A Summary of Muslim Mathematics

Establishing in Baghdad, a recently founded capital of Abbasid caliphs, of é Òom Ì P@ X Dāru l-H. ikmat (Abode of Wisdom) by caliph Ma’mūn who ruled during 813-833, was destined to play a pivotal role in the development of Mathematics in the lands conquered by muslim armies. Abode of Wisdomwas a sort of translation academy patronized by the caliph and wealthy families from his entourage. Works covering Mathematics, Astronomy, Engineering, and Medicine, were translated into Arabic, the language of the conquerors, from Greek, Syriac (Aramaic), Pahlavi (Classical Persian), and possibly from Sanskrit.1 Most of the mathematicians writing in Arabic between 9th and 13th Centuries were not Arabs, several were not muslims, others were first, or second-generation muslims. They translated, paraphrased, commented, and finally, appropriated for the islamic state, the work of Greek mathematicians. Some of the works of Greek scientists and philosphers survive only in Arabic. In the course of their studies they made several in-depth investigations in Geometry, Diophantine Analysis, and Combinatorics. Their indebtednes to Greek predecessors involved both major classics as well as minor sources (like a lemma appearing as a scholium in some versions of Theodosius’ Spherics2). Their “algebra” was concerned with solving polynomial equations; it was entirely verbal: no symbols of any kind were employed (the unknown quantity was referred to as ÈA Ó māl (“property”) which indicates connec-