Samuzi

**Samuzi** ni sayansi iyo yikulongosora vinthu nga ni manambara, malemba, na unandi. Likugaŵikana mu vigaŵa viŵiri: nthavi ya manambara, alijebra, jiometre, na analisisi. Kweni ŵasayansi ŵose ŵakukolerana yayi pa fundo yakuti Samuzi ni vichi.

Ntchito zinandi za Samuzi zikusazgapo kusanga maunenesko gha vinthu vakukoleka pakuviyimiliska na malembo. Vinthu ivi vikuŵa vyakufumira ku cilengiwa panji vinthu ivyo vikulongosoreka na vinthu vinyake, ivyo vikucemeka kuti axioms. Ukaboni mu Samuzi ukuŵa na nthowa zinandi izo zikugwiliskira nchito vifukwa vyakwambilira nga ni fundo izo zili kulongosoreka kale.

Samuzi zikugwiliskirika nchito mu vigaŵa vinandi nga ni sayansi, susanda vyozenga-zenga, munkhwala, ndalama, na sayansi ya kompyuta. Nangauli ŵakugwiliskira ntchito maukaboni agha pakulondezga vinthu vyaunenesko, kweni unenesko wa masamu ukuyana yayi na ivyo vikuchitika nadi. Vigaŵa vinyake vya masamu, nga ni manambara na chiphunzitso cha maseŵero, vikukolerana chomene na masuzgo agho ghakuchitika nadi ndipo vikuchemeka masamu ghakupangika. Vigaŵa vinyake, ivyo vikuchemeka masamu ghaunenesko, vikupangika kuti ŵanthu ŵamanye makora masamu. Kweni nyengo zinyake vinthu ivi vikugwiliskirika nchito para pajumpha nyengo. Mwaciyelezgero, cipinda ca RSA ico cikugwiliskirika nchito pa kompyuta cikuthemba pa suzgo la masamu ilo Euclid wakasambira mu 300 B.C.E.

Kale, masamu ghakagaŵikanga mu vigaŵa viŵiri, geometry na arithmetic. Kweni mu vyaka vya m'ma 1500 na 1700, ŵanthu ŵakamba kusambira vinthu viphya nga ni algebra na calculus. Kufuma waka pa nyengo iyi, masamu na sayansi vikukolerana pakupanga vinthu viphya. Kuumaliro wa vyaka vya m'ma 1800, pakaŵa suzgo la masamu ilo likawovwira kuti paŵe fundo izo zikovwira kuti munthu waŵe na mahara. Ivi vikawovwira kuti paŵe vigaŵa vinandi vya masamu na kuvigwiliskira ntchito. Mazuŵa ghano, pali vigaŵa vyakujumpha 60 vya masamu.

## Mbiri la lizgo
Lizgu lakuti masamu lili kufuma ku Chigiriki chakale, kufuma ku lizgu lakuti "máthēma", kung'anamura "chinthu icho munthu wakusambira". Nyengo yikati yajumphapo, likamba kwendera chomene masamu. Lizgu Lachigiriki lakuti "mathēmatikós" likung'anamura "kusambira" panji "kusambira", ndipo likung'anamuraso "masamu". Mazgu ghakuti "mathēmatik?? tékhnē" ghakung'anamura "masamu". Mu Pythagoreanism, mathemēmatikoi ŵakang'anamuranga "ŵakusambira", ndipo paumaliro ŵakang'anamuranga "ŵasayansi ŵa masamu".

Mu Cilatini na Cingelezi mpaka mu ma 1700, lizgu lakuti mathematics likang'anamuranga "astrology" panji "astronomy". Fundo iyi yikasintha pakati pa 1500 na 1800. Kusintha uku kwapangiska kuti ŵanthu ŵaleke kupulikiska fundo iyi, nga umo wakachitira Augustine.

In Latin, and in English until around 1700, the term *mathematics* more commonly meant "astrology" (or sometimes "astronomy") rather than "mathematics"; the meaning gradually changed to its present one from about 1500 to 1800. This change has resulted in several mistranslations: For example, Saint Augustine's warning that Christians should beware of *mathematici*, meaning "astrologers", is sometimes mistranslated as a condemnation of mathematicians.

Lizgu la Chingelezi lakuti mathematics, ilo lili mu unandi, lili kufuma ku lizgu Lachilatini lakuti neuter plural mathematica. Vingachitika kuti Cingelezi cikaŵa na lizgu lakuti mathematical (al) pera, ndipo cikaŵa na lizgu lakuti mathematics, ilo likukolerana na visambizgo vya Cigiriki. Mu Cingelezi, lizgu lakuti mathematics lili na lizgu limoza ndipo kanandi likuzgoreka kuti "maths" panji "math" mu North America.

## Vigaŵa vya samuzi
Pambere nyengo ya Renaissance yindize, masamu ghakagaŵikanga mu vigaŵa viŵiri: masamu, agho ghakukhwaskana na manambara, na masamu, agho ghakukhwaskana na umo vinthu viliri. Ndipouli, mitundu yinyake ya sayansi yautesi, nga ni manambara na vyamunthazi, yikaŵa yakupambana yayi na masamu.

Mu nyengo ya Renaissance, masamu ghakaŵaso ghaŵiri. Algebra, iyo yikusazgapo kusambira na kupanga malemba, yikamba chifukwa cha umo masamu ghakalembekera. Kuwerengera, uko kuli vigaŵa viŵiri vyakuchemeka kuwerengera kwa mphambano na kuwerengera kwa umoza, nkhusambira milimo yakulutilira iyo yikulongora umo vinthu vikupambanirana. Ŵanthu ŵakalutilira kuchita nthena m'paka kuumaliro wa m'ma 1800. Pa nyengo iyo, ŵasayansi ŵakamba kusambira vya maselo nga ni mechanics na solid mechanics, kweni mazuŵa ghano maselo agha ghakuchemeka physics.

Masamu ghakwendera lumoza, agho ghakusambira kupenda na kuŵika vinthu mu ndondomeko, ghakaŵako kwa nyengo yitali, kweni ghakazgoka chigaŵa cha masamu yayi m'paka m'ma 1700. Kuumaliro wa vyaka vya m'ma 1800, masamu ghakasintha chomene, ndipo ichi chikapangiska kuti paŵe vinandi mu masamu. Mu 2020 Mathematics Subject Classification muli vigaŵa 63, kusazgapo chiŵerengero cha manambara (zina la mazuŵa ghano la masamu ghapachanya) na geometry. Nangauli vigaŵa vinyake vinandi vya chigaŵa chakwamba vili na zina lakuti "geometry", kweni algebra na calculus ni vigaŵa vya chigaŵa chakwamba yayi. Vinthu vinyake vya mu chigaŵa chakwamba, nga ni mathematical logic na foundations, vikawoneka mu vyaka vya m'ma 1900 panji vikawonekanga kuti ni mathematical yayi.

### Fundo la nambara

Fundo ya manambara yikamba na kupangiska manambara ghaunenesko, ndipo pamasinda yikasazgikira ku manambara ghose na manambara ghakukolerana. Kale ŵakachemekanga kuti masamu, kweni mazuŵa ghano ŵanthu ŵakugwiliskira ntchito mazgu agha pakuchita masamu. Ŵanthu ŵakamba kusambira vya manambara kufuma kale chomene, ndipo ŵanyake awo ŵakasambizganga vya manambara ŵakaŵa Euclid wa ku Greece kweniso Diophantus wa ku Alexandria. Kafukufuku wamakono wa chiŵerengero cha manambala mu kawonekero kake kakukhalira Pierre de Fermat na Leonhard Euler, ndipo wakapangika na Adrien-Marie Legendre na Carl Friedrich Gauss. 

Nangauli masuzgo ghanandi gha manambara ghakupangika makora, kweni kuti ghazgoreke pakukhumbikwira nthowa zakupambanapambana. Mwaciyelezgero, fundo ya Fermat yakumalizgira, iyo Pierre de Fermat wakayowoya mu 1637, yikalongoreka mu 1994 na Andrew Wiles, uyo wakagwiliskira nchito vinthu nga ni masamu gha algebraic geometry, category theory, na homological algebra. Chiyelezgero chinyake ni fundo ya Goldbach, iyo yikayowoyeka mu 1742 na Christian Goldbach ndipo yikulongora kuti chiŵelengero chilichose chikuru kuluska 2 ntchiŵelengero cha manambara ghaŵiri ghakwamba. Nangauli ŵanthu ŵayezgayezga comene, kweni fundo iyi yindafiskike.

Fundo ya manambara yikusazgapo vigaŵa vichoko waka, nga ni analytic number theory, algebraic number theory, geometry of numbers (iyo yikukhwaskana na nthowa za kasovero), diophantine equations, na transcendence theory (iyo yikukolerana na suzgo).

### Jiometre

Jiometre ni munthavi wa masamu uwo waŵako kwa nyengo yitali. Vinthu ivi vikamba na kupanga vinthu nga ni mizere, makona, na vizingilika, ivyo vikagwiranga nchito pa vinthu nga nkhupima na kuzenga. Sono, geometry yili na vigaŵa vinandi.

Cimoza mwa vinthu vyakuzirwa comene ivyo vikacitika pa nkhani ya geometry cikaŵa apo Ŵagiriki ŵakamba kugwiliskira nchito maukaboni. Ichi chikung'anamura kuti mungamanya yayi kuti chinthu ntchaunenesko para mwachiyezga, kweni mukwenera kulongora kuti ntchaunenesko para mwagwiliskira ntchito vinthu vinyake ivyo mukumanya kuti ni vyaunenesko. Pali vinthu vinyake mu geometry ivyo ni vyaunenesko nyengo zose ndipo vikukhumbikwa yayi kuti viwoneke. Fundo izi zikuchemeka kuti postulates panji axioms. Euclid wakalemba fundo iyi mu buku lake la Elements.

Masamu gha Euclid ghakusanda umo vinthu viliri mu malo ghaŵiri panji ghatatu. Kwa nyengo yitali, ŵanthu ŵakagwiliskiranga ntchito nthowa na maghanoghano ghakuyana waka pakulemba masamu. Kweni mu ma 1700, munthu munyake zina lake René Descartes wakambiska nthowa yinyake. M'malo mwa kugwiliskira nchito waka vyakujambura na vipimo, wakasanga nthowa yakuyowoyera vinthu kwizira mu manambara na ma equation. Ivi vikawovwira kuti ŵanthu ŵamanye umo ŵangachitira vinthu vinyake nga ni algebra na calculus.

Jiometre ya Euclid ghakusanda umo vinthu viliri mu malo ghaŵiri panji ghatatu. Kwa nyengo yitali, ŵanthu ŵakagwiliskiranga ntchito nthowa na maghanoghano ghakuyana waka pakulemba masamu. Kweni mu ma 1700, munthu munyake zina lake René Descartes wakambiska nthowa yinyake. M'malo mwa kugwiliskira nchito waka vyakujambura na vipimo, wakasanga nthowa yakuyowoyera vinthu kwizira mu manambara na ma equation. Ivi vikawovwira kuti ŵanthu ŵamanye umo ŵangachitira vinthu vinyake nga ni algebra na calculus.

Sono pali mitundu yiŵiri ya geometry: yakupangika na ya analytic. Kawonekero ka vinthu kakuyana waka na umo ŵanthu ŵakugwiliskira ntchito vinthu vinyake. Masamu ghakuyelezgera ghakugwiliskira nchito ma equation na manambara kulongosora umo vinthu viliri. Ivi vikapangiska kuti paŵe mitundu yinyake ya geometry nga ni differential geometry na algebraic geometry. Kweniso masamu ghakulongosora vinthu ghakawovwira kuti ŵanthu ŵasambire vinthu ivyo vili na vipimo vinandi.

Mu vyaka vya m'ma 1800, ŵasayansi ŵakamanya kuti pali mitundu yinyake ya geometry padera pa geometry ya Euclid. Vinthu ivi vikuchemeka ma geometry gha Euklides yayi. Ici cikaŵa suzgo likuru comene ku masamu cifukwa vikawonekanga nga kuti fundo za mu masamu zingaŵa zautesi. Kweni paumaliro, ŵasayansi ŵakasanga nthowa yakugwilira ntchito ma geometry agha. Ichi chikung'anamura kuti mungasankha malango ghakupambanapambana kuti mulondezgenge, kweni mungachita makora masamu.

Mazuŵa ghano, vigaŵa vinyake vya geometry ni ivi:

Mu vyaka vya m'ma 1500, Girard Desargues wakambiska masamu ghakuyelezgera. Ivi vikovwira kuti vinthu vinandi vya mu geometry viŵe vyambura kukhumba vinandi.

Masamu ghakulongora umo vinthu viliri pa nyengo yimoza, ndipo ghakupambana na utali.

Geometry yakupambaniska, nkhusambira za makuni, malo, na umo ghakupambanirana, ivyo vikulongosoreka mwakugwiliskira nchito milimo yakupambana.

Fundo iyi yikulongosora umo vinthu viliri mu malo ghakupambanapambana.

Masamu gha Riemannian, agho ghakusanda umo mtunda uliri mu malo ghakupindika.

Algebraic geometry, ndiyo yikusambira za makuni, malo, na umo ghakusinthira vinthu.

Kusanda vinthu ivyo vikusintha nyengo zose.

Algebraic topology, kugwiliskira nchito nthowa za algebraic, comenecomene homological algebra.

Masamu ghakupambanapambana ghakusambizga umo vinthu viliri.

Geometry ya convex, ndiyo yikusanda maseti gha convex, ndipo yikupangiska kuti yiŵe yakukhumbikwa pakuchita vinthu.

Masamu ghakupambanapambana, agho ghakusangika para manambara ghaunenesko ghasinthika na manambara ghakupambanapambana.
Alijebra 

Algebra ni luso la kusintha ma equation na ma formulas. Ŵanthu ŵaŵiri awo ŵakambiska sayansi ya algebra ŵakaŵa Diophantus mu vyaka vya m'ma 200 C.E. na al-Khwarizmi mu vyaka vya m'ma 900 C.E. Diophantus wakasanga vinthu viphya pakati pa manambara ghaunenesko kuti wamazge ma equation. Al-Khwarizmi wakambiska nthowa zakusinthira ma equation, izo wakazitcha kuti "al-jabr".

François Viète ndiyo wakamba kugwiliskira ntchito vimanyikwiro mu algebra. Vyakusintha vikwimira manambara, ndipo vikovwira kuti ŵasayansi ŵa masamu ŵalongosore umo masamu ghakuchitira. M'paka m'ma 1800, algebra yikaghanaghaniranga waka pa vinthu vyakuyana waka (linear algebra) na algebraic equations.

Mu vyaka vya m'ma 1800, ŵasayansi ŵakamba kugwiliskira ntchito vimanyikwiro vinyake kuti ŵalongore vinthu vinyake, nga ni matrices, manambara ghakupambanapambana, na ma geometric transformations. Ivi vikapangiska kuti paŵe fundo ya algebraic structure, iyo yikusazgapo vinthu vinyake vyambura kuwoneka makora, milimo iyo yikuchita pa vinthu ivi, na malango agho ghakwenera kulondezga milimo iyi. Emmy Noether ndiyo wakambiska algebra ya mazuŵa ghano, iyo yikulongosora chomene vya masamu.

Kusanda umo vinthu vya algebra viliri kukazgoka chigaŵa cha algebra ndipo kukusazgapo mitundu yakupambanapambana iyo njakovwira mu masamu nthe:

fundo ya magulu; chiphunzitso cha munda; Malo gha vektara, agho ghakuyana waka na gha algebra. fundo ya mphete; Algebra ya commutative, iyo yikusambira za mphete za commutative, yikusazgapo kusambira za polynomials, ndipo ni cigaŵa cakuzirwa ca algebraic geometry; masamu gha homological algebra; Algebra ya utesi na cisambizgo ca magulu gha utesi; Algebra ya Boole, iyo yikugwiliskirika nchito comene pakusambira umo makompyuta ghakucitira vinthu.

Masamu gha algebra na chigaŵa cha masamu ni masamu agho ghakusanda chomene vinthu vya masamu. Fundo iyi yikugwira ntchito ku masamu ghose, ku algebra yayi. Likatumika pamoza na homological algebra kuti ŵanthu ŵasambirenge vinthu vinyake nga ni malo. Malo agha ghakuchemeka algebraic topology.

### Kakyula na analisisi

Mathematical calculus, agho kale ghakachemekanga kuti infinitesimal calculus, ghakalembeka na Newton kweniso Leibniz. Fundo iyi yikulongosora umo vinthu ivyo vikupambana vikukolerana. Mu vyaka vya m'ma 1800, Euler wakalutilira kusanda mawerengero gha malibwe. Mazuŵa ghano, lizgu lakuti "calculus" likung'anamura chigaŵa chakwamba cha fundo iyi, apo lizgu lakuti "analysis" likung'anamura chigaŵa chakwamba.

Kafukufuku wakugaŵikana mu vigaŵa viŵiri: Kafukufuku wanadi, apo vigaŵa vyakupambanapambana vikwimira manambara ghanadi, na Kafukufuku wakusuzga, apo vigaŵa vyakupambanapambana vikwimira manambara ghakupambanapambana. Pali vigaŵa vinandi ivyo ŵanthu ŵakumanya vya masamu, nga ni:

Calculus ya vyosintha vinandi

Kusanda kwa milimo, uko vimanyikwiro vikulongora milimo yakupambanapambana;

Fundo za kuwunjika vinthu, kupima vinthu, na kughanaghanira umo vinthu vingaŵira, vyose vikukolerana na fundo za kughanaghana za umo vinthu vingaŵira.

Ma equation gha common differential;

Ma equation gha vigaŵavigaŵa;

Kusanda manambara, comene nkhusanda pa kompyuta nthowa zakumazgira ma equation ghacilendo na ghacigaŵa-cigaŵa agho ghakucitika mu vigaŵa vinandi.

### Samuzi za udesi

Discrete mathematics, broadly speaking, is the study of individual, countable mathematical objects. An example is the set of all integers. Because the objects of study here are discrete, the methods of calculus and mathematical analysis do not directly apply.[lower-alpha 3] Algorithms—especially their implementation and computational complexity—play a major role in discrete mathematics.

Mu vyaka vya m'ma 1900, ŵakamazga masuzgo ghaŵiri ghakuru mu masamu ghapadera. Suzgo linyake lakuzirwa ilo lindamalizgike ni P versus NP, ilo lingakhwaska masuzgo ghanandi usange lingazengeka.

Masamu ghakupambanapambana ghakuŵa na vigaŵa vyakupambanapambana nga ni combinatorics, icho chikung'anamura kupenda vinthu vya masamu ivyo vikukolerana na fundo zinyake. Ivi vikusazgapo vigaŵavigaŵa vya vigaŵa na vyakuchita vya ma geometric mu geometry. Vigaŵa vinyake ni fundo ya graph, hypergraph, coding theory, matroid theory, discrete probability distributions, game theory, na discrete optimization. Vinthu ivi vikovwira chomene pa nkhani ya kupangiska vinthu mwakukolerana, kupanga mapulogiramu gha manambara, na kupanga mapulogiramu ghakukanizga vinthu.

Combinatorics ni cigaŵa ca masamu ico cikulaŵiska comene pa kupenda na kulemba vinthu ivyo vikulondezga malango ghanyake. Pakwamba wakawonanga vigaŵa panji vigaŵavigaŵa vya vinthu vinandi, kweni pasono vinthu vinandi vikusangika. Mwaciyelezgero, masamu ghakupambanapambana ghakulongosora umo vinthu viliri.

Kafukufuku wa ma graph na hypergraphs, kafukufuku wa ma code (uyo wakuyowoya za kuwongolera maubudi na ma cryptography), kafukufuku wa matroid, geometry yakupambana, ma disks gha ma probability, kafukufuku wa maseŵero (iyo yikusazgapo kusanda maseŵero nga ni chess na poker), na ma optimization ghakupambanapambana (kukusazgapo combination optimization, integer programming, na constraint programming) ni vigaŵa vinyake vya mathematics ghakupambanapambana ivyo vikusazgapo kumazga masuzgo ghakukhwaskana na kupenda na kupanga vinthu vyakupambanapambana.

### fundo za samuzi na fundo ya set

Masamu ghakwendera fundo za mathematical logic na set theory kufuma mu 19th century. Pambere ivi vindachitike, masamu ghakawonekanga nga ni vinthu vya masamu yayi ndipo fundo zaunenesko zikaŵa mu vinjeru vya ŵanthu m'malo mwa kusambizgika na ŵasayansi.

Ivyo Cantor wakachita pakusanda masamu ghambura kumara vikakwiyiska ŵanthu ŵanandi chifukwa wakawonanga kuti masamu ghambura kumara ghakupambana. Ivi vikapangiska kuti paŵe mphindano pa nkhani ya Cantor. Pa nyengo yeneyiyo, vikamanyikwa makora kuti fundo za mathematical objects zikukwana yayi kuti mathematical rigorousness yiŵepo.

Paumaliro, suzgo ili likamara chifukwa cha kughanaghanira makora fundo za mu Baibolo. Chinthu chilichose cha masamu chikulongosoreka na vinthu vyose vyakuyana waka na mikhaliro iyo vinthu ivi vikwenera kuŵa nayo. Fundo iyi yikulongolerathu kuti vinthu vikaŵako nadi yayi.

Vinthu ivyo vikulongosoreka mu nthowa iyi ni suzgo la vinjeru vya ŵanthu ilo ŵasayansi ŵa masamu ŵakulekera ŵasayansi. Nthowa iyi yikovwira kuti ŵanthu ŵawonenge fundo za mu masamu, maoremu, maukaboni, na vinyake nga ni vinthu vya masamu. Mu vyaka vya m'ma 1900, ŵasayansi ŵanyake ŵakasuska fundo iyi.

Masuzgo agha ghakawovwira kuti mathematical logic yambe kukura, ndipo pakaŵa vigaŵa vinyake nga ni model theory, proof theory, type theory, computability theory, na computational complexity theory. Nangauli vinthu ivi vikamba kuchitika pambere makompyuta ghandambe kugwira ntchito, kweni vikapangiska kuti ŵasambizgi ŵa makompyuta ŵambeso kugwiliskira ntchito fundo izi.

### Samuzi za kanandi na ma sayansi ghanyakheso ka kusankha fundo

Samuzi za kanandi ni munthavi wa masamu uwo ukugwiliskirika nchito pakusanga na kusanda vinthu. Ŵasayansi ŵakugwiliskira ntchito nthowa za masamu, chomenechomene za umo vinthu vingachitikira, kuti ŵasange vinthu mwambura kwenelera. Nthowa iyo ŵakucitira kuyezgelera panji kuyezgelera yikusankha nthowa izo ŵagwiliskirenge nchito.

Kusanda mauthenga kufuma ku ivyo ŵanthu ŵakuwona vikuchitika kwizira mu manambara na fundo za kughanaghana. Para vyaŵa nthena, maukaboni agho ghapangika ghakwenera kuyezgeka kuti ghaŵe ghaunenesko.

Kafukufuku wakulongosora umo vinthu vikupangikira wakusanda umo vinthu vikupangikira, nga nkhusankhira viwemi chomene. Fundo iyi yikung'anamura kuchepeska ntchito iyo munthu wakuchita, nga ni kutayika panji mtengo uwo wakulindilira. Mwachiyelezgero, para munthu wakunozga kafukufuku wakuchepeskako ndalama izo wakugwiliskira ntchito kuti wapime unandi wa ŵanthu.

Chifukwa chakuti manambara ghakugwiliskira nchito vyakukondweska vinthu, ghakwendera lumoza na sayansi zinyake za vyakucita nga ni kafukufuku wa vyakucitika, fundo ya kuwusa, na masamu gha vya cuma.

### Samuzi za ma Kompyuta
Masamu gha makompyuta ni chigaŵa cha masamu icho chikuyowoya za masamu agho ŵanthu ŵangamazga yayi. Likugwiliskira ntchito nthowa za masamu pakusanda masuzgo agho ghakuchitika pa nkhani ya manambara, kusanda vinthu mwakuyana na umo vinthu viliri, na kusanda vinthu mwakuyana na umo vikuchitikira. Kusanthula kwa manambala, komwe ndi gawo la masamu owerengera, kumayang'ana kwambiri njira zothetsera mavuto pakuwunika, monga kuyandikira ndi kusagwirizana, komanso kulingalira zolakwika zozungulira.

Kuwonjezera pa kusanthula manambala, masamu owerengera amaphunziranso nkhani zosasanthula mu sayansi ya masamu, monga chiphunzitso cha algorithmic-matrix-and-graph, kudzera mu kompyuta yasayansi. Vigaŵa vinyake vya mathematical computational ni computer algebra na symbolic computation, ivyo vikusazgapo kugwiliskira nchito kompyuta kuti yidumure masuzgo gha mathematical agho ghakusazgapo ma expressions na algebraic equations.

## Mbiri
 

### Chiyamwaka

Mu vyaka vyapakati pa 500 na 1500 C.E., ŵasayansi ŵa masamu ŵa chisopa cha Chisilamu ŵakawovwira chomene pa nkhani ya masamu. Muhammad ibn Musa al-Khwarizmi (c. 780-850 C.E.) wakuwoneka kuti ni dada wa algebra. 87] Al-Khwarizmi nayo wakambiska fundo ya algorithm, ndipo ntchito yake pa decimal fractions na decimal positional system yikawovwira chomene pakusintha ka Hindu-Arabic numeral system. 88]

Ku Europe, masamu ghakalutilira kukura mu vyaka vyapakati, ndipo Fibonacci (c. 1170-1250 AD), uyo wakambiska nthowa ya Hindu-Arabic ku Europe ndipo wakalemba buku lakuti Liber Abaci, ilo likawovwira chomene pakovwira ŵanthu kuti ŵamanye chiarabu. 89] Mu nyengo ya Renaissance, masamu ghakalutilira kukura, ndipo Leonardo da Vinci ndiyo wakawovwira chomene pa nkhani ya geometry na perspective, kweniso Galileo Galilei uyo wakawovwira chomene pa nkhani ya calculus.

Mu nyengo yithu yino, masamu ghakalutilira kukura mwaluŵiro chomene, ndipo pali vinandi ivyo vyachitika pa nkhani ya mawerengero, masamu, manambara, geometry, na topology. Mu vyaka vya m'ma 1900, masamu ghakasintha, kweniso masamu ghanyake ghakasintha. Mazuŵa ghano, masamu ghalutilira kusanda chomene nkhani za masamu, ndipo ghakwendera lumoza na vinyake nga sayansi ya sayansi ya vinthu vyamoyo, sayansi ya vyachuma, na kompyuta.

### Nyengo za mwaka za pakati-kati na mthazi

vinyakhe mwa vinthu vikuru ivyo vikachitika mu masamu mu vyaka vya m'ma 1900, ni fundo ya masamu iyo yikovwira chomene pa masamu, kusanda masamu na umo ghakugwilira ntchito pa masamu na kusanda vinthu, kusanda masamu gha vinthu ivyo vikusintha nadi, kusanda masamu gha algebra, kweniso kusanda fundo za masamu na ukaboni. Kweniso, makompyuta na ma algorithms ghapangiska kuti paŵe kusintha kukuru mu masamu, kusazgapo kusanda manambara, kupanga vinthu mwamahara, na kulemba malemba.

Mu vyaka vyasonosono apa, ŵasayansi ŵasanga vinthu viphya mu masamu nga ni masamu gha pa Intaneti, agho ghakusanda vinthu vyakupambanapambana nga ni masamu gha pa Intaneti na ghakwendeskera vinthu. Kuŵa na vinthu viphya vya masamu kwawovwira kuti ŵasayansi ŵasinthe vinthu vinyake nga ni sayansi ya vinthu vyakuthupi, injiniya, na kompyuta.

Pa vyose ivyo vikuchitika, masamu ghakusintha mwaluŵiro chomene ndipo ghakusanga vinthu viphya ivyo vikupangiska kuti ŵanthu ŵamanye vinandi.

## Kulemba kwa vimanyikwiro na mazgu

Masamu ghakusintha para pajumpha nyengo, ndipo pakuŵa vimanyikwiro viphya. Mwaciyelezgero, cimanyikwiro ca cambura kumara (∞) cikayowoyeka na John Wallis mu virimika vya m'ma 1700, ndipo cimanyikwiro ca cinthu cambura kanthu (??) cikayowoyeka na André Weil mu virimika vya m'ma 20.[ 99] Malembo ghakupambanapambana ghakupambana mu masamu, nanga ni pakati pa ŵalembi na masukulu ghakupambanapambana.

Padera pa malemba ghakumanyikwa na vimanyikwiro, paliso mitundu yinyake ya malemba gha masamu agho ghakugwiliskira ntchito vithuzithuzi panji vithuzithuzi. Mwaciyelezgero, vithuzithuzi vya Venn vingaŵa vyakulongora umo vinthu viliri pakati pa vigaŵa, ndipo vithuzithuzi vya khuni vingaŵa vyakulongora umo vinthu vikulongolera. Kanandi ŵanthu ŵakugwiliskira ntchito vithuzithuzi kuti ŵalongosore makora vinthu.

Masamu ghakukolerana chomene na sayansi ya kompyuta, ndipo umo kompyuta yikugwilira ntchito vikakhwaska chomene masamu. Mwachiyelezgero, para munthu wakugwiliskira ntchito kompyuta kuti wapange masamu na kuyerekeza vinthu, wakuŵa na nthowa ziphya zakulongosolera vinthu.

Pa vyose ivyo vikuchitika, masamu ni nthowa yiwemi chomene yakulongosolera makora fundo zakusuzga kweniso umo vinthu vikukolerana. Likuzomerezga ŵasayansi ŵa masamu kuti ŵagwirenge lumoza ntchito na ŵanthu ŵanyake kweniso kuti ŵateŵeterenge lumoza mu vigaŵa na mitheto yakupambanapambana.

## ubali na masayansi
Padera pa kugwiliskira ntchito sayansi, masamu ghakugwiliskirika ntchito pa vinthu vinandi mu umoyo wa zuŵa na zuŵa. Mwachiyelezgero, ŵakugwiliskira ntchito Baibolo kuti ŵanozge vinthu, kuŵikamo mauthenga, kusanda vinthu, na kusankha vyakuchita pa nkhani za ndalama. Masamu ngakukhumbikwa chomene pakusintha na kugwiliskira ntchito tekinoloje, nga nkhupangira mapulogiramu gha makompyuta na kupanga masamu ghakwendeskera vinthu.

Kweniso masamu ghali na ntchito yikuru chomene pa nkhani ya mbiri na mitheto. Ŵanthu ŵanandi ŵakasambira na kughanaghanirapo nkhani iyi, ndipo yikawovwira chomene pa nkhani ya luso, mabuku, na vinjeru. Ŵanthu ŵanandi ŵakumanyikwa pa nkhani ya masamu nga ni Euclid, Pythagoras, na Gauss, ŵakumanyikwaso na ivyo ŵakachita pa nkhani zinyake. Masamu ghakutowa chomene chifukwa ghakulongosora vinthu nga ni vyakuvwara, vyakuchita, na nthowa zakupangira vinthu. Lekani ŵanthu ŵanandi ŵakuwona kuti masamu ni chiyowoyero icho chikupambana chomene na mitheto.

### Masamu Ghakufikapo na Ghakugwiliskika

Ntchakuzirwa kumanya kuti mphambano pakati pa masamu ghaunenesko na ghapanthazi yikupambana mu vigaŵa na vyaru. Mwaciyelezgero, ku Russia na vyaru vinyake vya ku Eastern Europe, ŵanthu ŵakuŵika comene mahara pa masamu kuluska ku vyaru vya kumanjiliro gha dazi. Ku Japan, ŵanthu ŵakutemwa kusambizga masamu mu maofesi gha masamu yayi.

Kweniso, ŵasayansi ŵanyake ŵakuti pali mphambano yikuru pakati pa masamu ghaunenesko na ghaunenesko. Iwo ŵakughanaghana kuti masamu ghaunenesko ghangagwiriskirika ntchito, kweniso kuti masamu ghangatovwira kumanya vinandi.

Nangauli pali mphambano pakati pa masamu ghaunenesko na ghapanthazi, kweni ni nyengo zose yayi apo pali mphambano iyi. Ŵasayansi ŵa masamu ŵakufuma mu vigaŵa vyose viŵiri ivi ŵakukolerana ndipo ŵakugwiliskira ntchito ivyo ŵanyawo ŵakuchita.

### Kuneneska mwambura kwenelera

Chiyelezgero chinyake cha umo masamu ghakwendeskera kafukufuku wa sayansi ya vinthu vya mu mlengalenga ni umo ŵakasangira Higgs boson, iyo yikayowoyekerathu mu masamu gha Standard Model of particle physics. Cinthu ici cikaŵa cakwamba kuwoneka mu ma 1960, kweni cikawoneka yayi mu 2012 m'paka apo ŵakazengera Large Hadron Collider. Kusanga Higgs boson kukaŵa chinthu chakuzirwa chomene mu sayansi ya sayansi ndipo kukakhozga fundo yakuti chiyelezgero cha Higgs ntchakugomezgeka.

Padera pa sayansi, masamu ghakugwiraso ntchito mu vigaŵa vinyake nga ni kompyuta, ndalama, na biology. Mwaciyelezgero, fundo ya mathematical ya graph theory yikugwiliskirika nchito pa social networks, suzgo la wamalonda wakwendakwenda lakugwiliskirika nchito pakunozga nthowa zakwendeskera vinthu, ndipo ma equation gha ma differential ghakugwiliskirika nchito pakulongosora umo ŵanthu ŵakukulira ndiposo umo matenda ghakuthandazgikira.

Ŵanthu ŵakudumbiskana chomene vya sayansi na vinjeru vya ŵanthu pa nkhani ya umo masamu ghakugwilira ntchito. Ŵanyake ŵakuti ni ukaboni wakuti kuchanya na charu chapasi ni vyakukolerana, apo ŵanyake ŵakuti ni nthowa iyo ŵanthu ŵakugwiliskira ntchito pakusambira masamu. Kwali pali chifukwa wuli, kweni ntchakuwonekerathu kuti umo masamu ghakulongosolera na kuchitira vinthu ni nthowa yiwemi chomene yakovwilira ŵanthu kuti ŵasambire vinandi.

### Visezgero vya masayansi yenecho yenecho

#### Physics

Masamu na sayansi vyawovwira chomene ŵanthu mazuŵa ghano. Mazuŵa ghano ŵasayansi ŵakugwiliskira ntchito chomene masamu ndipo ŵasanga vinandi pa nkhani iyi. Pa cithuzithuzi apa pali viyelezgero vya umo vinthu viliri.

#### Luso lakwendeska ma computer
Kuwuka kwa sayansi mu vyaka vya m'ma 1900 kukawovwira kuti kompyuta yipange vinthu vinyake. Sayansi ya makompyuta yikuthemba pa masamu, apo sayansi ya kutumirana mauthenga yikugwiliskira ntchito masamu pakubisa na kulemba ma code. Masamu ghakupambanapambana nagho ghakovwira pa nkhani ya kompyuta.

Makompyuta ghakovwira chomene kusanga fundo ziphya za masamu kwizira mu masamu ghakuyezgelera. Kugwiliskira ntchito makompyuta pakulongosora fundo za mu Baibolo, kwasintha chomene masamu.

Suzgo likuru comene mu sayansi ya kompyuta ni P versus NP, ilo ni limoza mwa masuzgo ghankhondi na ghaŵiri gha Millennium Prize.

#### Kusanda umoyo na Visungunu

Vinthu ivyo vikuchitika pa umoyo vikulongora kuti vinthu vikachita kusintha. Vinthu ivyo vikusintha pa umoyo wa ŵanthu ndivyo vikovwira chomene pa nkhani ya ivyo vingachitika.

Mu sayansi ya vinthu vyakuthupi, ŵanthu ŵakugwiliskira ntchito vyakuyelezgera kuti ŵawone umo ŵanthu ŵakukhala, umo vyamoyo vikuŵira, umo kunangika kwa vinthu kukuŵira, kweniso umo vinthu vikusinthira. Ndipouli, pali masuzgo ghanyake agho ghakwiza cifukwa ca kuwona umo vinthu viliri, comenecomene para ivyo vyacitika vikukhwaska vyakusankha vya ndyali.

Fundo ya Hardy-Weinberg yingawovwira kuti munthu wasinthe mtundu wake. Kweniso ŵanthu awo ŵakulemba vinthu vya mu charu ŵakugwiliskira ntchito vinthu ivyo vingachitika.

Ŵanthu ŵakugwiliskira ntchito maukaboni kuti ŵamanye usange munkhwala uphya ngwakovwira.

Mu sayansi ya vinthu vyakuthupi, ŵanthu ŵakugwiliskira ntchito kompyuta kuti ŵamanye umo vinthu vyakuthupi viliri. Kawonekero ka macromolecules mu vyamoyo kakusintha ndipo kakovwira chomene pakumanya ntchito yawo. Para ŵakuchita nthena ŵakugwiliskira ntchito masamu gha Euclid, ndipo para pali vyamoyo vyakupambanapambana ŵakuŵa na mtunda na ngodya zakukwana.

#### Masayansi gha charu

Ŵanthu ŵakusambira vya malo na nyengo ŵakugwiliskira ntchito vinthu ivyo vingapangiska kuti masoka gha chilengiwa ghachitikenge. Mwakuyana waka, sayansi ya vya mlengalenga, nyanja, na mapulaneti nayo yikuthemba chomene pa masamu.