Muslims have made immense contributions to almost all branches of the sciences and arts, but mathematics was their favorites subject and its development owes a great deal to the genius of Arab and persian scholars. The advancement in different branches of mathematical science commenced during the Caliphate of Omayyads, and Hajjaj bin Yusuf, who was himself a translator of Euclid as well as a great patron of mathematicians.

Whatever mathematical knowledge Arabs inherited came from two sources--the Hindus and the Greeks. The scholars of the Darul Hukarna of Mamun did the largest amount of work for the advancement of the sciences and arts by the Arabs. Abu Abdulla Muhammad Ibrahim-al-Fazari in 772-773 A.D. translated Sidhanta from Sanskrit into Arabic, which, according to G. Sarton provided "possibly the vehicle by means of which the Hindu numerals were transmitted from India to Islam". The works of Greek mathematicians which were translated during the Abbasid Caliphate and served as the starting point for Arab mathematicians were those of Euclid, Ptolemy, Antolyscus, Aristarchos and Archimedes. Hajjaj bin Yusuf was the first to translate Euclid's Elements into Arabic while Abdur Rahman and Muhammad Ibn Muhammad Baqi wrote commentaries on the IOth book of Euclid. The latter's contribution was translated into Latin by Gerard of Cremona and edited by H. Suter in 1907. Ibrahim Ibn-uz-Zaya al-Misri who died in 912 A.D. has written commentaries on Ptolemy's Centiloquim and Proportions, which influenced modern thought immensely. Abul Abbas Nairizi wrote commentaries on the works of Ptolemy and Euclid, which also were later translated into Latin by Gerard of Cremona. Abul Wafa, the celebrated mathematician, included a simplified version of Ptolemy's Almagest in his well known works--Tahir al-Majisty and Kitab al-Kamil. The last of the Arab translators and commentators of Greek works was the eminent Arab mathematician Al-Buzjani who died in 998 A.D. He commented upon and simplified the works of Euclid, Ptolemy and Diophantus.

Arabic translations of the well-known mathematical works of those times gave the Arabs the sources to develop the science of mathematics to an admirably high degree and later scientists owe much to the Arab genius. Writing in The Spirit of Islam, Ameer Ali says, "Every branch of higher mathematics bears tracts of their genius. The Greeks are said to have invented algebra, but among them, as Oelsner has justly remarked, it was confined to furnishing amusement 'for the plays of the goblet'. The Muslims applied it to higher purposes, and thus gave it a value hitherto unknown. Under Mamun they had discovered the equations of the second degree, and very soon after they developed the theory of quadratic aquations and the binomial theorem. Not only alalgebra geometry and arithmetic, but optics and mechanics made remarkable progress in the hands of the Muslims. They invented spherical trigonometry; they were the first to apply algebra to geometry, to introduce the tangent, and to substitute the sine for the arc in trigonometrical calculations. Their progress in mathematical geography was no less remarkable". Even the so-called enlightened west which has at times taken pains to minimise the greatness of Muslim achievements in furthering the cause of human civilization, had to admit, though half heartedly, the outstanding part played by the Arabs. "For with this limited ambition", says Carra De Vaux in Legacy of Islam, "the Arabs have really achieved great things in science; they taught the use of ciphers, although they did not invent them, and thus became the founders of arithmetic of every day life; they made algebra an exact science and developed it considerably and laid the foundations of analytical geometry; they were indisputably the founders of plane and spherical trigonometry which, properly speaking, did not exist among the Greeks"." Thus Muslims were pioneers in the development of mathematical sciences in mediaeval times.