Al-Khwarizmi ni we wanditse ibirebana n’uko imibare y’ibice ikoreshwa. Nanone yasobanuye neza uburyo bwo gukora amahurizo amwe n’amwe yo mu mibare kandi abushishikariza abandi. Ubwo buryo yabusobanuye mu gitabo yanditse (The Book of Restoring and Balancing). Ijambo alijebure, ryakomotse ku ijambo al-jabr riboneka mu mutwe w’icyo gitabo mu cyarabu (Kitab al-jabr wa’l-muqabala). Ehsan Masood wanditse ibitabo bya siyansi, yavuze ko alijebure ari bwo “buryo bw’ingenzi kurusha ubundi bwifashishwa mu gukora imibare, kandi bufite akamaro mu nzego zitandukanye za siyansi.” *

Hari umwanditsi wateye urwenya avuga ko “abanyeshuri batagira ingano bo mu mashuri yisumbuye, bahora bavuga ko byari kuba byiza iyo [al-Khwarizmi] atirirwa yirushya ahimba iyo mibare.” Icyakora, avuga ko icyo yari agamije ari ukwerekana  uburyo bworoshye bwo gukora imibare yifashishwa mu bucuruzi, kugabana imirage, ubushakashatsi n’ibindi.

Nyuma y’ibinyejana byinshi, abahanga mu mibare bo mu bihugu byo mu Burengerazuba harimo Galilée na Fibonacci, bubahaga al-Khwarizmi cyane kuko yatanze ibisobanuro byumvikana mu birebana n’inganyagaciro. Inyandiko ze ni zo zaje gutuma habaho ubundi bushakashatsi bujyanye na alijebure, imibare y’imihiriko na tirigonometiri. Tirigonometiri yafashije intiti zo mu Burasirazuba bwo Hagati kumenya ubunini bw’imfuruka n’impande bya mpandeshatu, no gukora ubushakashatsi ku birebana n’inyenyeri. *

Nanone hari abifashishije ibyo al-Khwarizmi yagezeho, bahimba uburyo bushya bwo gukora imigabane n’ubwo gupima ubuso n’ubunini. Abahanga mu by’ubwubatsi bo mu Burasirazuba bwo Hagati bakoresheje ubwo buryo mbere cyane y’uko bagenzi babo bo mu Burengerazuba babukoresha mu gihe cy’intambara z’Abanyamisaraba. Nyuma yaho, ubwo bumenyi babujyanye iwabo babifashijwemo n’abahanga b’Abisilamu bafasheho iminyago hamwe n’abimukira.

Nyuma y’igihe, inyandiko za al-Khwarizmi zahinduwe mu kilatini. Umuhanga mu mibare witwa Fibonacci (wabayeho ahagana mu 1170-1250), nanone uzwi ku izina rya Léonard de Pise, azwiho kuba yaratumye imibare y’Abarabu n’Abahindu yamamara mu Burengerazuba. Yize iyo mibare igihe yari mu rugendo mu bihugu bituriye inyanja ya Mediterane, nyuma yaho yandika igitabo cy’imibare (Book of Calculation).

Kugira ngo ibisobanuro Al-Khwarizmi yatanze bisakare, byasabye ibinyejana byinshi. Ariko muri iki gihe imibare yahimbye n’ibifitanye isano na yo, birifashishwa cyane muri siyansi n’ikoranabuhanga, mu bucuruzi no mu nganda.