pmc=98983 |pmid=10704471 |postscript=none}} & "Technology" in {{cite journal |first=Bernard |last=Davis |author-link1=Bernard Davis (biologist) |date=Mar 2000 |title=The scientist's world |journal=[[Microbiology and Molecular Biology Reviews]] |volume=64 |issue=1 |pages=1–12 |doi=10.1128/MMBR.64.1.1-12.2000 |pmc=98983 |pmid=10704471}}</ref><ref>{{cite journal |first=James |last=McCormick |year=2001 |title=Scientific medicine—fact of fiction? The contribution of science to medicine |journal=Occasional Paper (Royal College of General Practitioners) |pages=3–6 |pmc=2560978 |pmid=19790950 |number=80}}</ref> === Kafukufuku wa mlengalenga === {{Excerpt|Blue skies research|paragraphs=1|only=paragraphs|hat=no}} === Pakugwiliskira ntchito makina === [[Computational science|Umanyi wa makina]] ukugwiliskira ntchito [[kuyezgelera kwa pakompyuta]] mu umanyi, icho chikupangiska kupulikiska makora masuzgo gha umanyi kuluska umo masamu pera ghangachitira. Kugwiliskira ntchito [[makina ghakusambira pande]] na [[luso lwakupangika na munthu mu makina]] kukuzgoka chigaŵa chikuru cha wovwiri wa makina mu umanyi, chiyelezgero mu [[vyachuma vyakusanda na makina]], [[makuni ghakupambana gha masamu]], [[kapangiro ka mitu ya nkhani]] na nthowa zinandi zakuyowoyerathu ivyo vichitikenge. Kweni, makina pa ghaŵo ghekha nyengo zinandi ghangasazgirako yayi umanyi chifukwa ghakukhumbikira mulongozgi wa munthu na nkhongono ya kughanaghanira; ndipo ghangasazgirako sankho pa magulu gha ŵanthu panji nyengo zinyake kugwira ntchito pasi pa nkhongono ya munthu.<ref>{{cite journal |last1=Breznau |first1=Nate |year=2022 |title=Integrating Computer Prediction Methods in Social Science: A Comment on Hofman et al. (2021) |journal=Social Science Computer Review |volume=40 |issue=3 |pages=844–853 |doi=10.1177/08944393211049776 |doi-access=free |s2cid=248334446 |url=[suspicious link removed] |access-date=16 August 2023 |archive-date=29 April 2024 |archive-url=https://web.archive.org/web/20240429040922/https://osf.io/adxb3/download |url-status=live}}</ref><ref>{{Cite journal |last1=Hofman |first1=Jake M. |last2=Watts |first2=Duncan J. |author2-link=Duncan J. Watts |last3=Athey |first3=Susan |author3-link=Susan Athey |last4=Garip |first4=Filiz |last5=Griffiths |first5=Thomas L. |author5-link=Tom Griffiths (cognitive scientist) |last6=Kleinberg |first6=Jon |author6-link=Jon Kleinberg |last7=Margetts |first7=Helen |author7-link=Helen Margetts |last8=Mullainathan |first8=Sendhil |author8-link=Sendhil Mullainathan |last9=Salganik |first9=Matthew J. |author9-link=Matthew J. Salganik |last10=Vazire |first10=Simine |author10-link=Simine Vazire |last11=Vespignani |first11=Alessandro |author11-link=Alessandro Vespignani |date=July 2021 |title=Integrating explanation and prediction in computational social science |url=https://www.nature.com/articles/s41586-021-03659-0 |url-status=live |journal=Nature |volume=595 |issue=7866 |pages=181–188 |bibcode=2021Natur.595..181H |doi=10.1038/s41586-021-03659-0 |issn=1476-4687 |pmid=34194044 |archive-url=https://web.archive.org/web/20210925074416/https://www.nature.com/articles/s41586-021-03659-0 |archive-date=25 September 2021 |access-date=25 September 2021 |s2cid=235697917}}</ref> === Kusazga masambiro === [[Interdisciplinary science|Umanyi wakusazga masambiro]] ukusazgapo kusazga masambiro ghaŵiri panji kujumpha kuŵa limoza,<ref>{{cite journal |last=Nissani |first=M. |year=1995 |title=Fruits, Salads, and Smoothies: A Working definition of Interdisciplinarity |url=https://archive.org/details/sim_journal-of-educational-thought_1995-08_29_2/page/121 |journal=The Journal of Educational Thought |volume=29 |issue=2 |pages=121–128 |doi=10.55016/ojs/jet.v29i2.52385 |jstor=23767672}}</ref> nga ni [[bioinformatics]], kusazgika kwa bioloji na umanyi wa kompyuta<ref>{{cite book |url=https://archive.org/details/digitalcodeoflif0000mood |title=Digital Code of Life: How Bioinformatics is Revolutionizing Science, Medicine, and Business |last=Moody |first=G. |year=2004 |isbn=978-0-471-32788-2 |url-access=registration |page=vii |publisher=John Wiley & Sons}}</ref> panji [[umanyi wa kaghanaliro]]. Fundo iyi yaŵako kwamba mu nyengo ya Greece yakale ndipo ikambaso kumanyikwa mu vyaka chitanda cha 20.<ref>{{cite book |last=Ausburg |first=Tanya |title=Becoming Interdisciplinary: An Introduction to Interdisciplinary Studies |url=https://archive.org/details/becominginterdis0000augs |publisher=Kendall/Hunt Publishing |year=2006 |edition=2nd |location=New York}}</ref> == Kafukufuku == Kafukufuku wa umanyi ungathyakika kuŵa kafukufuku wakwamba panji kafukufuku wakugwiliskira ntchito. [[Basic research|Kafukufuku wakwamba]] ni kupenja umanyi ndipo [[applied research|kafukufuku wakugwiliskira ntchito]] ni kupenja nthowa zamazgu ku masuzgo ghakuwoneka pakugwiliskira ntchito umanyi uwu. Kupulikiska vinandi kukufuma mu kafukufuku wakwamba, nangauli nyengo zinyake kafukufuku wakugwiliskira ntchito ukulazga ku masuzgo ghachindunji. Ichi chikupangiska kukura kwa luso ilo pakwamba likaŵa lakusuzga kughanaghanira.<ref>{{cite web |url=http://richarddawkins.net/articles/91 |archive-url=https://web.archive.org/web/20120119113522/http://richarddawkins.net/articles/91 |archive-date=19 January 2012 |title=To Live at All Is Miracle Enough |first=Richard |last=Dawkins |publisher=RichardDawkins.net |date=10 May 2006 |access-date=5 February 2012}}</ref> === Nthowa za umanyi === [[File:The Scientific Method.svg|thumb|Chithuzi chakulongora nthowa za umanyi nga ni [[Scientific method#Elements of the scientific method|ndondomeko yakulutilira]]|alt=Vigaŵa 6 vya nthowa za umanyi mu kamuzingizgi]] Shutterstock Kafukufuku wa umanyi ukusazgapo kugwiliskira ntchito [[scientific method|nthowa za umanyi]], izo zikupenja kulongosora vyakuchitika vya [[chilengiwa]] kwambura sankho mu nthowa iyo [[kuyezgeka so|ingachitika so]].<ref name="di Francia1976">{{cite book |last=di Francia |first=Giuliano Toraldo |chapter=The method of physics |title=The Investigation of the Physical World |url=https://archive.org/details/investigationofp0000tora |publisher=Cambridge University Press |year=1976 |pages=[https://archive.org/details/investigationofp0000tora/page/1 1]–52 |isbn=978-0-521-29925-1 |quote=The amazing point is that for the first time since the discovery of mathematics, a method has been introduced, the results of which have an intersubjective value!}}</ref> Ŵasanduzi kanandi ŵakupokelera fundo zinyake zakwamba izo zikukhumbikwa kuti nthowa za umanyi ziŵe zakwenelera: pali [[unenesko uwo ulipo]] uwo uliupange kwa ŵasanduzi wose; unenesko uwu ukulongozgeka na [[malango gha chilengiwa]]; malango agha ghakasangika kwizira mu [[kuwonelera]] kwakukhazikika na kuyezgelera.<ref name="Heilbron2003" /> Masamu ngakukhumbikwa chomene mu kupanga [[maghanoghano ghakuyezezgeka]], [[fundo za umanyi]], na malango, chifukwa ghakugwiliskira ntchito chomene mu kupanga vipangizgo, kuwonelera, na kusonkhanitsa [[milingo]].<ref name=Popper2002 />{{rp|pp=3-26}} Masamu gha dongo ghakugwiliskira ntchito pakudumura na kusanda uthenga, icho chikuzomerezga ŵasanduzi kupima kugomezgeka kwa ivyo vyasangika mu kuyezgelera.<ref>{{Cite book |last1=Diggle |first1=Peter J. |author-link=Peter Diggle |title=Statistics and Scientific Method: An Introduction for Students and Researchers |url=https://archive.org/details/statisticsscient0000digg |last2=Chetwynd |first2=Amanda G. |author2-link=Amanda Chetwynd |year=2011 |publisher=Oxford University Press |isbn=978-0-19-954318-2 |pages=[https://archive.org/details/statisticsscient0000digg/page/1 1]–2}}</ref> Mu nthowa za umanyi, [[kuyezgelera mu mutu]] panji maghanoghano ghakuyezezgeka ghakuŵikika nga ni malongosolero pakugwiliskira ntchito [[fundo yakudumura vinthu]] ndipo ghakulindilirika kupenja [[kukolerana]] – kuyana na unenesko unyake wakuzomerezgeka wakukhwaskana na ivyo vikuwoneka panji fumbo la umanyi.<ref>{{cite book |last=Wilson |first=Edward |title=Consilience: The Unity of Knowledge |url=https://archive.org/details/consilienceunity0000wils |publisher=Vintage |location=New York |year=1999 |isbn=978-0-679-76867-8}}</ref> Malongosolero agha ghakugwiliskira ntchito pakupanga vinthu ivyo [[vingasangika kuti mbutesi]], ivyo kanandi vikuŵikika pakweru pambere vindayezgeke na kuyezgelera. Kutondeka kwa ivyo vikayowoyerathu mbukaboni wa kukura kwa umanyi.<ref name="di Francia1976" />{{Rp|pages=4–5}}<ref>{{cite book |last=Fara |first=Patricia |author-link=Patricia Fara |year=2009 |chapter=Decisions |title=Science: A Four Thousand Year History |publisher=Oxford University Press |isbn=978-0-19-922689-4 |page=[https://archive.org/details/sciencefourthous00fara/page/408 408] |chapter-url=https://archive.org/details/sciencefourthous00fara/page/306}}</ref> Kuyezgelera nkhwakukhumbikwa chomene mu umanyi kuti kukhozge [[kukolerana kwa vyakuchitika]] kugega [[upusikizgi wa kukozgana kwa vinthu]], nangauli mu umanyi unyake nga ni wa mlengalenga panji wa malibwe, kuwonelera ivyo vikayowoyerathu kungaŵa kwakwenelera chomene.<ref>{{Cite journal |last=Aldrich |first=John |journal=Statistical Science |volume=10 |year=1995 |pages=364–376 |title=Correlations Genuine and Spurious in Pearson and Yule |url=https://archive.org/details/sim_statistical-science_1995-11_10_4/page/364 |jstor=2246135 |doi=10.1214/ss/1177009870 |issue=4 |bibcode=1995StaSc..1009870A |doi-access=free}}</ref> Usange maghanoghano ghakuyezezgeka ghasangika kuti ngakukhorweska yayi, ghakusinthika panji kutayika. Usange maghanoghano agha ghapona pa kuyezgelera, ghangapokelereka mu ndondomeko ya [[scientific theory|fundo ya umanyi]], iyo ni chakuwonelerapo chakukhazikika chakulongosora kakhaliro ka vyakuchitika vinyake vya chilengiwa. Fundo ya umanyi kanandi yikulongosora kakhaliro ka vinthu vinandi chomene kuluska maghanoghano ghakuyezezgeka; kanandi, maghanoghano ghanandi ghangakolerana pamoza na fundo yimoza ya umanyi. Ntheura, fundo ya umanyi ni maghanoghano ghakulongosora maghanoghano ghanyake ghanandi. Mu nthowa yimoza iyi, fundo za umanyi zikupangika kuyana na malango gha umanyi ghakuyana na gha maghanoghano ghakuyezezgeka. Ŵasanduzi ŵangapanga [[Scientific modelling|chakuwonelerapo]], kuyezga kulongosora panji kuwoneska ivyo vikuwoneka mu nthowa ya masamu panji ya thupi, na kupanga maghanoghano ghaphya agho ghangayezgeka na kuyezgelera.<ref>{{cite book |last1=Nola |first1=Robert |last2=Irzik |first2=Gürol |year=2005 |title=Philosophy, science, education and culture |volume=28 |series=Science & technology education library |isbn=978-1-4020-3769-6 |publisher=Springer |pages=207–230}}</ref> Pachita kuyezgelera kuti ŵayezge maghanoghano, ŵasanduzi ŵangaŵa na kakhumbiro ka kuti chinthu chimoza chichitike kuluska chinyake.<ref>{{cite web |last=van Gelder |first=Tim |year=1999 |url=http://www.philosophy.unimelb.edu.au/tgelder/papers/HeadsIWin.pdf |title="Heads I win, tails you lose": A Foray Into the Psychology of Philosophy |publisher=University of Melbourne |access-date=28 March 2008 |archive-url=https://web.archive.org/web/20080409054240/http://www.philosophy.unimelb.edu.au/tgelder/papers/HeadsIWin.pdf |archive-date=9 April 2008}}</ref><ref>{{cite web |last=Pease |first=Craig |date=6 September 2006 |archive-url=https://web.archive.org/web/20100619154617/http://law-and-science.net/Science4BLJ/Scientific_Method/Deliberate.bias/Text.htm |archive-date=19 June 2010 |title=Chapter 23. Deliberate bias: Conflict creates bad science |website=Science for Business, Law and Journalism |publisher=Vermont Law School |url=http://law-and-science.net/Science4BLJ/Scientific_Method/Deliberate.bias/Text.htm}}</ref> Kuwuskapo sankho kungaoneka kwizira mu kachitiro kakweru, [[kapangiro kawemi ka kuyezgelera]], na nthowa ya [[kusanda kwa ŵasanduzi ŵanyake]] pa ivyo vyasangika. Pamanyuma pa kupharazga ivyo vyasangika, ni kakhaliro kakwenelera kuti ŵasanduzi ŵanyake ŵazakaŵereso umo kafukufuku ukayendera, na kuchita kuyezgelera kwakuyana kuti ŵawone usange ivyo vyasangika vingagomezgeka.<ref>{{cite book |first1=Ruth Ellen |last1=Bulger |year=2002 |last2=Heitman |first2=Elizabeth |last3=Reiser |first3=Stanley Joel |title=The Ethical Dimensions of the Biological and Health Sciences |edition=2nd |isbn=978-0-521-00886-0 |publisher=Cambridge University Press}}</ref> Pakuwona kose, nthowa za umanyi zikuzomerezga kumazga masuzgo mu nthowa ya luso uku zikuchepeska sankho na [[kukhozgera maghanoghano gha munthu]]. [[Kusimikizga kwa ŵanthu ŵanandi]], nkhongono ya kufika pa kukolerana na kupangika so kwa ivyo vyasangika, nkhwakukhumbikwa chomene pa kupanga umanyi wose wa umanyi.<ref>{{cite book |last=Ziman |first=John |title=Reliable knowledge: An exploration of the grounds for belief in science |publisher=Cambridge University Press |year=1978c |isbn=978-0-521-22087-3 |pages=[https://archive.org/details/reliableknowledg00john/page/42 42–76] |chapter=Common observation |chapter-url=https://archive.org/details/reliableknowledg00john/page/42}}</ref> === Mabuku === {{Main|Scientific literature|Lists of important publications in science}} [[File:Nature cover, November 4, 1869.jpg|thumb|Chifupi cha nkhani yakwamba ya ''[[Nature (journal)|Nature]]'', 4 Novemba 1869|alt=Lilembo la "NATURE" pakati, na malemba gha umanyi kusi]] Kafukufuku wa umanyi ukupharazgika mu mabuku ghanandi.<ref>{{cite journal |author-link=John Ziman |last=Ziman |first=J. M. |journal=Science |title=The proliferation of scientific literature: a natural process |url=https://archive.org/details/sim_science_1980-04-25_208_4442/page/369 |year=1980 |volume=208 |issue=4442 |pages=369–371 |doi=10.1126/science.7367863 |pmid=7367863 |bibcode=1980Sci...208..369Z}}</ref> [[Scientific journal|Mabuku gha umanyi]] ghakupharazga na kusunga ivyo vyasangika mu kafukufuku uwo ukuchitika mu maunivesite na malo gha kafukufuku, kuŵa nga ni nkhokwe ya umanyi. Mabuku ghakwamba gha umanyi, {{lang|fr|[[Journal des sçavans]]}} kulondezgana na ''[[Philosophical Transactions]]'', ghakamba kupharazgika mu chaka cha 1665. Kufuma nyengo iyo, unandi wa mabuku agha wakulutilira kukura. Mu chaka cha 1981, unandi wa mabuku gha umanyi na luso ukaŵa pafupifupi 11,500.<ref>{{cite book |first1=Krishna |last1=Subramanyam |last2=Subramanyam |first2=Bhadriraju |year=1981 |title=Scientific and Technical Information Resources |publisher=CRC Press |isbn=978-0-8247-8297-9}}</ref> Mabuku ghanandi gha umanyi ghakuyowoya za chigaŵa chimoza cha umanyi; kafukufuku kanandi wakuŵikika mu nthowa ya [[nkhani ya umanyi]]. Umanyi wazara chomene mu magulu gha ŵanthu mazuŵa gano mwakuti nkhwakukhumbikwa kupharazga ivyo vyachitika, uthenga, na makhumbiro gha ŵasanduzi kwa ŵanthu ŵanandi.<ref name="Bush1945">{{cite web |last=Bush |first=Vannevar |date=July 1945 |title=Science the Endless Frontier |url=https://www.nsf.gov/od/lpa/nsf50/vbush1945.htm |url-status=live |archive-url=https://web.archive.org/web/20161107221306/https://www.nsf.gov/od/lpa/nsf50/vbush1945.htm |archive-date=7 November 2016 |access-date=4 November 2016 |publisher=National Science Foundation}}</ref> == Fundo za kaghanaliro == {{anchor|ConjectureAndRefutation}} [[File:Epicycle and deferent.svg|thumb|Kwayana na [[Thomas Kuhn|Kuhn]], kusazgirako [[maghanoghano gha mizere]] mu umanyi wa Ptolemy kukaŵa "umanyi wa bweka" mu ndondomeko yimoza, uku [[The Structure of Scientific Revolutions#Copernican Revolution|Kusintha kwa Copernicus]] kukaŵa kusintha kukuru kwa ndondomeko.|alt=Chithuzi cha mizere ya kuzingilira, apo polaneti yikuzingilira mu nthambo yikuru]] Pali magulu gha kaghanaliro ghakupambana mu [[philosophy of science|fundo za kaghanaliro ka umanyi]]. Kaghanaliro kamanyikwa chomene ni [[empiricism]], ako kakusambizga kuti umanyi ukupangika kwizira mu kuwonelera; fundo za umanyi zikusazga ivyo vikuwonelereka.<ref name=pGS2003 />{{rp|pp=39-56}} Empiricism kanandi yikusazgapo [[inductivism]], iyo yikulongosora umo fundo zikuru zingapangikira kufuma pa ukaboni wa maso uchoko uwo ulipo. Pali nthowa zinandi za empiricism, izo zikumanyikwa chomene ni [[Bayesianism]] na [[hypothetico-deductive method]].<ref name=pGS2003 />{{rp|pp=219-232}} Empiricism yakhala yakupambana na [[rationalism]], kaghanaliro ako pakwamba kakavikilirika na [[Descartes]], ako kakusambizga kuti umanyi ukupangika na nzeru ya munthu, osati na kuwonelera.<ref name=pGS2003 >{{cite book |last=Godfrey-Smith |first=Peter |url=https://archive.org/details/theoryrealityint00godf |title=Theory and Reality: An Introduction to the Philosophy of Science |publisher=University of Chicago |year=2003 |isbn=978-0-226-30062-7 }}</ref>{{rp|pp=19-38}} [[Critical rationalism]] ni nthowa yakupambana ya vyaka chitanda cha 20, iyo yikambika na wakughanaghanira wa ku Austria-Britain [[Karl Popper]]. Popper wakakana nthowa iyo empiricism yikulongosolera kukolerana pakati pa fundo na kuwonelera. Iye wakati fundo zikupangika na kuwonelera yayi, kweni kuwonelera kukuchitika chifukwa cha fundo, ndipo nthowa yekha iyo fundo A yingakhwaskika na kuwonelera ni ''pamanyuma'' pakuti fundo A yagalukira kuwonelera, kweni fundo B yapona pa kuwonelera uko.<ref name=pGS2003/>{{rp|pp=57-74}} Popper wakayowoya kuti malo ghakusimikizga vinthu ghaŵe [[falsifiability]] (kusangika kuŵa utesi) nga ni chimanyikwiro cha fundo za umanyi, kusintha nthowa ya kusanda na nthowa ya kusanga utesi nga ni nthowa ya kafukufuku. Popper wakayowoyaso kuti kuli nthowa yimoza pera pa charu chose, osati ya umanyi pera: nthowa ya kususka, [[kuyezga na kutondeka]], ikusazgapo vyose ivyo nzeru ya munthu yapanga, kusazgapo umanyi, masamu, kaghanaliro, na luso.<ref>{{Cite book |last=Popper |first=Karl |title=Objective Knowledge |url=https://archive.org/details/objectiveknowled0000karl |year=1972}}</ref> Nthowa yinyake, [[instrumentalism]], yikulongora uwemi wa fundo nga ni vipangizgo vyakulongosolera na kuyowoyerathu vyakuchitika. Yikuwona fundo za umanyi nga ni mabokosi ghafifi, apo ivyo vikuŵikikamo (mikhalidwe yakwamba) na ivyo vikufumamo (ivyo vikayowoyerathu) ndivyo ni vyakukhumbikwa. Ivyo vikuchitika, vigaŵa vya fundo, na kapangiro ka maghanoghano vikuyowoyeka kuti ni vinthu ivyo vikwenera kulekeka.<ref>{{cite book |last=Newton-Smith |first=W. H. |url=https://archive.org/details/rationalityofsci0000newt |title=The Rationality of Science |publisher=Routledge |year=1994 |isbn=978-0-7100-0913-5 |location=London |page=[https://archive.org/details/rationalityofsci0000newt/page/30 30] |url-access=registration}}</ref> Pafupi na instrumentalism pali [[constructive empiricism]], kuyana na iyo chimanyikwiro chikuru cha kupambana kwa fundo ya umanyi ni usange icho yikuyowoya pa vinthu ivyo vikuwoneka ni unenesko.<ref>{{cite thesis |last=Votsis |first=I. |year=2004 |title=The Epistemological Status of Scientific Theories: An Investigation of the Structural Realist Account |publisher=University of London, London School of Economics |degree=PhD |page=39}}</ref> [[Thomas Kuhn]] wakayowoya kuti ndondomeko ya kuwonelera na kupima ikuchitika mkati mwa ndondomeko yakukhazikika ya kaghanaliro (paradigm), "chithuzi" cha charu icho chikukolerana na kuwonelera uko kukuchitika. Iye wakati ''umanyi wa bweka'' ni ndondomeko ya kuwonelera na "kumazga fumbo", icho chikuchitika mkati mwa ndondomeko iyo, apo ''umanyi wakusintha vinthu'' ukuchitika apo ndondomeko yimoza yikuwira yinyake mu [[paradigm shift|kusintha kwa kaghanaliro]].<ref>{{Cite encyclopedia |last=Bird |first=Alexander |year=2013 |editor1-last=Zalta |editor1-first=Edward N. |title=Thomas Kuhn |url=http://plato.stanford.edu/archives/fall2013/entries/thomas-kuhn/ |url-status=live |archive-url=https://web.archive.org/web/20200715191833/https://plato.stanford.edu/archives/fall2013/entries/thomas-kuhn/ |archive-date=15 July 2020 |access-date=26 October 2015 |encyclopedia=Stanford Encyclopedia of Philosophy}}</ref> Ndondomeko yiliyose ili na mafumbo ghake, makhumbiro, na malongosolero ghake. Kusankha pakati pa ndondomeko kuli nga nkhuyelezgera "vithuzi" viŵiri panji kujumpha pa charu na kusankha icho chikuwoneka kuti nchakugomezgeka chomene. Kusintha kwa kaghanaliro kukuchitika apo masuzgo ghanandi ghakuwoneka mu ndondomeko yakale ndipo ndondomeko yiphya yikulongosora makora. Ntheura, kusankha ndondomeko yiphya kukuzikira pa kuwonelera, nangauli kuwonelera uko kukuchitika mu chithuzi cha ndondomeko yakale. Kwa Kuhn, kupokelera panji kukana ndondomeko ni kakhaliro ka ŵanthu kukuluka kakhaliro ka maghanoghano. Kweni kaghanaliro ka Kuhn si kaghanaliro ka [[relativism]].<ref>{{Cite book |last=Kuhn |first=Thomas S. |url=https://philpapers.org/rec/KUHTSO-2 |title=The Structure of Scientific Revolutions |publisher=University of Chicago Press |year=1970 |isbn=978-0-226-45804-5 |edition=2nd |page=206 |access-date=30 May 2022 |archive-date=19 October 2021 |archive-url=https://web.archive.org/web/20211019102817/https://philpapers.org/rec/KUHTSO-2 |url-status=live}}</ref> Nthowa yinyake iyo yikuzunulika chomene mu kudumbiskana kwa [[scientific scepticism|kukayikira umanyi]] kususka magulu nga ni "[[creation science|umanyi wa chilengiwa]]" ni [[methodological naturalism]]. Ŵasanduzi ŵa kaghanaliro aka ŵakusimikizga kuti mphaukaboni uŵepo pakati pa chilengiwa na vyamizimu, ndipo umanyi ukwenera kuŵa pa malongosolero gha chilengiwa pera.<ref name=pGS2003 />{{rp|pp=149-162}} Methodological naturalism yikusambizga kuti umanyi ukukhumbikira kulondezga chomene kafukufuku wa [[empirical|ukaboni wa maso]] na kusimikizga kwambura kuthemba chinthu chinyake.<ref>{{cite journal |last=Brugger |first=E. Christian |year=2004 |title=Casebeer, William D. Natural Ethical Facts: Evolution, Connectionism, and Moral Cognition |journal=The Review of Metaphysics |volume=58 |issue=2}}</ref> == Gulu == [[Scientific community|Gulu la umanyi]] ni nthambo ya kukolerana kwa ŵasanduzi awo ŵakuchita kafukufuku wa umanyi. Gulu ili lili na magulu ghachoko awo ŵakugwira ntchito mu vigaŵa vya umanyi. Pakuŵa na [[peer review|kusanda kwa ŵasanduzi ŵanyake]], kwizira mu kudumbiskana mu mabuku na misonkhano, ŵasanduzi ŵakusunga mukhaliro wa nthowa za kafukufuku na kuleka sankho pakulongosora ivyo vyasangika.<ref>{{cite journal |last1=Kornfeld |first1=W. |last2=Hewitt |first2=C. E. |year=1981 |title=The Scientific Community Metaphor |url=http://dspace.mit.edu/bitstream/handle/1721.1/5693/AIM-641.pdf?sequence=2 |journal=IEEE Transactions on Systems, Man, and Cybernetics |volume=11 |issue=1 |pages=24–33 |doi=10.1109/TSMC.1981.4308575 |bibcode=1981ITSMC..11...24K |hdl-access=free |hdl=1721.1/5693 |s2cid=1322857 |access-date=26 May 2022 |archive-date=8 April 2016 |archive-url=https://web.archive.org/web/20160408100757/http://dspace.mit.edu/bitstream/handle/1721.1/5693/AIM-641.pdf?sequence=2 |url-status=live}}</ref> === Ŵasanduzi === [[File:Marie Curie c. 1920s.jpg|thumb|upright=.8|[[Marie Curie]] wakaŵa muntu wakwamba kupokera vyawanangwa viŵiri vya Nobel: [[Nobel Prize in Physics|Physics]] mu chaka cha 1903 na [[Nobel Prize in Chemistry|Chemistry]] mu chaka cha 1911.<ref name="Estreicher1938" />|alt=Chithuzi cha mwanakazi mulara]] Ŵasanduzi ni ŵanthu awo ŵakuchita kafukufuku wa umanyi kuti ŵasazgireko umanyi mu chigaŵa chakukhumbikwa.<ref>{{cite web |url=https://eowilsonfoundation.org/wp-content/uploads/2014/11/the-big-read-eusocial-climbers.pdf |title=Eusocial climbers |publisher=E. O. Wilson Foundation |access-date=3 September 2018 |quote=But he's not a scientist, he's never done scientific research. My definition of a scientist is that you can complete the following sentence: 'he or she has shown that...'," Wilson says. |archive-date=27 April 2019 |archive-url=https://web.archive.org/web/20190427085753/https://eowilsonfoundation.org/wp-content/uploads/2014/11/the-big-read-eusocial-climbers.pdf |url-status=live}}</ref><ref>{{cite web |url=https://sciencecouncil.org/about-science/our-definition-of-a-scientist/ |title=Our definition of a scientist |publisher=Science Council |access-date=7 September 2018 |quote=A scientist is someone who systematically gathers and uses research and evidence, making a hypothesis and testing it, to gain and share understanding and knowledge. |archive-date=23 August 2019 |archive-url=https://web.archive.org/web/20190823135636/https://sciencecouncil.org/about-science/our-definition-of-a-scientist/ |url-status=live}}</ref> Ŵasanduzi ŵangaŵa na khumbiro likuru lakumanya unenesko na kakhumbiro ka kugwiliskira ntchito umanyi wa umanyi kuti ŵawovye umoyo wa ŵanthu, vyaru, vyakuzingilizga, panji mafakitale; vifukwa vinyake ni kumanyikwa na ŵasanduzi ŵanyake na uchindami.<ref name=leeEtal2007/> Mu nyengo zino, ŵasanduzi ŵanandi ŵakusambira vigaŵa vinyake mu [[academic institution|malo gha masambiro ghapachanya]], kanandi ŵakupokera [[terminal degree|madigiri ghapachanya]] mu nthowa iyi.<ref>{{cite journal |last1=Cyranoski |first1=David |last2=Gilbert |first2=Natasha |last3=Ledford |first3=Heidi |last4=Nayar |first4=Anjali |author4-link=Anjali Nayar |last5=Yahia |first5=Mohammed |year=2011 |title=Education: The PhD factory |journal=Nature |volume=472 |issue=7343 |pages=276–279 |doi=10.1038/472276a |pmid=21512548 |bibcode=2011Natur.472..276C |doi-access=free}}</ref> Ŵasanduzi ŵanandi ŵakuchita ntchito mu vigaŵa vyakupambana nga ni mu maunivesite, mafakitale, boma, na magulu ghambura kupanga phindu.<ref name=kwok2017>{{cite journal |last1=Kwok |first1=Roberta |title=Flexible working: Science in the gig economy |journal=Nature |volume=550 |pages=419–421 |doi=10.1038/nj7677-549a |year=2017 |issue=7677 |doi-access=free}}</ref><ref name=woolston2024 >{{cite journal |year=2024 |title=How researchers in remote regions handle the isolation |journal=Nature |url=https://www.nature.com/articles/d41586-024-01523-5 |last1=Woolston |first1=Chris |volume=629 |issue=8014 |pages=1193–1195 |doi=10.1038/d41586-024-01523-5 |pmid=38789626 |bibcode=2024Natur.629.1193W }}</ref><ref name=leeEtal2007>{{cite journal |last1=Lee |first1=Adrian |last2=Dennis |first2=Carina |last3=Campbell |first3=Phillip |year=2007 |title=Nature's guide for mentors |journal=Nature |volume=447 |issue=7677 |pages=791–797 |doi=10.1038/447791a |doi-access=free |pmid=17568738 |bibcode=2007Natur.447..791L }}</ref> Umanyi mwa mbiri waŵa chigaŵa chakuŵalamulika na ŵanalume, nangauli pakaŵa ŵanakazi ŵanyake ŵakuzirwa. Ŵanakazi ŵakumana na sankho likuru mu umanyi, nga umo viliri mu vigaŵa vinyake vya magulu gha ŵanthu ghakulamulika na ŵanalume. Chiyelezgero, ŵanakazi kanandi ŵakaŵanyimanga mwaŵi wa ntchito na kuleka kupika uchindami pa ntchito yawo.<ref>{{cite book |last=Whaley |first=Leigh Ann |title=Women's History as Scientists |url=https://archive.org/details/womenshistoryass0000whal |location=Santa Barbara, CA |publisher=ABC-CLIO |year=2003}}</ref> Ivyo [[women in science|ŵanakazi mu umanyi]] ŵafika navyo vyayowoyeka kuti ni chifukwa cha kukana kukhala mu kakhaliro kaŵo ka mbiri nga mbanchito ŵa pa nyumba.<ref>{{Cite book |last=Spanier |first=Bonnie |title=Im/partial Science: Gender Identity in Molecular Biology |url=https://archive.org/details/impartialscience0000span |publisher=Indiana University Press |year=1995 |isbn=978-0-253-20968-9 |chapter=From Molecules to Brains, Normal Science Supports Sexist Beliefs about Difference}}</ref> === Mawungano gha ŵanthu ŵa vinjeru === [[File:200 y Anniversary of Berlin Academy 1900.jpg|thumb|upright=1.15|Ŵasayansi pa kukwaniska vilimika 200 vya [[Prussian Academy of Sciences]], 1900|left]] [[Learned societies|Mawungano gha ŵanthu ŵa vinjeru]] ghakukolerana na kutandazga maghanoghano gha vinjeru vya chilengiwa na kuyezga vinthu ghaliko kufuma mu nyengo ya kuwuka kwa vinjeru.<ref>{{cite web |last=Parrott |first=Jim |date=9 August 2007 |url=http://www.scholarly-societies.org/1599andearlier.html |title=Chronicle for Societies Founded from 1323 to 1599 |publisher=Scholarly Societies Project |access-date=11 September 2007 |url-status=live |archive-url=https://web.archive.org/web/20140106185404/http://www.scholarly-societies.org/1599andearlier.html |archive-date=6 January 2014}}</ref> Ŵasayansi ŵanandi ŵali mu mawungano gha ŵanthu ŵa vinjeru agho ghakovwira pa nkhani ya luso lwawo, [[profession|mulimo wawo]], panji magulu gha maluso ghakuyana.<ref>{{cite web |url=http://www.esac.ca/about/what-is-a-learned-society/ |title=The Environmental Studies Association of Canada – What is a Learned Society? |access-date=10 May 2013 |archive-url=https://web.archive.org/web/20130529163615/http://www.esac.ca/about/what-is-a-learned-society/ |archive-date=29 May 2013}}</ref> Kuŵa chiŵaro kungaŵa kwa waliyose, panji kukukhumbikwa kuŵa na maukaboni gha vinjeru, panji kusankhika na ŵanthu ŵanji.<ref>{{cite web |url=http://www.britishcouncil.org/science-uk-organisations-learned-societies.htm |title=Learned societies & academies |access-date=10 May 2013 |archive-url=https://web.archive.org/web/20140603140851/http://www.britishcouncil.org/science-uk-organisations-learned-societies.htm |archive-date=3 June 2014}}</ref> Mawungano ghanandi gha vinjeru ni mawupu ghamasambiro agho ghakupenja phindu yayi,<ref>{{Cite web |date=24 June 2019 |title=Learned Societies, the key to realising an open access future? |url=https://blogs.lse.ac.uk/impactofsocialsciences/2019/06/24/learned-societies-the-key-to-realising-an-open-access-future/ |access-date=22 January 2023 |website=Impact of Social Sciences |publisher=London School of Economics |archive-date=5 February 2023 |archive-url=https://web.archive.org/web/20230205140831/https://blogs.lse.ac.uk/impactofsocialsciences/2019/06/24/learned-societies-the-key-to-realising-an-open-access-future/ |url-status=live}}</ref> ndipo ghanandi ni [[professional association|mawungano gha ŵanthu ŵa maluso]]. Milimo yawo kanandi yikusazgapo kuchita [[academic conference|maungano]] ghakukhazikika ghakupeleka na kudumbiskana vinthu viphanya ivyo vasangika pakufufuza, na kusindikiza panji kovwira [[academic journal|mabuku gha maluso]] pa luso lwawo. Mawungano ghanji ghakugwira ntchito nga ni [[professional bodies|mawupu gha maluso]], ghakulongozga milimo ya viŵaro vyawo kuti ŵanthu wose panji viŵaro vose visange chandulo. Kuzgora sayansi kuŵa mulimo wa luso kukayamba mu vilimika vya m'ma 1800, ndipo chovwiro chikuru chikafuma mu kulengeka kwa mawupu ghakumanyikwa gha m'charu chose gha [[academy of sciences|nyumba za vinjeru]] nga ni Italian {{lang|it|[[Accademia dei Lincei]]}} mu 1603,<ref>{{cite web |year=2006 |url=http://positivamente.lincei.it/ |title=Accademia Nazionale dei Lincei |language=it |access-date=11 September 2007 |url-status=live |archive-url=https://web.archive.org/web/20100228005402/http://positivamente.lincei.it/ |archive-date=28 February 2010}}</ref> British [[Royal Society]] mu 1660,<ref>{{cite web |date=7 July 2004 |title=Prince of Wales opens Royal Society's refurbished building |url=http://royalsociety.org/News.aspx?id=973&terms=prince+of+wales |access-date=7 December 2009 |publisher=The Royal Society |archive-date=9 April 2015 |archive-url=https://web.archive.org/web/20150409010143/https://royalsociety.org/News.aspx?id=973&terms=prince+of+wales |url-status=live}}</ref> the [[French Academy of Sciences]] mu 1666,<ref>{{cite web |first=G. G. |last=Meynell |url=http://www.haven.u-net.com/6text_7B2.htm#Appendix%202 |title=The French Academy of Sciences, 1666–91: A reassessment of the French Académie royale des sciences under Colbert (1666–83) and Louvois (1683–91) |access-date=13 October 2011 |url-status=dead |archive-url=https://web.archive.org/web/20120118174108/http://www.haven.u-net.com/6text_7B2.htm#Appendix%202 |archive-date=18 January 2012}}</ref> American [[National Academy of Sciences]] mu 1863,<ref>{{cite web |title=Founding of the National Academy of Sciences |url=http://www7.nationalacademies.org/archives/nasfounding.html |access-date=12 March 2012 |publisher=.nationalacademies.org |archive-date=3 February 2013 |archive-url=https://web.archive.org/web/20130203154802/http://www7.nationalacademies.org/archives/nasfounding.html |url-status=live}}</ref> German [[Kaiser Wilhelm Society]] mu 1911,<ref>{{Cite web |title=The founding of the Kaiser Wilhelm Society (1911) |url=https://www.mpg.de/946619/5_event2-1911 |access-date=30 May 2022 |publisher=Max-Planck-Gesellschaft |archive-date=2 March 2022 |archive-url=https://web.archive.org/web/20220302052520/https://www.mpg.de/946619/5_event2-1911 |url-status=live}}</ref> na [[Chinese Academy of Sciences]] mu 1949.<ref>{{Cite web |title=Introduction |url=https://english.cas.cn/about_us/introduction/201501/t20150114_135284.shtml |access-date=31 May 2022 |website=Chinese Academy of Sciences |archive-date=31 March 2022 |archive-url=https://web.archive.org/web/20220331215338/https://english.cas.cn/about_us/introduction/201501/t20150114_135284.shtml |url-status=live}}</ref> Mawupu gha sayansi gha m'charu chose, nga ni [[International Science Council|Wupu wa Vinjeru wa mu Vyaru Vyose]], ghakuyezgayezga pa nkhani ya [[international cooperation|kukolerana kwa vyaru vyose]] kuti vinjeru vilute panthazi.<ref>{{Cite web |date=5 July 2018 |title=Two main Science Councils merge to address complex global challenges |url=https://en.unesco.org/news/two-main-science-councils-merge-address-complex-global-challenges |access-date=21 October 2018 |publisher=UNESCO |archive-date=12 July 2021 |archive-url=https://web.archive.org/web/20210712044005/https://en.unesco.org/news/two-main-science-councils-merge-address-complex-global-challenges |url-status=live}}</ref> === Vyawanangwa === [[Lists of science and technology awards|Vyawanangwa vya vinjeru]] kanandi vikupelekeka kwa ŵanthu panji mawupu agho ghachita vinthu vikulu mu luso lwawo. Kanandi vikupelekeka na mawupu ghakumanyikwa; ntheura, chikuŵa chinthu cha ulemu ukulu kwa wasayansi uyo wapokera. Kufuma mu nyengo ya kuwuka kwa vinjeru, ŵasayansi kanandi ŵakumanyikwa na vyawanangwa vya mendulo, ndalama, na mazina gha ulemu. Chawanangwa cha Nobel, icho chikumanyikwa chomene m'charu chose, chikupelekeka chaka chilichose kwa awo ŵachita vinjeru viphanya mu vigaŵa vya munkhwala, vya makhaliro gha vinthu, na [[chemistry|luso lwa mankhwala]].<ref>{{cite news |last=Stockton |first=Nick |date=7 October 2014 |title=How did the Nobel Prize become the biggest award on Earth? |newspaper=Wired |url=https://www.wired.com/2014/10/whats-nobel-prize-become-biggest-award-planet |url-status=live |access-date=3 September 2018 |archive-url=https://web.archive.org/web/20190619044702/https://www.wired.com/2014/10/whats-nobel-prize-become-biggest-award-planet/ |archive-date=19 June 2019}}</ref> == Banthu na kukhala kwawo == {{Redirect-distinguish|Science and society|Science & Society|Sociology of scientific knowledge}} === Chovwiro na malango === [[File:NASA-Budget-Federal.svg|thumb|upright=1.4|[[Budget of NASA]] nga ni chiŵerengero cha [[United States federal budget]], apo chikafika pa 4.4% mu 1966 ndipo chayamba kukhira kufuma nyengo iyo|alt=see caption]] [[Funding of science|Chovwiro cha ndalama mu vinjeru]] kanandi chikuchitika mu nthowa ya kuphalizgana umo milimo ya kufufuza yikuwunikika ndipo iyo njakovwira chomene ndiyo yikupokera ndalama. Nthowa izi, izo zikulongozgeka na boma, makampani, panji mawupu ghakupeleka chovwiro, zikugaŵa ndalama zichoko izo ziliko. Chovwiro chose cha kufufuza mu vyaru ivyo [[developed countries|vyatukuka kale]] chili pakati pa 1.5% na 3% ya usambazi wose wa charu.<ref>{{cite web |url=http://www.oecd.org/dataoecd/49/45/24236156.pdf |title=Main Science and Technology Indicators – 2008-1 |publisher=[[OECD]] |archive-url=https://web.archive.org/web/20100215172528/http://www.oecd.org/dataoecd/49/45/24236156.pdf |archive-date=15 February 2010}}</ref> Mu mawupu gha [[OECD]], pafupifupi vigaŵa viŵiri pa vitatu vya [[research and development|kufufuza na kutukuska]] mu vigaŵa vya vinjeru na maluso chikuchitika na makampani, ndipo 20% na 10% chikuchitika na mayunivesite na boma. Chovwiro cha boma mu vigaŵa vinyake ntchikulu chomene, ndipo chikuluska mu kufufuza kwa nkhani za ŵanthu na [[humanities|maluso gha kukhala kwa ŵanthu]]. Mu vyaru ivyo vindatukuke chomene, boma ndilo likupeleka chovwiro chikuru pa nkhani za kufufuza kwa vinjeru vyakwamba.<ref>{{Cite book |url=http://www.oecd-ilibrary.org/science-and-technology/oecd-science-technology-and-industry-scoreboard-2015_sti_scoreboard-2015-en |title=OECD Science, Technology and Industry Scoreboard 2015: Innovation for growth and society |publisher=OECD |year=2015 |isbn=978-92-64-23978-4 |page=156 |doi=10.1787/sti_scoreboard-2015-en |via=oecd-ilibrary.org |access-date=28 May 2022 |archive-date=25 May 2022 |archive-url=https://web.archive.org/web/20220525063455/https://www.oecd-ilibrary.org/science-and-technology/oecd-science-technology-and-industry-scoreboard-2015_sti_scoreboard-2015-en |url-status=live}}</ref> Maboma ghanandi ghali na mawupu ghake ghakovwira pakufufuza vinjeru, nga ni [[National Science Foundation]] ku United States,<ref>{{cite journal |last=Kevles |first=Daniel |year=1977 |title=The National Science Foundation and the Debate over Postwar Research Policy, 1942–1945 |url=https://archive.org/details/sim_isis_1977-03_68_241/page/n5 |journal=Isis |volume=68 |issue=241 |pages=4–26 |doi=10.1086/351711 |pmid=320157 |s2cid=32956693}}</ref> [[National Scientific and Technical Research Council]] ku Argentina,<ref>{{Cite web |title=Argentina, National Scientific and Technological Research Council (CONICET) |url=https://council.science/member/argentina-national-scientific-and-technological-research-council-conicet/ |access-date=31 May 2022 |website=International Science Council |archive-date=16 May 2022 |archive-url=https://web.archive.org/web/20220516220311/https://council.science/member/argentina-national-scientific-and-technological-research-council-conicet/ |url-status=live}}</ref> [[Commonwealth Scientific and Industrial Research Organisation]] ku Australia,<ref>{{Cite news |last=Innis |first=Michelle |date=17 May 2016 |title=Australia to Lay Off Leading Scientist on Sea Levels |work=The New York Times |url=https://www.nytimes.com/2016/05/18/world/australia/australia-to-lay-off-leading-scientist-on-sea-levels.html |url-status=live |url-access=limited |access-date=31 May 2022 |archive-url=https://web.archive.org/web/20210507080237/https://www.nytimes.com/2016/05/18/world/australia/australia-to-lay-off-leading-scientist-on-sea-levels.html |archive-date=7 May 2021 |issn=0362-4331}}</ref> [[National Centre for Scientific Research]] ku France,<ref>{{Cite web |date=20 October 2021 |title=Le CNRS recherche 10.000 passionnés du blob |url=https://www.lefigaro.fr/flash-actu/le-cnrs-recherche-10-000-passionnes-du-blob-20211020 |access-date=31 May 2022 |website=[[Le Figaro]] |language=fr |archive-date=27 April 2022 |archive-url=https://web.archive.org/web/20220427225305/https://www.lefigaro.fr/flash-actu/le-cnrs-recherche-10-000-passionnes-du-blob-20211020 |url-status=live}}</ref> the [[Max Planck Society]] ku Germany,<ref>{{Cite news |last=Bredow |first=Rafaela von |date=18 December 2021 |title=How a Prestigious Scientific Organization Came Under Suspicion of Treating Women Unequally |work=Der Spiegel |url=https://www.spiegel.de/international/germany/how-a-prestigious-scientific-organization-came-under-suspicion-of-treating-women-unequally-a-96da63b5-19af-4fde-b044-445f9cfd6159 |access-date=31 May 2022 |issn=2195-1349 |archive-date=29 May 2022 |archive-url=https://web.archive.org/web/20220529004707/https://www.spiegel.de/international/germany/how-a-prestigious-scientific-organization-came-under-suspicion-of-treating-women-unequally-a-96da63b5-19af-4fde-b044-445f9cfd6159 |url-status=live}}</ref> na [[Spanish National Research Council|National Research Council]] ku Spain.<ref>{{Cite web |date=12 May 2022 |title=En espera de una "revolucionaria" noticia sobre Sagitario A*, el agujero negro supermasivo en el corazón de nuestra galaxia |url=https://www.elmundo.es/ciencia-y-salud/ciencia/2022/05/12/627cca26fdddff17068b4590.html |access-date=31 May 2022 |website=ELMUNDO |language=es |archive-date=13 May 2022 |archive-url=https://web.archive.org/web/20220513185034/https://www.elmundo.es/ciencia-y-salud/ciencia/2022/05/12/627cca26fdddff17068b4590.html |url-status=live}}</ref> Mu milimo ya bizinesi ya kutukuska na kufufuza, makampani ghanandi ghakufwilirapo chomene pa vinthu ivyo vingaguliskika mwaluŵiro kuluska kufufuza uko kuli na chilato cha kumanya waka vinthu. <ref>{{Cite journal |last1=Fletcher |first1=Anthony C. |last2=Bourne |first2=Philip E. |date=27 September 2012 |title=Ten Simple Rules To Commercialize Scientific Research |journal=PLOS Computational Biology |volume=8 |issue=9 |article-number=e1002712 |doi=10.1371/journal.pcbi.1002712 |issn=1553-734X |pmc=3459878 |pmid=23028299 |bibcode=2012PLSCB...8E2712F |doi-access=free}}</ref> [[Science policy|Ndondomeko ya vinjeru]] yikukhwaskana na malango agho ghakukhwaska makhaliro gha ntchito ya vinjeru, kusazgapo [[research funding|chovwiro cha kufufuza]], kanandi pakuya pa vilato vinyake vya boma nga ni kulenga vinthu viphanya vya luso kuti vitukuske katundu wa bizinesi, kulenga vilwero, chovwiro cha vya chipatala, na kulaŵilira chilengiwa. Ndondomeko ya vinjeru nyengo zinyake yikung'anamura nchito ya kugwiliskira ntchito vinjeru vya chilengiwa na kukolerana kwa maghanoghano pa nkhani ya kulenga malango gha boma. Pakuti malango gha boma ghakulaŵilira makhaliro ghawemi gha ŵanthu, chilato cha ndondomeko ya vinjeru nkhuwona umo vinjeru na luso vingawovwilira ŵanthu m'nthowa yiwemi chomene.<ref>{{Cite book |last=Marburger |first=John Harmen III |title=Science policy up close |url=https://archive.org/details/sciencepolicyupc0000marb |date=10 February 2015 |others=Crease, Robert P. |isbn=978-0-674-41709-0 |location=Cambridge, MA |publisher=Harvard University Press}}</ref> Malango gha boma ghangaŵa na nkhongono pa chovwiro cha [[capital equipment|vithandizgo vikulu]] na vinthu vya vinjeru pakufufuza kwa makampani mwa kupeleka mwaŵi wa kukhizga msonkho kwa mawupu agho ghakovwira pakufufuza.<ref name="Bush1945" /> === Kusambizga na kumanyiska === {{Main|2 = Public awareness of science|3 = Science journalism}} [[File:Dinosaur exhibit - Houston Museum of Natural Science - DSC01881.JPG|thumb|upright=1.13|Chiwonetsero cha Dinosaulo pa [[Houston Museum of Natural Science]]]] [[Science education|Masambiro gha vinjeru]] kwa ŵanthu wose ghali mu ndondomeko ya masambiro gha pa sukulu, ndipo ghakusazgirika na [[YouTube in education|vinthu vya masambiro pa Intaneti]] (chiyelezgero, YouTube na Khan Academy), nyumba zakusungiramo vinthu vyakale (museums), na mabuku gha vinjeru. Mawupu ghakulu gha [[scientist|ŵasayansi]] nga ni American Association for the Advancement of Science (AAAS) ghakuwona vinjeru vya chilengiwa nga ni chigaŵa cha masambiro gha maluso ghakuyana na mahala (philosophy) na mbiri (history).<ref>{{cite book |last1=Gauch |first1=Hugh G. |title=Scientific Method in Brief |year=2012 |publisher=Cambridge University Press |location=New York |isbn=978-1-107-66672-6 |pages=7–10}}</ref> Kumanya vya vinjeru kuli na chilato cha kupulikiska [[scientific method|nthowa zakufufuzira]], vithandizgo na nthowa za [[measurement|kupima]], [[empiricism|kugwiliskira ntchito ukaboni wakuwoneka]], kupulikiska vigaŵa vya manambala ([[correlations|kukolerana kwa vinthu]], [[Qualitative research|kawonekero]] na [[Quantitative research|chiŵerengero]]), na kupulikiska vigaŵa vyakwamba vya vinjeru nga ni makhaliro gha vinthu, [[chemistry|luso lwa mankhwala]], [[biology|vinjeru vya vyamoyo]], makhaliro gha chilengiwa, vya malibwe, na [[computation|kugwiliskira ntchito makompyuta]]. Apo mwana akuluta panthazi mu [[formal education|masambiro gha pa sukulu]], ndondomeko yikufika pakuzikira chomene. Masambiro agho ghakumanyikwa chomene mu sukulu ni vinjeru vya chilengiwa na vinjeru vya manambala, nangauli mazuŵa ghano ghakusazgapo vinjeru vya kukhala kwa ŵanthu na vinjeru vyakugwiliskira ntchito luso. <ref>{{Cite journal |last1=Benneworth |first1=Paul |last2=Jongbloed |first2=Ben W. |date=31 July 2009 |title=Who matters to universities? A stakeholder perspective on humanities, arts and social sciences valorisation |journal=Higher Education |volume=59 |issue=5 |pages=567–588 |doi=10.1007/s10734-009-9265-2 |issn=0018-1560 |doi-access=free |url=https://ris.utwente.nl/ws/files/47901538/Benneworth2010Who.pdf |access-date=16 August 2023 |archive-date=24 October 2023 |archive-url=https://web.archive.org/web/20231024214150/https://ris.utwente.nl/ws/files/47901538/Benneworth2010Who.pdf |url-status=live}}</ref> Manyuzipepara na mawayilesi ghali na masuzgo agho ghangatondeska kulongora makora unenesko wa vinjeru ivyo vikupambana mwakuyana na umo ŵasayansi ŵanandi ŵakuvipulikira. Kusankha unenesko uwo uli na nkhongono chomene pa [[scientific debate|kudumbiskana kwa vinjeru]] kungakhumbikwa luso lukulu pa nkhani iyo.<ref>{{cite web |last=Dickson |first=David |date=11 October 2004 |title=Science journalism must keep a critical edge |url=http://www.scidev.net/en/editorials/science-journalism-must-keep-a-critical-edge.html |archive-url=https://web.archive.org/web/20100621053624/http://www.scidev.net/en/editorials/science-journalism-must-keep-a-critical-edge.html |archive-date=21 June 2010 |publisher=Science and Development Network}}</ref> Mbachoko chomene ŵatola nkhani awo ŵali na vinjeru vya sayansi veneko, ndipo nanga ŵangeŵa [[beat reporter|ŵatola nkhani]] awo ŵakumanya nkhani zinyake za vinjeru, ŵangaŵa kuti ŵakumanya yayi nkhani zinyake za vinjeru izo ŵapempheka kuti ŵazilembe mwadzidzi.<ref>{{cite magazine |last=Mooney |first=Chris |date=Nov–Dec 2004 |title=Blinded By Science, How 'Balanced' Coverage Lets the Scientific Fringe Hijack Reality |url=http://blogs.discovermagazine.com/intersection/2010/01/15/blinded-by-science-how-balanced-coverage-lets-the-scientific-fringe-hijack-reality/ |url-status=live |magazine=Columbia Journalism Review |volume=43 |issue=4 |archive-url=https://web.archive.org/web/20100117181240/http://blogs.discovermagazine.com/intersection/2010/01/15/blinded-by-science-how-balanced-coverage-lets-the-scientific-fringe-hijack-reality/ |archive-date=17 January 2010 |access-date=20 February 2008}}</ref><ref>{{cite journal |last1=McIlwaine |first1=S. |last2=Nguyen |first2=D. A. |year=2005 |title=Are Journalism Students Equipped to Write About Science? |url=http://espace.library.uq.edu.au/view/UQ:8064 |url-status=live |journal=Australian Studies in Journalism |volume=14 |pages=41–60 |archive-url=https://web.archive.org/web/20080801163322/http://espace.library.uq.edu.au/view/UQ:8064 |archive-date=1 August 2008 |access-date=20 February 2008}}</ref> [[Science magazines|Mabuku gha vinjeru]] nga ni ''[[New Scientist]]'', ''[[Science & Vie]]'', na ''[[Scientific American]]'' ghakovwira ŵanthu ŵanandi chomene na kupeleka mwakudumura nkhani za kufufuza m'nthowa yipusu, kusazgapo ivyo vasangika viphanya na kukura kwa vinjeru mu vigaŵa vinyake vya kufufuza.<ref>{{cite journal |author-last=Webb |author-first=Sarah |title=Popular science: Get the word out |url=https://archive.org/details/sim_nature-uk_2013-12-05_504_7478/page/177 |journal=Nature |volume=504 |issue=7478 |pages=177–179 |date=December 2013 |pmid=24312943 |doi=10.1038/nj7478-177a |doi-access=free}}</ref> Nkhani za m'maghanoghano (science fiction), chomenechomene [[speculative fiction|nkhani za vyam'tsogolo]], zingatandazga maghanoghano na nthowa za vinjeru kwa ŵanthu wose.<ref>{{Cite web |last=Wilde |first=Fran |author-link=Fran Wilde (author) |date=21 January 2016 |title=How Do You Like Your Science Fiction? Ten Authors Weigh In On 'Hard' vs. 'Soft' SF |url=https://www.tor.com/2016/01/21/how-do-you-like-your-science-fiction-ten-authors-weigh-in-on-hard-vs-soft-sf/ |url-status=live |archive-url=https://web.archive.org/web/20190404025029/https://www.tor.com/2016/01/21/how-do-you-like-your-science-fiction-ten-authors-weigh-in-on-hard-vs-soft-sf/ |archive-date=4 April 2019 |access-date=4 April 2019 |website=Tor.com}}</ref> Kuyezgayezga kwa mazuŵa ghano kwa kukoleraniska vinjeru vya chilengiwa na maluso ghanyake, nga ni mabuku panji ndakatulo, kukusazgapo chinthu cha ''Creative Writing Science'' icho chikapangika kwizira mu [[Royal Literary Fund]].<ref>{{cite web |first=Mario |last=Petrucci |url=http://writeideas.org.uk/creativescience/index.htm |title=Creative Writing – Science |access-date=27 April 2008 |archive-url=https://web.archive.org/web/20090106015539/http://writeideas.org.uk/creativescience/index.htm |archive-date=6 January 2009}}</ref> === Maghanoghano ghakususka vinjeru vya chilengiwa === {{Main|Antiscience}} Nangauli nthowa ya vinjeru yakalika mwa ŵasayansi, vigaŵa vinyake vya ŵanthu vikukana maghanoghano gha vinjeru vinyake panji vikuŵa na kukayika pa nkhani ya vinjeru. Viyelezgero ni maghanoghano ghakumanyikwa akuti [[COVID-19]] ni nthenda yakofya yayi ku US (maghanoghano agha ghakaŵa na 39% ya ŵanthu ŵa ku America mu mwezi wa Ogasiti 2021)<ref>{{Cite web |last1=Tyson |first1=Alec |last2=Funk |first2=Cary |last3=Kennedy |first3=Brian |last4=Johnson |first4=Courtney |date=15 September 2021 |title=Majority in U.S. Says Public Health Benefits of COVID-19 Restrictions Worth the Costs, Even as Large Shares Also See Downsides |url=https://www.pewresearch.org/science/2021/09/15/majority-in-u-s-says-public-health-benefits-of-covid-19-restrictions-worth-the-costs-even-as-large-shares-also-see-downsides/ |access-date=4 August 2022 |website=Pew Research Center Science & Society |archive-date=9 August 2022 |archive-url=https://web.archive.org/web/20220809114234/https://www.pewresearch.org/science/2021/09/15/majority-in-u-s-says-public-health-benefits-of-covid-19-restrictions-worth-the-costs-even-as-large-shares-also-see-downsides/ |url-status=live}}</ref> panji chipulikano chakuti [[climate change|kusinthika kwa nyengo]] nkhwakofya yayi ku US (maghanoghano agho ghakaŵa na 40% ya ŵanthu ŵa ku America, kuumaliro kwa 2019 na kukwambira kwa 2020).<ref>{{Cite web |last=Kennedy |first=Brian |title=U.S. concern about climate change is rising, but mainly among Democrats |url=https://www.pewresearch.org/fact-tank/2020/04/16/u-s-concern-about-climate-change-is-rising-but-mainly-among-democrats/ |access-date=4 August 2022 |website=Pew Research Center |date=16 April 2020 |archive-date=3 August 2022 |archive-url=https://web.archive.org/web/20220803101033/https://www.pewresearch.org/fact-tank/2020/04/16/u-s-concern-about-climate-change-is-rising-but-mainly-among-democrats/ |url-status=live}}</ref> Ŵasayansi ŵa vya maghanoghano (psychologists) ŵalongora vinthu vinyake ivyo vikuchitiska kukana ivyo vinjeru vasanga:<ref>{{Cite journal |last1=Philipp-Muller |first1=Aviva |last2=Lee |first2=Spike W. S. |last3=Petty |first3=Richard E. |date=26 July 2022 |title=Why are people antiscience, and what can we do about it? |journal=Proceedings of the National Academy of Sciences |volume=119 |issue=30 |article-number=e2120755119 |doi=10.1073/pnas.2120755119 |doi-access=free |issn=0027-8424 |pmc=9335320 |pmid=35858405 |bibcode=2022PNAS..11920755P}}</ref> Ŵanthu ŵa mazaza mu vinjeru nyengo zinyake ŵakuwoneka nga mbambura luso, ŵambura kugomezgeka, panji [[academic bias|ŵali na chitemwano]]. Magulu ghanji gha ŵanthu agho [[marginalised|ghatondeka kuŵa na mazaza]] ghali na maghanoghano ghakususka vinjeru, chifukwa chakuti magulu agha nyengo zinandi ghakanyengetereka mu [[Unethical human experimentation|vilingo vyambura ulemu]].<ref>{{cite journal |title=A Test of Three Theories of Anti-Science Attitudes |url=https://archive.org/details/sim_sociological-focus_2008-11_41_4/page/337 |year=2008 |doi=10.1080/00380237.2008.10571338 |last1=Gauchat |first1=Gordon William |journal=Sociological Focus |volume=41 |issue=4 |pages=337–357 |s2cid=144645723}}</ref> Uthenga wakufuma kwa ŵasayansi ungasuska vigomezgo panji makhaliro gha ulemu agho ŵanthu ŵali nawo. Maghanoghano ghakususka vinjeru kanandi ghakuwoneka kuti ghakuchitika chifukwa cha kopa kukanika mu magulu gha ŵanthu. Chiyelezgero, kusinthika kwa nyengo kukuwoneka nga nkhwakofya na 22% ya ŵanthu ŵa ku America awo ŵali ku mbali ya malango ghakale (right side), kweni na 85% ya awo ŵali ku mbali ya malango phanya (left).<ref>{{Cite web |last1=Poushter |first1=Jacob |last2=Fagan |first2=Moira |last3=Gubbala |first3=Sneha |date=31 August 2022 |title=Climate Change Remains Top Global Threat Across 19-Country Survey |url=https://www.pewresearch.org/global/2022/08/31/climate-change-remains-top-global-threat-across-19-country-survey/ |access-date=5 September 2022 |website=Pew Research Center's Global Attitudes Project |archive-date=31 August 2022 |archive-url=https://web.archive.org/web/20220831225832/https://www.pewresearch.org/global/2022/08/31/climate-change-remains-top-global-threat-across-19-country-survey/ |url-status=live}}</ref> Ndiposo, usange m'modzi wa ku mbali ya malango phanya wakuleka kuwona kusinthika kwa nyengo nga nkhwakofya, munthu uyu wanganyoŵeka na kukanika mu gulu ilo. Unenesko ngwakuti, ŵanthu ŵangazomera kukana unenesko wa vinjeru kuluska kutaya panji kuŵika pa ngozi makhaliro ghawo mu gulu lawo.<ref>{{Cite book |last=McRaney |first=David |title=How Minds Change: The Surprising Science of Belief, Opinion, and Persuasion |url=https://archive.org/details/howmindschangesu0000davi |publisher=Portfolio/Penguin |year=2022 |isbn=978-0-593-19029-6 |location=New York}}</ref> === Vyandyale === {{See also|Politicization of science}} [[File:2021 Survey on existence of global warming and responsibility for climate change - bar chart.svg|alt=Result in bar graph of two questions ("Is global warming occurring?" and "Are oil/gas companies responsible?"), showing large discrepancies between American Democrats and Republicans|thumb|[[Public opinion on global warming#United States|Maghanoghano gha ŵanthu pa kuthukira kwa charu mu United States]] kuyana na magulu gha vyandyale<ref>{{cite news |last1=McGreal |first1=Chris |date=26 October 2021 |title=Revealed: 60% of Americans say oil firms are to blame for the climate crisis |work=The Guardian |url=https://www.theguardian.com/environment/2021/oct/26/climate-change-poll-oil-gas-companies-environment |url-status=live |archive-url=https://web.archive.org/web/20211026122356/https://www.theguardian.com/environment/2021/oct/26/climate-change-poll-oil-gas-companies-environment |archive-date=26 October 2021 |quote=Source: Guardian/Vice/CCN/YouGov poll. Note: ±4% margin of error.}}</ref>|upright=1.4]] Maghanoghano pa nkhani ya vinjeru kanandi ghakusankhika na maghanoghano gha vyandyale na vilato. Boma, bizinesi na [[advocacy group|magulu gha vyakukhumba]] ŵakumanyikwa kuti ŵakugwiliskira ntchito malango na ndalama kuti ŵakhwaske ŵafufuzi ŵa vinjeru. Vinthu vinandi vingachitika nga ni vigaŵa vya [[politicisation of science|vinjeru vyakuŵikika mu vyandyale]] nga ni [[anti-intellectualism|kukana ŵanthu ŵa vinjeru]], kuwona nga vigomezgo vya chisopa vili pa ngozi, na kopa kwa bizinesi.<ref>{{cite journal |last1=Goldberg |first1=Jeanne |year=2017 |title=The Politicization of Scientific Issues: Looking through Galileo's Lens or through the Imaginary Looking Glass |url=https://www.csicop.org/si/show/politicization_of_scientific_issues |journal=[[Skeptical Inquirer]] |volume=41 |issue=5 |pages=34–39 |archive-url=https://web.archive.org/web/20180816182350/https://www.csicop.org/si/show/politicization_of_scientific_issues |archive-date=16 August 2018 |access-date=16 August 2018}}</ref> Vinjeru vyakuŵikika mu vyandyale kanandi vikuchitika usange uthenga wa vinjeru ukupelekeka mu nthowa iyo yikulongora kukayika uko kuli pa [[scientific evidence|ukaboni wa vinjeru]].<ref>{{cite journal |last1=Bolsen |first1=Toby |last2=Druckman |first2=James N. |author2-link=James N. Druckman |year=2015 |title=Counteracting the Politicization of Science |journal=Journal of Communication |issue=65 |page=746}}</ref> Nthowa nga ni kusintha nkhani, kutondeka kuzomera unenesko, na kugwiliskira ntchito kukayika pa [[scientific consensus|kukolerana kwa ŵasayansi]] zikugwiliskirika ntchito kuti ŵapokere chitemwa pa maghanoghano agho ghali kukanika kale na ukaboni wa vinjeru.<ref name="Freudenberg2008">{{cite journal |last1=Freudenberg |first1=William F. |last2=Gramling |first2=Robert |last3=Davidson |first3=Debra J. |year=2008 |title=Scientific Certainty Argumentation Methods (SCAMs): Science and the Politics of Doubt |url=http://sciencepolicy.colorado.edu/students/envs_5720/freudenberg_etal_2008.pdf |url-status=live |journal=Sociological Inquiry |volume=78 |issue=1 |pages=2–38 |doi=10.1111/j.1475-682X.2008.00219.x |archive-url=https://web.archive.org/web/20201126214329/http://sciencepolicy.colorado.edu/students/envs_5720/freudenberg_etal_2008.pdf |archive-date=26 November 2020 |access-date=12 April 2020 |doi-access=free}}</ref> Viyelezgero vya nkhani izo zikukhwaska vinjeru vyakuŵikika mu vyandyale ni [[global warming controversy|kudumbiskana kwa kuthukira kwa charu]], [[health effects of pesticides|uheni wa mankhwala gha vinkhumbira pa umoyo]], na [[health effects of tobacco|uheni wa hona pa umoyo]].<ref name="Freudenberg2008" /><ref>{{cite journal |last1=van der Linden |first1=Sander |last2=Leiserowitz |first2=Anthony |last3=Rosenthal |first3=Seth |last4=Maibach |first4=Edward |year=2017 |title=Inoculating the Public against Misinformation about Climate Change |url=https://www.repository.cam.ac.uk/bitstream/1810/270860/1/global%20challenges.pdf |url-status=live |journal=Global Challenges |volume=1 |issue=2 |page=1 |doi=10.1002/gch2.201600008 |pmc=6607159 |pmid=31565263 |bibcode=2017GloCh...100008V |archive-url=https://web.archive.org/web/20200404185312/https://www.repository.cam.ac.uk/bitstream/handle/1810/270860/global%20challenges.pdf?sequence=1 |archive-date=4 April 2020 |access-date=25 August 2019}}</ref> === Masuzgo === {{See also|Criticism of science|Academic bias}} [[replication crisis|Suzgo la kutondeka kuwirizga]] ni suzgo ilo lichilipo mu [[methodological|nthowa zakufufuzira]] ilo likukhwaska vigaŵa vya vinjeru vya [[social science|kukhala kwa ŵanthu]] na [[life science|vinjeru vya vyamoyo]]. Mu kufufuza kwinyake, ivyo vasangika mu masambiro ghanandi gha vinjeru vyalongoreka kuti [[reproducibility|vingawirizgika yayi]].<ref>{{Cite journal |doi=10.1038/515009a |title=Metascience could rescue the 'replication crisis' |url=https://archive.org/details/sim_nature-uk_nature_2014-11-06_515_7525/page/n19 |journal=Nature |volume=515 |issue=7525 |page=9 |year=2014 |last1=Schooler |first1=J. W. |pmid=25373639 |bibcode=2014Natur.515....9S |doi-access=free}}</ref> Suzgo ili lili na misisi yakale; lizina ili likapelekeka kukwambira kwa vilimika vya m'ma 2010<ref>{{Cite journal |doi=10.1177/1745691612465253 |title=Editors' Introduction to the Special Section on Replicability in Psychological Science: A Crisis of Confidence? |journal=Perspectives on Psychological Science |volume=7 |issue=6 |pages=528–530 |year=2012 |last1=Pashler |first1=Harold |last2=Wagenmakers |first2=Eric Jan |pmid=26168108 |s2cid=26361121 |doi-access=free}}</ref> nga ni chigaŵa cha kumanya kukuru kwa suzgo ili. Suzgo la kutondeka kuwirizga likulongora chigaŵa chakuzirwa cha kufufuza mu [[metascience|vinjeru vya vinjeru]], icho chili na chilato cha kunozga makhaliro gha kufufuza kose kwa vinjeru kwinaku chikukhizga kusakaza. <ref>{{Cite journal |last1=Ioannidis |first1=John P. A. |last2=Fanelli |first2=Daniele |last3=Dunne |first3=Debbie Drake |last4=Goodman |first4=Steven N. |date=2 October 2015 |title=Meta-research: Evaluation and Improvement of Research Methods and Practices |journal=PLOS Biology |volume=13 |issue=10 |pages=–1002264 |doi=10.1371/journal.pbio.1002264 |pmid=26431313 |pmc=4592065 |issn=1545-7885 |doi-access=free}}</ref> Mazgu ghakuti [[scientific misconduct|makhaliro ghaheni mu vinjeru]] ghakung'anamura nyengo izo ŵafufuzi ŵakugolozga unenesko wa ivyo ŵasangapo mwadala, panji kupeleka ulemu wa chinthu icho chasangika kwa munthu uyo wandachichite mwakukhumba.<ref>{{cite journal |title=Coping with fraud |journal=The COPE Report 1999 |pages=11–18 |url=http://www.publicationethics.org.uk/reports/1999/1999pdf3.pdf |archive-url=https://web.archive.org/web/20070928151119/http://www.publicationethics.org.uk/reports/1999/1999pdf3.pdf |quote=It is 10 years, to the month, since Stephen Lock ... Reproduced with kind permission of the Editor, The Lancet. |archive-date=28 September 2007 |url-status=usurped |access-date=21 July 2011}}</ref> Chigaŵa cha masambiro panji maghanoghano agho ghakujizgora kuŵa nga ni vinjeru vya chilengiwa kuti ghawoneke nga ngaunenesko kweni ndimo ghaliri yayi, nyengo zinyake ghakuchemeka kuti [[pseudoscience|vinjeru vyautesi]], [[fringe science|vinjeru vya m'mbali]], panji [[junk science|vinjeru vyambura ntchito]].<ref>{{cite encyclopedia |url=https://plato.stanford.edu/archives/fall2021/entries/pseudo-science |title=Science and Pseudoscience |at=Section 2: The "science" of pseudoscience |encyclopedia=Stanford Encyclopedia of Philosophy |first1=Sven Ove |last1=Hansson |editor-last=Zalta |editor-first=Edward N. |date=3 September 2008 |access-date=28 May 2022 |archive-date=29 October 2021 |archive-url=https://web.archive.org/web/20211029205141/https://plato.stanford.edu/archives/fall2021/entries/pseudo-science/ |url-status=live}}</ref><ref>{{cite book |last=Shermer |first=Michael |author-link=Michael Shermer |year=1997 |title=Why people believe weird things: pseudoscience, superstition, and other confusions of our time |url=https://archive.org/details/isbn_9780965594875 |url-access=registration |location=New York |publisher=W. H. Freeman & Co. |isbn=978-0-7167-3090-3 |page=17}}</ref> Wasayansi [[Richard Feynman]] wakapanga chizina chakuti "[[cargo cult science|vinjeru vyakuyezgera waka]]" pa nkhani izo ŵafufuzi ŵakugomezga, ndipo pakuŵala ŵakuwoneka nga ŵakuchita sayansi, kweni ŵalije unenesko wakuti ivyo ŵasangapo viwunnikike makora na ŵanji.<ref>{{cite web |url=http://neurotheory.columbia.edu/~ken/cargo_cult.html |title=Cargo Cult Science |last=Feynman |first=Richard |year=1974 |website=Center for Theoretical Neuroscience |publisher=Columbia University |archive-url=https://web.archive.org/web/20050304032544/http://neurotheory.columbia.edu/~ken/cargo_cult.html |archive-date=4 March 2005 |access-date=4 November 2016}}</ref> Nthowa zakupambanapambana zakusatsira malonda, kufuma pa kukulisha nkhani kufika pa uuryezi, zingaŵa mu vigaŵa ivi. Vinjeru vya chilengiwa vyalongosoreka nga ni "chiŵiya chakuzirwa chomene" pakupatula unenesko ku utesi.<ref>{{Cite book |last=Novella |first=Steven |title=The Skeptics' Guide to the Universe: How to Know What's Really Real in a World Increasingly Full of Fake |title-link=The Skeptics' Guide to the Universe (book) |publisher=Hodder & Stoughton |year=2018 |isbn=978-1-4736-9641-9 |page=[https://archive.org/details/skepticsguidetou0000nove/page/162 162] |author-link=Steven Novella}}</ref> Nyengo zinyake, kufufuza kungaŵa na chilato chiwemi kweni kungaŵa kwakubudika, kwachikale, kwambura kukwana, panji kulongosora vinjeru m'nthowa yipusu chomene yakujumpha muyero. Paliso chigaŵa cha [[political bias|kutemwera vya ndale]] panji maghanoghano ghakuŵa ku mbali yimoza mu vinjeru. Ŵasayansi mu vyaru vinyake ŵasangika kuti ŵali na chitemwano pa nkhani ya [[political party|vipani vya ndale]] pakuyaniska na ŵanthu bweka.<ref name="y499">{{cite journal | last1=Duarte | first1=José L. | last2=Crawford | first2=Jarret T. | last3=Stern | first3=Charlotta | last4=Haidt | first4=Jonathan | last5=Jussim | first5=Lee | last6=Tetlock | first6=Philip E. | title=Political diversity will improve social psychological science | journal=Behavioral and Brain Sciences | volume=38 | date=2015 | issn=0140-525X | doi=10.1017/S0140525X14000430 | url=https://www.cambridge.org/core/product/identifier/S0140525X14000430/type/journal_article | access-date=2026-02-12 | page=}}</ref> == Wonaniso ivi == [[List of scientific occupations|Mndandanda wa milimo ya sayansi]] [[List of years in science|Mndandanda wa vilimika mu sayansi]] [[v:Science|Vinjeru vya Chilengiwa]] (Wikiversity) [[Scientific integrity|Unenesko mu vinjeru]] == Mazgu ghanyake == {{notelist}} == Ukaboni == {{Reflist}} == Mahamba ghakuwaro == {{Wiktionary|science}} {{Philosophy of science}} {{Science and the public}} {{Glossaries of science and engineering}} {{Science and technology studies}} {{Subject bar|auto=1|portal1=Science}} {{Authority control}} [[Category:Vinjeru vya Chilengiwa| ]] [[Category:Kulaŵiska na Kuwona]] [[Category:Nkhani zikulu]] [[Category:Kufumbilira]] [[Category:Milimo ya ŵanthu]] eh62mve77jxe4bz9wcc581rlqsu7y5l 3 47402 122211 122208 2026-09-21T19:00:32Z Anthonymunthali44 5642 /* Legacy and emergency */ Zgolo 122211 wikitext text/x-wiki <center><big>⚠️ Do you want articles translated? Go to [[User:Viyowoyero-vya-Malaŵi/TranslateCentral|TranslateCentral]] and follow the formats given. ⚠️</big></center> {{VvM Talk 1}} {{Archives}} == congrats! == Hi @[[User:Viyowoyero-vya-Malaŵi|Viyowoyero-vya-Malaŵi]], You currently appear as Mulembi wa Mwezi on the Tumwiki Main Page. 🎉 This is an automatic system, not a manually selected award. The gadget checks editors' contributions during the previous 30 days and identifies the registered editor with the highest number of qualifying article edits. The current criteria are: * registered editors only; * edits in the main/article namespace; * contributions from the previous 30 days; * bot edits are excluded; * anonymous/IP edits are excluded; * obvious undo/rollback edits are excluded where they can be identified. The result is calculated automatically, so whoever meets the criteria at the time is displayed on the Main Page. Your name appeared first under the current calculation. Congratulations, and yewo chomene for your contributions to Tumwiki! 🎉 [[user:Tumbuka Arch|<span style='color: #FFFFFF;background-color: #191970;'>'''''Tumbuka Arch'''''</span>]][[user talk:Tumbuka Arch|'''<span style='color: #B20000;background-color: #FFFFFF;'>^★_★^★</span>''']] 21:02, 7 Lupya 2026 (UTC) == <span lang="en" dir="ltr">Tech News: 2026-38</span> == <div lang="en" dir="ltr"> <section begin="technews-2026-W38"/><div class="plainlinks"> Latest '''[[m:Special:MyLanguage/Tech/News|tech news]]''' from the Wikimedia technical community. Please tell other users about these changes. Not all changes will affect you. [[m:Special:MyLanguage/Tech/News/2026/38|Translations]] are available. '''Weekly highlight''' * The Future Audiences team has started a [[en:Special:MyLanguage/Wikipedia:Village pump (proposals)#New proposed experiment to let readers know about “Google preferred sources”|discussion on English Wikipedia]] about a proposed new experiment to show a temporary notice about the new [https://blog.google/products-and-platforms/products/search/original-high-quality-content-search/ Google Preferred Sources] feature to Wikipedia readers coming from Google. The experiment is to test whether this notice makes visitors come back to Wikipedia more often. Preferred Sources feature lets users choose websites they trust so Google can highlight content from those sources more prominently in Search and AI experiences. We are interested in testing this on other languages that Google supports and would welcome assistance with starting conversations on other wikis. If interested, please reach out to Future Audiences on the [[m:Special:MyLanguage/Future Audiences/Preferred sources|talk page]]. '''Updates for editors''' * The chat platform Discord is releasing a new self-service framework that websites can use to specify how their links should look when shared on Discord. The Future Audiences team is planning to start using this new framework to improve how Wikipedia links look when shared on Discord, giving better attribution and credit to contributors. The link appearance and behavior won't change in the first phase of this project as we want to first collect some baseline data to assess the impact of future changes. However, if community members who are active on Discord spot any issues, they can reach out on [[phab:tag/future-audiences/|Phabricator]] or [[m:Special:MyLanguage/Future Audiences|Metawiki]]. * The Reader Growth team will be running an experiment to test whether [[mw:Special:MyLanguage/Readers/Reader_Growth/Compact Lead|compacting article lead sections on mobiles]] with the addition of a "read more" button improves reader retention. The test will begin on September 17 on Arabic, Spanish, French, Indonesian, Italian, Japanese, Portuguese, Vietnamese, and Chinese Wikipedias and will run for four weeks. * All wikis will be [[m:Special:MyLanguage/Tech/Server switch|read-only for a few minutes]] on September 23. This is planned at 14:00 UTC. More information will be published in Tech News and will also be posted on individual wikis in the coming week. [https://phabricator.wikimedia.org/T433363] * [[File:Reload icon with two arrows.svg|12px|link=|class=skin-invert|Recurrent item]] View all {{formatnum:28}} community-submitted {{PLURAL:28|task|tasks}} that were [[m:Special:MyLanguage/Tech/News/Recently resolved community tasks|resolved last week]]. For example, an issue where [https://wikistats.wmcloud.org/ Wikistats] for Wikipedias was returning an HTTP 500 error and could not be reached, has now been fixed. [https://phabricator.wikimedia.org/T435959] '''Updates for technical contributors''' * Developers who maintain a tool that queries the Wikimedia Commons links tables need to update their code to connect to the new x4 database cluster. The links tables have been moved from the s4 cluster to x4, and will no longer receive updates on s4. The page and redirect tables remain available on both clusters. A wiki replica for the x4 cluster will be set up afterwards. The change is being made because the s4 cluster has grown too large to operate efficiently. You can [[wikitech:Special:MyLanguage/News/2026 Commons links tables database split|read more]]. * [[File:Reload icon with two arrows.svg|12px|link=|class=skin-invert|Recurrent item]] Detailed code updates later this week: [[mw:MediaWiki 1.47/wmf.20|MediaWiki]] '''''[[m:Special:MyLanguage/Tech/News|Tech news]]''' prepared by [[m:Special:MyLanguage/Tech/News/Writers|Tech News writers]] and posted by [[m:Special:MyLanguage/User:MediaWiki message delivery|bot]]&nbsp;• [[m:Special:MyLanguage/Tech/News#contribute|Contribute]]&nbsp;• [[m:Special:MyLanguage/Tech/News/2026/38|Translate]]&nbsp;• [[m:Tech|Get help]]&nbsp;• [[m:Talk:Tech/News|Give feedback]]&nbsp;• [[m:Global message delivery/Targets/Tech ambassadors|Subscribe or unsubscribe]].'' </div><section end="technews-2026-W38"/> </div> <bdi lang="en" dir="ltr">[[User:MediaWiki message delivery|MediaWiki message delivery]]</bdi> 15:31, 14 Lupya 2026 (UTC) <!-- Message sent by User:STei (WMF)@metawiki using the list at https://meta.wikimedia.org/w/index.php?title=Global_message_delivery/Targets/Tech_ambassadors&oldid=31039826 --> == welcome to abstract wikipedia == Your articles about languages and cities are well done! [[User:ReXLer|ReXLer]] ([[User talk:ReXLer|pakuchezgela]]) 15:41, 18 Lupya 2026 (UTC) :Thank you! I will continue to make more to help AW grow! '''''[[User:Viyowoyero-vya-Malaŵi|Viyowoyero-vya-Malaŵi]]'''''[[User talk:Viyowoyero-vya-Malaŵi|'''<span style='color: #00008b;background-color: #FFFFFF;'>_★^★_★</span>''']] 00:41, 19 Lupya 2026 (UTC) == Legacy and emergency == @[[User:Viyowoyero-vya-Malaŵi|Viyowoyero-vya-Malaŵi]] Hello, if you see that I am not active for more than 4 months, it means that something is wrong as I am far from home (country). Since you are one of the users I can trust on this wiki, along native @[[User:Anthonymunthali44|Anthonymunthali44]] who doesn't know much about templates and how home page works, I will leave this with you. If you see that the home page is broken or the home is showing broken links of templates, such as red links with dates or month, please update it. If you see that the home is entirely gone, you can use any of these '''emergency stable basic backup interface ''' diffs: <br> [https://tum.wikipedia.org/w/index.php?title=Jani_likulu&oldid=26301 1,] <br> [https://tum.wikipedia.org/w/index.php?title=Jani_likulu&oldid=24431 2,] <br> [https://tum.wikipedia.org/w/index.php?title=Jani_likulu&oldid=105397 3,] <br> [https://tum.wikipedia.org/w/index.php?title=Jani_likulu&oldid=108878 4,] <br> [https://tum.wikipedia.org/w/index.php?title=Jani_likulu&oldid=109763 5,] <br> Our needed home page is located [[Chikaya chikulu 9 demo|here]], which is currently down. How to fix the current broken page? Since it says: <br> [[Wikipedia:Nkhani yamwahuno mu ChiTumbuka/Lupya/19]], etc, them move the page [[Wikipedia:Nkhani yamwahuno mu ChiTumbuka/Sekutembala/19]] into [[Wikipedia:Nkhani yamwahuno mu ChiTumbuka/Lupya/19]] them move the page [[Wikipedia:Nkhani yamwahuno mu ChiTumbuka/Sekutembala/19]]. You only need to change the month name, nothing else. And importantly, leave a redirect behind as an alternative, don't delete the behind page. If you do that, you can see changes [[Chikaya chikulu 9 demo|here]], and not on main page, unless you swap it with [https://tum.wikipedia.org/w/index.php?title=Template:Vyose&oldid=120042 this revision]. Yewo chomene. [[user:Tumbuka Arch|<span style='color: #FFFFFF;background-color: #191970;'>'''''Tumbuka Arch'''''</span>]][[user talk:Tumbuka Arch|'''<span style='color: #B20000;background-color: #FFFFFF;'>^★_★^★</span>''']] 09:28, 19 Lupya 2026 (UTC) :Ok, its a lot of work to do, I can't be certain I'd get it all done, but I'll try. Yewo chomene. '''''[[User:Viyowoyero-vya-Malaŵi|Viyowoyero-vya-Malaŵi]]'''''[[User talk:Viyowoyero-vya-Malaŵi|'''<span style='color: #00008b;background-color: #FFFFFF;'>_★^★_★</span>''']] 09:32, 19 Lupya 2026 (UTC) :@[[User:Tumbuka Arch|Tumbuka Arch]] Also, can you give me a list of English months and Tumbuka months? I know I previously asked but I really want to know. Yewo chomene. '''''[[User:Viyowoyero-vya-Malaŵi|Viyowoyero-vya-Malaŵi]]'''''[[User talk:Viyowoyero-vya-Malaŵi|'''<span style='color: #00008b;background-color: #FFFFFF;'>_★^★_★</span>''']] 09:37, 19 Lupya 2026 (UTC) :Alright thank you will work on that. Hope your situation gets better whatever it is. And thank you for the message you left me a few weeks back. I saw it just forgot to respond. [[User:Anthonymunthali44|Anthonymunthali44]] ([[User talk:Anthonymunthali44|pakuchezgela]]) 19:00, 21 Lupya 2026 (UTC) == Wikipedia translation of the week: 2026-39 == <div lang="en" dir="ltr" style="width:100%; margin:0; background: var(--background-color-neutral-subtle,#f8f9fa); border:1px solid var(--border-color-base,#BBBBBB); padding .4em;color: inherit;"> <div style="text-align:center;">The winner this [[m:Translation of the week/2026 translations|Translation of the week]] is <div style="font-size:140%;">'''[[:en:Scotty (dinosaur)]]'''<br /> </div> Please be bold and help translate this article! </div> ---- [[File:Scotty Tyrannosaurus.jpg|300px|center|]] <div style="text-align:left; padding: .4em;"> '''Scotty''' is the nickname for the Tyrannosaurus rex fossil, catalogued as RSM P2523.8, that was discovered in Saskatchewan, Canada in 1991.[3] The fossilised remains were painstakingly removed, almost completely by hand, over two decades from the rock in which they were embedded. When the preparation was complete in 2011, an around 65% complete T. rex skeleton was revealed. <small>(Please update the interwiki links on [[d:|Wikidata]] of your language version of the article after each week's translation is finished so that all languages are linked to each other.)</small> ---- [[File:TOTW.svg|24px|]] ''[[m:Translation of the week|About]] · '''[[m:Translation of the week/Translation candidates|Nominate/Review]]''' · [[m:Translation of the week/MassMessage|Subscribe/Unsubscribe]] · [[m:MassMessage|Global message delivery]]'' </div> </div> --[[User:MediaWiki message delivery|MediaWiki message delivery]] ([[User talk:MediaWiki message delivery|pakuchezgela]]) 02:02, 21 Lupya 2026 (UTC) <!-- Message sent by User:Shizhao@metawiki using the list at https://meta.wikimedia.org/w/index.php?title=Translation_of_the_week/MassMessage&oldid=31045260 --> p54lymijnu7n9a6dlvokhz3bedsh3rs 0 48169 122212 118043 2026-09-21T23:59:15Z InternetArchiveBot 6449 Add 1 book for [[en:Wikipedia:Verifiability|verifiability]] (20260921sim)) #IABot (v2.0.9.6) ([[User:GreenC bot|GreenC bot]] 122212 wikitext text/x-wiki {{Revision}} Fupa la '''Lebombo''' ni [[chida cha fupa]] icho chikapangika kufuma ku [[fibula]] ya nyani (baboon) ndipo chili na malemba ghakujobeka agho ghakasangika mu [[Pango la Border]] mu [[Mapiri gha Lebombo]] agho ghali pakati pa [[South Africa]] na [[Eswatini]].<ref>{{cite journal |last1=Beaumont |first1=Peter B. |year=1973 |title=Border Cave – A Progress Report |journal=[[South African Journal of Science]] |volume=69 |pages=41–46}}</ref> Kusintha kwa vigaŵa vya malo agho ghakajobekeka kukulongora kuti pakagwiliskirika ntchito mphonje zakupambana zakudulira. Munthu uyo wakasanga fupa ili, Peter Beaumont, wakuwona kuti ichi ntchisimikizgo chakuti malemba agha, nga ni malemba ghanyake agho ghakusangika pa charu chose, ghakapangika apo ŵanthu ŵakachitanga [[miyambo ya chisopa]]. Fupa ili lili pafupifupi masentimita 8<ref>{{cite web |last=Bruderer |first=Herbert |title=Technical Marvels, Part 2: Lebombo and Ishango Bones |url=https://cacm.acm.org/blogcacm/technical-marvels-part-2-lebombo-and-ishango-bones/ |website=Communications of the ACM |date=7 June 2024 |access-date=7 April 2026}}</ref> kutalika, ndipo lili na vyaka vyapakati pa 42,000 na 43,000, mwakuyana na vipimo 24 vya [[radiocarbon dating|kupima msinkhu wa radiocarbon]].<ref>Likuyowoyeka kuti ni fupa la mabowo, lakulongoreka mu Chithuzi 1, ''12'' cha {{cite journal |title=Early evidence of San material culture represented by organic artifacts from Border Cave, South Africa |url=https://archive.org/details/sim_proceedings-of-the-national-academy-of-sciences-usa_2012-08-14_109_33/page/n91 |doi=10.1073/pnas.1204213109 |volume=109 |issue=33 |journal=Proceedings of the National Academy of Sciences |pages=13214–13219 |year=2012 |last1=d'Errico |first1=F. |last2=Backwell |first2=L. |last3=Villa |first3=P. |last4=Degano |first4=I. |last5=Lucejko |first5=J. J. |last6=Bamford |first6=M. K. |last7=Higham |first7=T. F. G. |last8=Colombini |first8=M. P. |last9=Beaumont |first9=P. B. |pmc=3421171 |pmid=22847420|bibcode=2012PNAS..10913214D |doi-access=free |quote=[Layer] 1BS Lower B-C [is dated] between 43 ka and 42 ka.}}</ref> Ichi ntchakale chomene kuluska [[fupa la Ishango]] ilo nyengo zinyake ŵakulipambaniska nalo. Maufupa ghanyake agho ghali na mabowo ghali na vyaka 80,000, kweni vikumanyikwa makora yayi usange mabowo agha ghakaŵa gha kupangika waka chifukwa cha uyo wakakhumbanga kupangiska ulemu panji ghakaŵa na ntchito yakwambura kumanyikwa.<ref>{{cite journal |last1=Vogelsang|first1=Ralf|last2=Richter|first2=Jürgen|last3=Jacobs|first3=Zenobia|last4=Eichhorn|first4=Barbara|last5=Linseele|first5=Veerle|last6=Roberts|first6=Richard G.|display-authors=etal |title=New Excavations of Middle Stone Age Deposits at Apollo 11 Rockshelter, Namibia: Stratigraphy, Archaeology, Chronology and Past Environments |journal=[[Journal of African Archaeology]] |year=2010 |volume=8 |issue=2 |pages=185–218 |doi=10.3213/1612-1651-10170 |url=https://www.academia.edu/4106767}}</ref> Ŵanthu ŵakughanaghana kuti fupa ili likaŵa [[chida cha kuŵerengera]] (tally stick).<ref>{{cite journal | doi=10.1098/rstb.2016.0518 | title=From number sense to number symbols. An archaeological perspective | date=2018 | last1=d'Errico | first1=Francesco | last2=Doyon | first2=Luc | last3=Colagé | first3=Ivan | last4=Queffelec | first4=Alain | last5=Le Vraux | first5=Emma | last6=Giacobini | first6=Giacomo | last7=Vandermeersch | first7=Bernard | last8=Maureille | first8=Bruno | journal=Philosophical Transactions of the Royal Society B: Biological Sciences | volume=373 | issue=1740 | pmid=29292345 | pmc=5784044 }}</ref> ==Wonani so== *[[Mbiri ya masamu]] *[[Mikuni ya kuŵerengera]] *[[Fupa la Ishango]] ==Mabuku gha umo vyafumira== {{Reflist|2}} ==Maulalo ghakuwalo== *[https://afrolegends.com/2019/05/17/the-lebombo-bone-the-oldest-mathematical-artifact-in-the-world/ Vithuzi vya Fupa la Lebombo pa African Heritage] {{Prehistoric technology|state=expanded}} [[Category:Vyakugwiliskira ntchito vya masamu]] [[Category:Vinthu vya m'mabwinja ivyo vikapelekeka mu South Africa]] [[Category:Afilika ya Nyengo ya Malibwe]] [[Category:Mbiri ya masamu]] [[Category:Kujoba pa maufupa]] [[Category:Vya m'mabwinja vya Kummwera kwa Afilika ]] bm4ov58p53qtczmpvnh1bayqgmt8l3m 0 49706 122209 2026-09-21T14:11:13Z Viyowoyero-vya-Malaŵi 11606 Created page with "{{Databox}} '''{{PAGENAME}}''' ni [[munthu]] wakufuma ku {{#invoke:wd|property|linked|references|P27}}. Iwo ni {{#invoke:wd|property|linked|references|P21}}. Ndiyo CEO wa [[Roblox]]. ==Moyo== {{PAGENAME}} wakababika mu {{#invoke:wd|property|linked|references|P569}} ku {{#invoke:wd|property|linked|references|P19}}. ==Ukaboni== {{reflist}} [[Category:Ŵanthu ŵamoyo]]" 122209 wikitext text/x-wiki {{Databox}} '''{{PAGENAME}}''' ni [[munthu]] wakufuma ku {{#invoke:wd|property|linked|references|P27}}. Iwo ni {{#invoke:wd|property|linked|references|P21}}. Ndiyo CEO wa [[Roblox]]. ==Moyo== {{PAGENAME}} wakababika mu {{#invoke:wd|property|linked|references|P569}} ku {{#invoke:wd|property|linked|references|P19}}. ==Ukaboni== {{reflist}} [[Category:Ŵanthu ŵamoyo]] ixfhj2idtu54txjwynqfiq0qybdtzpy 0 49707 122216 2026-09-22T00:38:31Z Viyowoyero-vya-Malaŵi 11606 Created page with "{{Databox}} '''{{PAGENAME}}''' ni [[munthu]] wakufuma ku {{#invoke:wd|property|linked|references|P27}}. Iwo ni {{#invoke:wd|property|linked|references|P21}}. Wakaŵa mulara wa wupu wa maseŵero gha Evil Geniuses kufuma mu 2019 m'paka 2023. ==Moyo== {{PAGENAME}} wakababika mu {{#invoke:wd|property|linked|references|P569}} ku {{#invoke:wd|property|linked|references|P19}}. ==Ukaboni== {{reflist}} [[Category:Ŵanthu ŵamoyo]]" 122216 wikitext text/x-wiki {{Databox}} '''{{PAGENAME}}''' ni [[munthu]] wakufuma ku {{#invoke:wd|property|linked|references|P27}}. Iwo ni {{#invoke:wd|property|linked|references|P21}}. Wakaŵa mulara wa wupu wa maseŵero gha Evil Geniuses kufuma mu 2019 m'paka 2023. ==Moyo== {{PAGENAME}} wakababika mu {{#invoke:wd|property|linked|references|P569}} ku {{#invoke:wd|property|linked|references|P19}}. ==Ukaboni== {{reflist}} [[Category:Ŵanthu ŵamoyo]] 6ya195wc17bxfq1jvvko4hsdkitprgz 0 49708 122217 2026-09-22T00:43:21Z Viyowoyero-vya-Malaŵi 11606 Created page with "{{Databox}} '''{{PAGENAME}}''' ni [[munthu]] wakufuma ku {{#invoke:wd|property|linked|references|P27}}. Iwo ni {{#invoke:wd|property|linked|references|P21}}. Wakasayinirana na Columbia Records apo wakathandazgika pa TikTok mu 2023 chifukwa cha sumu zake zinyake. ==Moyo== {{PAGENAME}} wakababika mu {{#invoke:wd|property|linked|references|P569}} ku {{#invoke:wd|property|linked|references|P19}}. ==Ukaboni== {{reflist}} [[Category:Ŵanthu ŵamoyo]]" 122217 wikitext text/x-wiki {{Databox}} '''{{PAGENAME}}''' ni [[munthu]] wakufuma ku {{#invoke:wd|property|linked|references|P27}}. Iwo ni {{#invoke:wd|property|linked|references|P21}}. Wakasayinirana na Columbia Records apo wakathandazgika pa TikTok mu 2023 chifukwa cha sumu zake zinyake. ==Moyo== {{PAGENAME}} wakababika mu {{#invoke:wd|property|linked|references|P569}} ku {{#invoke:wd|property|linked|references|P19}}. ==Ukaboni== {{reflist}} [[Category:Ŵanthu ŵamoyo]] tra67i0q0nppt1n239cauxdvjbnoe6n 0 49709 122218 2026-09-22T03:00:15Z ~2026-51022-03 12228 i translated it to tumbuka 122218 wikitext text/x-wiki [[File:Various_scalpels.png|thumb|Ma mpeni wa opaleshoni ghakupambanapambana. Wakwamba (kufuma ku mazere), wachiŵiri, na wachinayi ghali na vingwe ivyo vingasinthika. Yachisanu ni lancet.]] '''Mpeni wa opaleshoni''', Scalpel, ni chipangizo chichoko ndiposo chakuthwa chomene icho chikugwiriskirika nchito pa opareshoni, kugaŵa thupi, kupanga malundi na kupanga vinthu vyakupambanapambana vya mawoko. [[Lancet]] ni scalpel ya mizere yiŵiri. Kanandi vingwe vya scalpel vikupangika na visulo vyakukhozga na vyakukhozga, visulo vyambura zimbiri, panji visulo vya carbon yinandi; kusazgirapo apa, titanium, ceramic, dayamondi nanga ni vipeni vya obsidian ni vyambura kumanyikwa. Mwaciyelezgero, para ŵakucita opareshoni mwakulongozgeka na MRI, vingwe vya visulo vikugwiliskirika nchito yayi (vingwe ivi vingakoleka ku maginito ndiposo vingapangiska kuti vithuzithuzi viŵe vyakupangika). Kuyana na mdauko, chinthu icho ŵakatemwanga chomene kupanga vingwe vya opareshoni chikaŵa siliva. Mabala gha scalpel ghakupelekekaso na ŵakupanga ŵanyake awo ŵali na zirconium nitride–coated mphonje kuti ŵaŵe ŵakuthwa na kusunga mphonje. Ŵanyake ŵakupanga vingwe ivyo vikupangika na polymer kuti viŵe na mafuta ghanandi para ŵakudumura. Mpeni wa opaleshoni zingaŵa zakugwiriskira ncito kamoza panji zakugwiriskira ncitoso. Ma scalpel agho ghakugwiriskira ncitoso ghangaŵa na vingwe vyakuŵikikapo nyengo zose ivyo vingaŵa vyakuthwa panji, kanandi, vingwe ivyo vingafumiskikapo vyakugwiriskira ncito kamoza. Kanandi scalpels zakuponyeka zikuŵa na chakukolera cha pulasitiki icho chili na chingwe chakutambasuka (nga ni mpeni wakugwiliskira ntchito) ndipo zikugwiriskirika nchito kamoza, ndipo pamanyuma pake chida chose chikutayika. Kanandi vingwe vya scalpel vikuŵikika paŵekha mu matumba ghambura kuŵa na nthenda kweni vikupelekekaso vyambura nthenda. Nthowa zinyake izo zingagwiliskirika nchito na mapeni wa opaleshoni ni electrocautery na laser. ifhamif93vnkaywlwpjui9w3lxl4y3o 122219 122218 2026-09-22T03:03:07Z Viyowoyero-vya-Malaŵi 11606 Seems a Typo 122219 wikitext text/x-wiki [[File:Various_scalpels.png|thumb|Ma mpeni wa opaleshoni ghakupambanapambana. Wakwamba (kufuma ku mazere), wachiŵiri, na wachinayi ghali na vingwe ivyo vingasinthika. Yachisanu ni lancet.]] '''Mpeni wa opaleshoni''', Scalpel, ni chipangizo chichoko ndiposo chakuthwa chomene icho chikugwiriskirika nchito pa opareshoni, kugaŵa thupi, kupanga malundi na kupanga vinthu vyakupambanapambana vya mawoko. [[Lancet]] ni scalpel ya mizere yiŵiri. Kanandi vingwe vya scalpel vikupangika na visulo vyakukhozga na vyakukhozga, visulo vyambura zimbiri, panji visulo vya carbon yinandi; kusazgirapo apa, titanium, ceramic, dayamondi nanga ni vipeni vya obsidian ni vyambura kumanyikwa. Mwaciyelezgero, para ŵakucita opareshoni mwakulongozgeka na MRI, vingwe vya visulo vikugwiliskirika nchito yayi (vingwe ivi vingakoleka ku maginito ndiposo vingapangiska kuti vithuzithuzi viŵe vyakupangika). Kuyana na mdauko, chinthu icho ŵakatemwanga chomene kupanga vingwe vya opareshoni chikaŵa siliva. Mabala gha scalpel ghakupelekekaso na ŵakupanga ŵanyake awo ŵali na zirconium nitride–coated mphonje kuti ŵaŵe ŵakuthwa na kusunga mphonje. Ŵanyake ŵakupanga vingwe ivyo vikupangika na polymer kuti viŵe na mafuta ghanandi para ŵakudumura. Mpeni wa opaleshoni zingaŵa zakugwiriskira ncito kamoza panji zakugwiriskira ncitoso. Ma scalpel agho ghakugwiriskira ncitoso ghangaŵa na vingwe vyakuŵikikapo nyengo zose ivyo vingaŵa vyakuthwa panji, kanandi, vingwe ivyo vingafumiskikapo vyakugwiriskira ncito kamoza. Kanandi scalpels zakuponyeka zikuŵa na chakukolera cha pulasitiki icho chili na chingwe chakutambasuka (nga ni mpeni wakugwiliskira ntchito) ndipo zikugwiriskirika nchito kamoza, ndipo pamanyuma pake chida chose chikutayika. Kanandi vingwe vya scalpel vikuŵikika paŵekha mu matumba ghambura kuŵa na nthenda kweni vikupelekekaso vyambura nthenda. Nthowa zinyake izo zingagwiliskirika nchito na mpeni wa opaleshoni ni electrocautery na laser. o6m7tbibtsids81l55tqhfgm9bd1b44 122222 122219 2026-09-22T03:18:55Z Viyowoyero-vya-Malaŵi 11606 122222 wikitext text/x-wiki [[File:Various_scalpels.png|thumb|Ma mpeni wa opaleshoni ghakupambanapambana. Wakwamba (kufuma ku mazere), wachiŵiri, na wachinayi ghali na vingwe ivyo vingasinthika. Yachisanu ni lancet.]] '''Mpeni wa opaleshoni''', Scalpel, ni chipangizo chichoko ndiposo chakuthwa chomene icho chikugwiriskirika nchito pa opareshoni, kugaŵa thupi, kupanga malundi na kupanga vinthu vyakupambanapambana vya mawoko. [[Lancet]] ni mpeni wa opaleshoni ya mizere yiŵiri. Kanandi vingwe vya mpeni wa opaleshoni vikupangika na visulo vyakukhozga na vyakukhozga, visulo vyambura zimbiri, panji visulo vya carbon yinandi; kusazgirapo apa, titanium, ceramic, dayamondi nanga ni vipeni vya obsidian ni vyambura kumanyikwa. Mwaciyelezgero, para ŵakucita opareshoni mwakulongozgeka na MRI, vingwe vya visulo vikugwiliskirika nchito yayi (vingwe ivi vingakoleka ku maginito ndiposo vingapangiska kuti vithuzithuzi viŵe vyakupangika). Kuyana na mdauko, chinthu icho ŵakatemwanga chomene kupanga vingwe vya opareshoni chikaŵa siliva. Mabala gha mpeni wa opaleshoni ghakupelekekaso na ŵakupanga ŵanyake awo ŵali na zirconium nitride–coated mphonje kuti ŵaŵe ŵakuthwa na kusunga mphonje. Ŵanyake ŵakupanga vingwe ivyo vikupangika na polymer kuti viŵe na mafuta ghanandi para ŵakudumura. Mpeni wa opaleshoni zingaŵa zakugwiriskira ncito kamoza panji zakugwiriskira ncitoso. Ma mpeni wa opaleshoni agho ghakugwiriskira ncitoso ghangaŵa na vingwe vyakuŵikikapo nyengo zose ivyo vingaŵa vyakuthwa panji, kanandi, vingwe ivyo vingafumiskikapo vyakugwiriskira ncito kamoza. Kanandi mpeni wa opaleshoni zakuponyeka zikuŵa na chakukolera cha pulasitiki icho chili na chingwe chakutambasuka (nga ni mpeni wakugwiliskira ntchito) ndipo zikugwiriskirika nchito kamoza, ndipo pamanyuma pake chida chose chikutayika. Kanandi vingwe vya mpeni wa opaleshoni vikuŵikika paŵekha mu matumba ghambura kuŵa na nthenda kweni vikupelekekaso vyambura nthenda. Nthowa zinyake izo zingagwiliskirika nchito na mpeni wa opaleshoni ni electrocautery na laser. m3ihsj2ur1bms1o08sddonrlktn3c0n 122223 122222 2026-09-22T03:20:33Z Viyowoyero-vya-Malaŵi 11606 122223 wikitext text/x-wiki [[File:Various_scalpels.png|thumb|Ma mpeni wa opaleshoni ghakupambanapambana. Wakwamba (kufuma ku mazere), wachiŵiri, na wachinayi ghali na vingwe ivyo vingasinthika. Yachisanu ni lancet.]] '''Mpeni wa opaleshoni''', Scalpel, ni chipangizo chichoko ndiposo chakuthwa chomene icho chikugwiriskirika nchito pa opareshoni, kugaŵa thupi, kupanga malundi na kupanga vinthu vyakupambanapambana vya mawoko. [[Lancet]] ni mpeni wa opaleshoni ya mizere yiŵiri. Kanandi vingwe vya mpeni wa opaleshoni vikupangika na visulo vyakukhozga na vyakukhozga, visulo vyambura zimbiri, panji visulo vya carbon yinandi; kusazgirapo apa, titanium, ceramic, dayamondi nanga ni vipeni vya obsidian ni vyambura kumanyikwa. Mwaciyelezgero, para ŵakucita opareshoni mwakulongozgeka na MRI, vingwe vya visulo vikugwiliskirika nchito yayi (vingwe ivi vingakoleka ku maginito ndiposo vingapangiska kuti vithuzithuzi viŵe vyakupangika). Kuyana na mdauko, chinthu icho ŵakatemwanga chomene kupanga vingwe vya opareshoni chikaŵa siliva. Mabala gha mpeni wa opaleshoni ghakupelekekaso na ŵakupanga ŵanyake awo ŵali na zirconium nitride–coated mphonje kuti ŵaŵe ŵakuthwa na kusunga mphonje. Ŵanyake ŵakupanga vingwe ivyo vikupangika na polymer kuti viŵe na mafuta ghanandi para ŵakudumura. Mpeni wa opaleshoni zingaŵa zakugwiriskira ncito kamoza panji zakugwiriskira ncitoso. Ma mpeni wa opaleshoni agho ghakugwiriskira ncitoso ghangaŵa na vingwe vyakuŵikikapo nyengo zose ivyo vingaŵa vyakuthwa panji, kanandi, vingwe ivyo vingafumiskikapo vyakugwiriskira ncito kamoza. Kanandi mpeni wa opaleshoni zakuponyeka zikuŵa na chakukolera cha pulasitiki icho chili na chingwe chakutambasuka (nga ni mpeni wakugwiliskira ntchito) ndipo zikugwiriskirika nchito kamoza, ndipo pamanyuma pake chida chose chikutayika. Kanandi vingwe vya mpeni wa opaleshoni vikuŵikika paŵekha mu matumba ghambura kuŵa na nthenda kweni vikupelekekaso vyambura nthenda. Nthowa zinyake izo zingagwiliskirika nchito na mpeni wa opaleshoni ni electrocautery na laser. [[Category:Mipeni yachipatala]] lfphnvhxc8m8bnx1hbzaxylwo5ovyhd 122228 122223 2026-09-22T09:32:20Z Viyowoyero-vya-Malaŵi 11606 122228 wikitext text/x-wiki [[File:Various_scalpels.png|thumb|Ma mpeni wa opaleshoni ghakupambanapambana. Wakwamba (kufuma ku mazere), wachiŵiri, na wachinayi ghali na vingwe ivyo vingasinthika. Yachisanu ni lancet.]] '''Mpeni wa opaleshoni''', Scalpel, ni chipangizo chichoko ndiposo chakuthwa chomene icho chikugwiriskirika nchito pa opareshoni, kugaŵa thupi, kupanga malundi na kupanga vinthu vyakupambanapambana vyachipatala. [[Lancet]] ni mpeni wa opaleshoni ya mizere yiŵiri. Kanandi vingwe vya mpeni wa opaleshoni vikupangika na visulo vyakukhozga na vyakukhozga, visulo vyambura zimbiri, panji visulo vya carbon yinandi; kusazgirapo apa, titanium, ceramic, dayamondi nanga ni vipeni vya obsidian ni vyambura kumanyikwa. Mwaciyelezgero, para ŵakucita opareshoni mwakulongozgeka na MRI, vingwe vya visulo vikugwiliskirika nchito yayi (vingwe ivi vingakoleka ku maginito ndiposo vingapangiska kuti vithuzithuzi viŵe vyakupangika). Kuyana na mdauko, chinthu icho ŵakatemwanga chomene kupanga vingwe vya opareshoni chikaŵa siliva. Mabala gha mpeni wa opaleshoni ghakupelekekaso na ŵakupanga ŵanyake awo ŵali na zirconium nitride–coated mphonje kuti ŵaŵe ŵakuthwa na kusunga mphonje. Ŵanyake ŵakupanga vingwe ivyo vikupangika na polymer kuti viŵe na mafuta ghanandi para ŵakudumura. Mpeni wa opaleshoni zingaŵa zakugwiriskira ncito kamoza panji zakugwiriskira ncitoso. Ma mpeni wa opaleshoni agho ghakugwiriskira ncitoso ghangaŵa na vingwe vyakuŵikikapo nyengo zose ivyo vingaŵa vyakuthwa panji, kanandi, vingwe ivyo vingafumiskikapo vyakugwiriskira ncito kamoza. Kanandi mpeni wa opaleshoni zakuponyeka zikuŵa na chakukolera cha pulasitiki icho chili na chingwe chakutambasuka (nga ni mpeni wakugwiliskira ntchito) ndipo zikugwiriskirika nchito kamoza, ndipo pamanyuma pake chida chose chikutayika. Kanandi vingwe vya mpeni wa opaleshoni vikuŵikika paŵekha mu matumba ghambura kuŵa na nthenda kweni vikupelekekaso vyambura nthenda. Nthowa zinyake izo zingagwiliskirika nchito na mpeni wa opaleshoni ni electrocautery na laser. [[Category:Mipeni yachipatala]] blaoagynxsfzlo1fukuw95xsmmw6zlv 3 49710 122220 2026-09-22T03:03:57Z Viyowoyero-vya-Malaŵi 11606 Created page with "==Tamupokelelani== {{Welcome}} ~~~~" 122220 wikitext text/x-wiki ==Tamupokelelani== {{Welcome}} '''''[[User:Viyowoyero-vya-Malaŵi|Viyowoyero-vya-Malaŵi]]'''''[[User talk:Viyowoyero-vya-Malaŵi|'''<span style='color: #00008b;background-color: #FFFFFF;'>_★^★_★</span>''']] 03:03, 22 Lupya 2026 (UTC) ladmx7to6hzaz6b242lbqm4c84o9am2 0 49711 122221 2026-09-22T03:05:12Z Viyowoyero-vya-Malaŵi 11606 Redirected page to [[Mpeni wa opaleshoni]] 122221 wikitext text/x-wiki #REDIRECT [[Mpeni wa opaleshoni]] f51qwk3rsqozxd8l39e72czn9u70erc 14 49712 122224 2026-09-22T03:20:59Z Viyowoyero-vya-Malaŵi 11606 Created page with "[[Category:Mipeni]]" 122224 wikitext text/x-wiki [[Category:Mipeni]] inaopuvyogo1pwtj9p7jblv18otwe20 14 49713 122225 2026-09-22T03:22:16Z Viyowoyero-vya-Malaŵi 11606 Created page with "{{Commonscat|Knives}} {{Cat main|Mpeni}}" 122225 wikitext text/x-wiki {{Commonscat|Knives}} {{Cat main|Mpeni}} aozx65tmr0wq9ddh59nlzl3wkqz4d2b 0 49714 122229 2026-09-22T09:58:37Z Viyowoyero-vya-Malaŵi 11606 Created page with "{{Databox}} '''Mpeni '''ni chipangizo icho chili na mphepete yakudumura, kanandi chikuŵikika pa [[chakukolera]]. Chimoza mwa vipangizo vyakwamba ivyo ŵanthu ŵakagwiliskiranga ntchito, vipeni vikawoneka vyaka pafupifupi 2.5 miliyoni ivyo vyajumpha, nga umo vikulongolera na vipangizo vya [[Oldowan]].<ref>{{cite magazine|title=No. 1 The knife |magazine=Forbes|url=https://www.forbes.com/2005/08/31/technology-tools-knife_cx_de_0831knife.html |access-date=2007-05-07 |date=2..." 122229 wikitext text/x-wiki {{Databox}} '''Mpeni '''ni chipangizo icho chili na mphepete yakudumura, kanandi chikuŵikika pa [[chakukolera]]. Chimoza mwa vipangizo vyakwamba ivyo ŵanthu ŵakagwiliskiranga ntchito, vipeni vikawoneka vyaka pafupifupi 2.5 miliyoni ivyo vyajumpha, nga umo vikulongolera na vipangizo vya [[Oldowan]].<ref>{{cite magazine|title=No. 1 The knife |magazine=Forbes|url=https://www.forbes.com/2005/08/31/technology-tools-knife_cx_de_0831knife.html |access-date=2007-05-07 |date=2005-08-31 |archive-url=https://archive.today/20120731184748/http://www.forbes.com/2005/08/31/technology-tools-knife_cx_de_0831knife.html |archive-date=2012-07-31 }}</ref><ref name="palomar.edu">{{cite web|title=Early Human Evolution: Early Human Culture |url=http://anthro.palomar.edu/homo/homo_3.htm |access-date=2007-05-07 |archive-url=https://web.archive.org/web/20070512035553/http://anthro.palomar.edu/homo/homo_3.htm |archive-date=2007-05-12 }}</ref> Pakwamba ŵakapanga na makuni, viwangwa, na malibwe (nga ni flint na obsidian), kwa vilimika vinandi, mwakuyana na kusinthika kwa vyakupangika na visulo, vingwe vya vipeni vyapangika na mkuŵa, chisulo, ceramic, na titanium. Mipeni yinandi ya mazuŵa ghano yili na vingwe vyakukhazikika panji vyakupindika, ndipo masitayilo ghake ghakupambana kuyana na uyo wakupanga na charu. == Ukaboni == {{reflist}} ==Malinki gha kuwaro== *{{Commons category-inline|Knives}} [[Category:Mipeni| ]] 8b7orzawp23ari9hs4r57n5uvyukp4v 122231 122229 2026-09-22T10:02:21Z Viyowoyero-vya-Malaŵi 11606 122231 wikitext text/x-wiki {{Databox}} [[File:Damascus Bowie.jpg|thumb|upright=1.5|alt=Mpeni ukuru uwo uli na chakukolera cha khuni lakutowa, pafupi na chikopa|[[Mpeni wa Bowie]] wa chisulo chakupangika na chithunzithunzi]] '''Mpeni '''ni chipangizo icho chili na mphepete yakudumura, kanandi chikuŵikika pa [[chakukolera]]. Chimoza mwa vipangizo vyakwamba ivyo ŵanthu ŵakagwiliskiranga ntchito, vipeni vikawoneka vyaka pafupifupi 2.5 miliyoni ivyo vyajumpha, nga umo vikulongolera na vipangizo vya [[Oldowan]].<ref>{{cite magazine|title=No. 1 The knife |magazine=Forbes|url=https://www.forbes.com/2005/08/31/technology-tools-knife_cx_de_0831knife.html |access-date=2007-05-07 |date=2005-08-31 |archive-url=https://archive.today/20120731184748/http://www.forbes.com/2005/08/31/technology-tools-knife_cx_de_0831knife.html |archive-date=2012-07-31 }}</ref><ref name="palomar.edu">{{cite web|title=Early Human Evolution: Early Human Culture |url=http://anthro.palomar.edu/homo/homo_3.htm |access-date=2007-05-07 |archive-url=https://web.archive.org/web/20070512035553/http://anthro.palomar.edu/homo/homo_3.htm |archive-date=2007-05-12 }}</ref> Pakwamba ŵakapanga na makuni, viwangwa, na malibwe (nga ni flint na obsidian), kwa vilimika vinandi, mwakuyana na kusinthika kwa vyakupangika na visulo, vingwe vya vipeni vyapangika na mkuŵa, chisulo, ceramic, na titanium. Mipeni yinandi ya mazuŵa ghano yili na vingwe vyakukhazikika panji vyakupindika, ndipo masitayilo ghake ghakupambana kuyana na uyo wakupanga na charu. == Ukaboni == {{reflist}} ==Malinki gha kuwaro== *{{Commons category-inline|Knives}} [[Category:Mipeni| ]] h3zeyqvpfwgej1gmxbv53td7m8yme3h 122232 122231 2026-09-22T10:02:38Z Viyowoyero-vya-Malaŵi 11606 122232 wikitext text/x-wiki [[File:Damascus Bowie.jpg|thumb|upright=1.5|alt=Mpeni ukuru uwo uli na chakukolera cha khuni lakutowa, pafupi na chikopa|[[Mpeni wa Bowie]] wa chisulo chakupangika na chithunzithunzi]] '''Mpeni '''ni chipangizo icho chili na mphepete yakudumura, kanandi chikuŵikika pa [[chakukolera]]. Chimoza mwa vipangizo vyakwamba ivyo ŵanthu ŵakagwiliskiranga ntchito, vipeni vikawoneka vyaka pafupifupi 2.5 miliyoni ivyo vyajumpha, nga umo vikulongolera na vipangizo vya [[Oldowan]].<ref>{{cite magazine|title=No. 1 The knife |magazine=Forbes|url=https://www.forbes.com/2005/08/31/technology-tools-knife_cx_de_0831knife.html |access-date=2007-05-07 |date=2005-08-31 |archive-url=https://archive.today/20120731184748/http://www.forbes.com/2005/08/31/technology-tools-knife_cx_de_0831knife.html |archive-date=2012-07-31 }}</ref><ref name="palomar.edu">{{cite web|title=Early Human Evolution: Early Human Culture |url=http://anthro.palomar.edu/homo/homo_3.htm |access-date=2007-05-07 |archive-url=https://web.archive.org/web/20070512035553/http://anthro.palomar.edu/homo/homo_3.htm |archive-date=2007-05-12 }}</ref> Pakwamba ŵakapanga na makuni, viwangwa, na malibwe (nga ni flint na obsidian), kwa vilimika vinandi, mwakuyana na kusinthika kwa vyakupangika na visulo, vingwe vya vipeni vyapangika na mkuŵa, chisulo, ceramic, na titanium. Mipeni yinandi ya mazuŵa ghano yili na vingwe vyakukhazikika panji vyakupindika, ndipo masitayilo ghake ghakupambana kuyana na uyo wakupanga na charu. == Ukaboni == {{reflist}} ==Malinki gha kuwaro== *{{Commons category-inline|Knives}} [[Category:Mipeni| ]] ai5k3pztj7e6fmvn9i8nmfaft028wfr 1 49715 122230 2026-09-22T10:00:07Z Viyowoyero-vya-Malaŵi 11606 Created page with "{{talk header}}" 122230 wikitext text/x-wiki {{talk header}} frwy0ondkbaajki04xjgq9mnxpg47li