Mathematics in medieval Islam

In the history of mathematics, mathematics in medieval Islam, often called Islamic mathematics or Arabic mathematics, covers the body of mathematics preserved and advanced under the Islamic civilization between circa 622 and c.160. Islamic science and mathematics flourished under the Islamic caliphate established across the Middle East, extending from the Iberian Peninsula in the west to the Indus in the east and to the Almoravid Dynasty and Mali Empire in the south.

In his A History of Mathematics, Victor Katz says that:

A complete history of mathematics of medieval Islam cannot yet be written, since so many of these Arabic manuscripts lie unstudied... Still, the general outline... is known. In particular, Islamic mathematicians fully developed the decimal place-value number system to include decimal fractions, systematised the study of algebra and began to consider the relationship between algebra and geometry, studied and made advances on the major Greek geometrical treatises of Euclid, Archimedes, and Apollonius, and made significant improvements in plane and spherical geometry.

An important role was played by the translation and study of Greek mathematics which was the principal route of transmission of these texts to Western Europe. Smith notes that:

The world owes a great debt to Arab scholars for preserving and transmitting to posterity the classics of Greek mathematics... their work was chiefly that of transmission, although they developed considerable ingenuity in algebra and showed some genius in their work in trigonometry.

Adolph P. Yushkevich states regarding the role of Islamic mathematics
The Islamic mathematicians exercised a prolific influence on the development of science in Europe, enriched as much by their own discoveries as those they had inherited by the Greeks, the Indians, the Syrians, the Babylonians,etc.

by Ayna Nadira