Contributions of Muslims' Mathematicians
Ø Muslims have made immense contributions to almost all branches of the sciences and arts, but mathematics was their favorite subject and its development owes a great deal to the genius of Arab and Persian scholars.
Ø 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.
Ø 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 Abdullah 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
Ø 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.
Ø 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 10th book of Euclid
Ø The latter's contribution was translated into Latin by Gerard of Cremona
Ø The last of the Arab translators and commentators of Greek works was the eminent Arab mathematician Al-Buzjani who died in 998 A.D.
Ø 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.
Ø Not only algebra geometry and arithmetic, but optics and mechanics made remarkable progress in the hands of the Muslims.
Ø 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
Arithmetic
Ø Is a word derived from the Arabic source AlJabar and is the product of Arabic genius.
Ø Al-Khwarizmi the celebrated mathematician is also the author of Hisab Al-Jabr Wal Muqabla, an outstanding work on algebra which contains analytical solutions of linear and quadratic equations.
Ø Musa al-Khwarizmi (780--850 A.D.) a native of Khwarizm, who lived in the reign of Mamun-ar-Rashid, was one of the greatest mathematicians of all times. He composed the oldest Islamic works on arithmetic and algebra which were the principal source of knowledge on the subject for a fairly long time.
Ø He championed the use of Hindu numerals and has the distinction of being the author of the oldest Arabic work on arithmetic known as Kitab-ul Jama wat Tafriq.
Ø Al-Nasavi is the author of Abnugna Fil Hissab Al-Kindi short extracts of which were published by F. Woepeke in the journal Asiatique in 1863. His arithmetic explains the division of fractions and the extraction of square and cubic roots in an almost modern manner. He introduced the decimal system in place of sexagesimal system.
Ø Al-Karkhi was primarily responsible for popularizing Hindu numerals before the advent of Arabic ones. His book 'Al-kafi fil Hissab was translated into German by Hochhevin and published at Halle
Ø AL-Hissar was the first mathematician who started writing fractions in their present form with a horizontal line.
Ø Nasir-ud-din Toosi, a versatile genius, who was a prolific writer and has written more than hundreds of valuable books to his credit, has the distinction of being one of the greatest scientists and mathematicians of Islam.
Ø Nasir-uddin has written Al-mutawassat and a short but concise book on arithmetic which is available both in Arabic and Persian.
Ø Omar Khayyam, the celebrated poet, philosopher, astronomer and mathematician has left behind an excellent book on algebra. His works on algebra were translated in 1851, while his Ruhaiyat were first published in 1859. The manuscripts of his principal works exist in Paris and in the India Office London; Mosadrat, researches on Euclid 's axioms, and Mushkilat-i-Hissab, dealing with complicated arithmetical problems, have been preserved in Munich (Germany
Ø According to V· Minorsky, "He was the greatest mathematician of mediaeval times." His primary contribution is in algebra in which he has registered much advance on the work of the Greeks.
Ø Abul Kamil improved upon the algebra of Khwarizmi. He dealt with quadratic equations, multiplication and division of algebraic quantities, addition and subtraction of radicals and the algebraic treatment of' pentagons and decagons.
Ø Abu Bakr Karkhi, who adorned the court' of Fakhrul Mulk in the beginning of 11th century wrote an outstanding treatise on algebra known as AlFakhri. This is one of the best books on the subject left by a Muslim mathematician and was published by Woepeke in Paris
Ø Geometry, like other branches of mathematics, geometry made much headway in the hands of Muslims. The three famous brothers Muhammad, Ahmad and Hassan, sons of Musa bin Shakir, wrote an excellent work on geometry which was translated into Latin by Gerard of Cremona. This was later translated into German by M. Kurtaza.
Ø Abul Wafa Al-Buzjani, (940--997, 998 A. D.) is the author of Kitab al-Hindusa which was rendered into Persian by one of his friends. "It had a large number of" says H. Suter, "geometrical problems for the fundamental construction of plane geometry to the constructions of the corners of a regular polyhedron on the circumscribed sphere of special interest is the fact that a number of these problems are solved by a single span of the compass, a condition which we find for the first time here."'
Trigonometry
Ø It has been universally acknowledged that plane and spherical trigonometry were founded by Muslims who developed it considerably. The Greeks and other advanced nations of the ancient world were ignorant of this essential branch of mathematics.
Ø Khwarizmi, the Muslim mathematician has made valuable contributions to this branch of mathematics also..His trigonometrical tables which deal with the sine and tangent were translated into Latin in 1126 A. D. by Adelard of Bath.
Ø Al-Battani (Latin Albategnius). The nation of trigonometrical ratios, which is now prevalent, owes its birth to the mathematical talents of Al-Battani. The third chapter, of his astronomical work, dealing with trigonometry, was several times translated into Latin and Spanish languages.
Ø Jabir Bin Afiah is the author of the celebrated book Kitab Elahia which deals with astronomy and trigonometry.
Ø Abul Wafa (939--997, 998 A.D.) born at Buzjan in Khorasan later on established in Iraq
Ø Abul Hasan Koshiyar (971--1029 A. D.) was a Persian mathematician who wrote his works in Arabic. He played a dominant role in the development of trigonometry. His main subject was the elaboration and explanation of the tangent.
Ø Such were the great mathematical giants which the Muslim world produced, who were not only the pioneers of mathematical science during mediaeval times, but are considered to be authorities on several mathematical problems even during the modern age. The development of mathematics owes a great deal to the genius of these Muslim luminaries.
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