Muslims were part of the major designers and founders of the Mathematics of today. They might have translated some works from the then Creek and other great nations before Islam. Lots of work was translated and mitigated, and thereafter innovations erupted. Huge works in different spheres of life have the impacts of such mathematical innovations to speak for them. In any case, below is a very brief outlook on the commonest mathematical inputs of the Muslims in history.
In Arithmetic, Musa al-Khwarizmi, 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. George Sarton pays glowing tribute to this outstanding Muslim mathematician and considers him "one of the greatest scientists of his race and the greatest of his time".' He systematised Greek and Hindu mathematical knowledge and profoundly influenced mathematical thought during mediaeval times. 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. The original version of this work has disappeared but its Latin translation Trattati a" Arithmetic edited by Bon Compagni in 1157 at Rome is still in existence.
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.
Al-Karkhi was primarily responsible for popularising Hindu numerals before the advent of Arabic ones. His book 'Al-kafi fil Hissab was translated into German by Hochhevin and published at Halle in 1878--80.
MAbu Zakariya Muhammad Al-Hissar who probably lived in the 12th century A. D. is the author of Kitab-us-sagh ir-Jil-h issab . One of its important sections was translated and published by H. Suter in 1901. AL-Hissar was the first mathematician who started writing fractions in their present form with a horizontal line. A commentary on his treatise on arithmetic, written by Ibn al-Banna, gained much popularity and was published in French by A. Narre in 1864 and reprinted in Rome in 1865.
Arabic numerals including zero were the greatest contributions made by the Arabs to the mathematical science. The outstanding quality of Arabic numerals lies in the fact that they possess an absolute value. Huroful Ghubar was a novel form of numerals adopted in Spain by 950 A. D. The most significant numeral invented by the Arabs was zero which according to Carra De Vaux "was used by the Arabs at least 250 years before it became known in the west". Before the introduction of the zero it was necessary to arrange all figures in columns to differentiate between tens, hundreds, thousands, etc. The earliest use of the zero is given as 873 A. D.
Algebra, a branch of mathematics, is a word derived from the Arabic source AlJabar and is the product of Arabic genius.
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. Khwarizmi has the distinction of being one of the founders of algebra who developed this branch of science to an exceptionally high degree. He also gives geometric solutions of quadratic equations, which was repeated by later mathematicians. Robert Chester was the first to translate this book into Latin in 1145 A. D. which introduced Algebra into Europe. Later on this book was translated by Gerard of Cremona also. The Algebra written by Al-Khwarizmi is lucid and well-arranged. After dealing with equations of the second degree, the learned mathematician discussed algebraic multiplications and divisions. Writing in The Legacy of Islam Carra De Vaux says, "In the 18th century Leonardo Fibonacci of Pisa, an algebraist of considerable importance says he owed a great deal to the Arabs."' He travelled in Egypt, Syria, Greece and Sicily and learned the Arabic methods there, recognised it to be superior to the method of Pythagoras and composed a liber Abaci in 15 chapters, the rest of which deals with algebraic calculations. Leonardo enumerates the six cases of the quadratic equations just as Al-Khwarizmi gives them. The translation by Robert Chester of Khwarizmi's algebra marks the beginning of the era of the introduction and advancement of this branch of science in Europe. "The importance of Robert's Latin translation of Khwarizmi's algebra", says a modern orientalist, "can hardly be exaggerated because it marked the beginning of European Algebra."
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 in 1853 A.D.
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.
Thabit bin Qurra is universally recognised as the greatest Muslim geometer. He was born in Harran and knew Greek and Syraic languages very well, so that he could read books of these countries in original. He wrote a number of short treatises on astronomy and mathematics. His treatise on Balance was translated into Latin by Gerard of Cremona. Al-Isfahani has contributed to conics. Isfahani also translated Greek works on Conics.
These are few examples of some of the works and contributions of Muslims and Arabs to modern mathematics. And 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.