Umchazazibalo

**Umchazazibalo** iyindawo yokucwaninga ethola futhi ihlele izindlela, izinkolelo-mbono kanye nama-theorems asungulwa futhi afakazelwe ngezidingo zesayensi ye-empirical kanye ne-mathematics ngokwayo. Kunezindawo eziningi zezibalo, ezihlanganisa inkolelo-mbono yezinombolo (ukuhlolwa kwezinombolo), i-algebra (ukuhlongwa kwamamula nezakhiwo ezihlobene), umchazabukhulu (ukuhlushwa kokuma nezindawo eziqukethe), ukuhlaziywa (ukuhlutwa kwezinguquko eziqhubekayo), kanye nenkolelo-mbongo yezinombolo.

Umchazazibalo ihilela ukuchazwa nokusetshenziswa kwezinto ezingaqondakali eziqukethe noma ukungaqondakali kwemvelo noma - kwi-umchazazibalo yanamuhla - izinto ezingaqondakali kuphela ezibekwe ukuthi zinezici ezithile, ezibizwa ngokuthi Ama-axioms. Umchazazibalo isebenzisa ukucabanga okuhlanzekile ukufakazela izakhiwo zezinto, *ubufakazi* obuhlanganisa ukulandelana kokusetshenziswa kwemithetho ye-deductive emiphumeleni esevele ikhona. Le miphumela ihlanganisa ama-theorems, ama-axioms, futhi - uma kwenzeka kungaqondakali emvelweni - ezinye izakhiwo eziyisisekelo ezibhekwa njengeziqalo zangempela zenkolelo-mbono ecatshangelwayo.

Umchazazibalo zibalulekile kuyinzululwazi yemvelo, umngcikisho, umuthi, ezomnotho, isayensi yekhompyutha, kanye isayensi yezenhlalo. Yize izibalo zisetshenziswa kabanzi ekwakheni imodeli, amaqiniso ayisisekelo ezibalo azimele kunoma yikuphi ukuhlolwa kwesayensi. Ezinye izindawo izibalo, njengezibalo kanye nenkolelo-mbono yomdlalo, zenziwa ngokuhambisana kakhulu nokusetshenziswa kwazo futhi zivame ukuhlanganiswa ngaphansi kwezibalo ezisetshenzisiwe. Ezinye izindawo zenziwa ngokuzimela kunoma yikuphi ukusetshenziswa (ngakho-ke zibizwa ngokuthi izibalo ezihlanzekile) kodwa ngokuvamile kamuva zithola ukusetshenziswa okuwusizo.

## Izincazelo Zomchazazibalo
uLeonardo Fibonacci, uSoZibalo waseItaly owadidiyela uhlelozibalo lwe-Hindu–Arabic olwahlelwa ngamaNdiya phakathi kwekhulu leminyaka lokuqala nelesine (100 - 400 BC), lwase lwabhekiswe emazweni aseNtshonalanga. Umchazazibalo awunayo incazelo eyamukelwe ngokugcwele jikelele. uAristotle obe nguSoNzululwazi wayichaza ngokuthi, "ufundondalo lokuqala ngqo!", ngakho le ncazelo yasetshenziswa kwaze kwaba ikhulu leminyaka leshumi nesishiyagalombili (iKh. 18).

uGalileo Galilei (1564 - 1642) wathi, "Umkhathi ngokugcwele kwawo ngeke ufundeke size sifunde ulimi futhi sizijwayeze ngohlelo lwezimpawu okubhalwe ngazo (umkhathi). Ubhalwe ngolimi lwe-mathemathiki, izimpawu ongxantathu, izindingiliza nezinye izimpawu ze-geometry, okungukuthi ngaphandle kwazo; kunzima kakhulu ukuqonda ngisho igama elilodwa vo! Ngaphandle kokuqonda lezimpawu nolimi lwe-mathemathiki, kuyize ukuthola ulwazi ngomkhathi nomhlaba." 
uCarl Friedrich Gauss (1777 - 1855) wachaza imathemathiki njenge "Ndlovukazi yezinhlaka ze-Sayensi".

uBenjamin Peirce (1809 - 1880) wabiza umchazazibalo ngo "Fundandalo olubeka imiphumela edingekayo". uDavid Hilbert wathi ngomchazazibalo: "Asikhulumi la ngesingathekiso nje. Umchazazibalo awufani nje nomdlalo onemithetho nje yokuzenzela. Kodwa, uhlelo oluqukethe isizathu sokwenzeka esingakwazi ukuba enye into ngaphandle kwaso kuphela ngqo!"
uAlbert Einstein (1879 - 1955) wabeka wathi, "Ngakuba imithetho yomchazazibalo isho ngempilo, ayinaso isiqiniseko; ngakuba imithetho inesiqiniseko, ayisho ngempilo."

## Ireferensi