Rediscover Arabic-Islamic mathematics

We now talk about "Arabic numerals" but we often completely ignore the successive or competing notation systems that were used in Islamic countries. Similarly, it is said – and readily repeated – that algebra was born with al-Khwārizmī, and one sometimes knows that he was interested in inheritance questions to refine his solving methods, but who has ever looked at the exact way he approached them? We also often forget all the other mathematicians, particularly those who came later, who structured algebra over the centuries. And one should not neglect all the development of arithmetic, especially recreational, which could pervade many texts sometimes with no apparent connection to mathematics.

Arab-Muslim geometry is based on Greek treatises in order to study them more deeply. This is the case of Euclid's treatises, some of which were lost in the original Greek, but which we are able to reconstruct thanks to commentators in the Arabic language who, moreover, offer us original works such as very clever proofs of the Pythagorean theorem. This is also the case with astronomy, long considered a fundamentally geometric science. More surprisingly, this geometric deepening is also found in algebra where it is used to develop general methods of resolution. Thus, geometry is part of a tradition that scholars from Islamic lands considerably extend and refine.

Arab-Muslim mathematics hold particular importance for their heritage: the Latin translations that were made from them allowed the West to rediscover ancient texts but also and especially to benefit from the advances made by scholars from the lands of Islam. Sometimes, these Latin translations made it possible to preserve the core of certain Arabic texts whose original is today lost. However, one should not overlook the mathematical developments after what is often characterized as the "golden age" of Arabic science, which continue to be nourished by fascinating cultural exchanges.