|Algebra, the Decimal System, Mathematics
The science of algebra owes much to the gifted mathematicians of the Islamic era during its ascendancy. Algebra’s very name proves the magnitude of this debt (Arabic Al Jabr (a binding together)). Though of Greek origin, algebra was greatly expanded by Muslim mathematicians. From about 800 to 1200 C.E., the Muslims evolved a more critical study of equations giving them for the first time some elements of scientific treatment. Algebra was then handed on to Europe via Spain and Sicily.64
While the Arabic Numerals are believed to have originated in India, Muslims popularized them. Muhammad Bin Ahmed of the 10th century invented the concept of zero (sifr or void from which the terms cipher and decipher were derived). This did not only replace the cumbersome Roman numerals (I, V, X, L, C), but it was a new revolution in Mathematics.65
It was the Hindu philosophic genius that first conceived the idea that nothing, represented by zero, could have any mathematical value. Further, the value of less than nothing could be indicated algebraically as negative quantities. Working on Hindu foundations, the Muslims elaborated on what has become the present-day decimal system. They also introduced the Arabic numerals, that is, an adaptation of the ten Hindu digits, which gradually displaced cumbersome Greek symbols and Roman numerals.66
The seven centuries beginning with 800 C.E. saw a development of computational mathematics with the Muslim intellectual and logical community, surpassing achievements of the past. The use of the decimal system spread gradually into Europe through the work of Leonardo of Pisa, a Latin Christian who lived for years in North Africa, where he picked up Arabic numerals and the use of decimals. Leonardo’s work, as the Oxford History of Technology observers, was the most important western work by a European in which the system of numerals, then long in use by Arab craftsmen and merchants, was expounded for technical and commercial use in the West. It took Europe three hundred years, however, to fully accept and become adept in the use of the decimal system.67
As Algebra comes from Arabic Al Jabr, likewise, Algorithm comes from the name of the famous Muslim mathematician Muhammad Bin Musa Al Khawarizmi (780-850 C.E.) of the 9th century, who was described by George Sarton in his book An Introduction to the History of Science as “one of the founders of analysis or algebra as distinct from geometry.” Al Khawarizmi’s work was completed early in the 10th century by Abul Wafa who also worked on quadratic equations.68
Muslims’ works in Mathematics were translated into Latin and made available to the West through Robert of Chester, Adelard of Bath and John of Seville. Had it not been for Muslim scholars, the famous works of Euclid would have been lost. Al Tusi (13th century) had a major influence on the development of non-Euclidean Geometry. His legacy is found in practically every field of knowledge from theology to philosophy to mathematics and astronomy. His influence in the Muslim world, particularly in Asia is immense. In the West, however, only his works in astronomy and mathematics were translated and became quite important and influential during the Middle Ages and the Renaissance. Al Khawarismi was followed by many famous mathematicians, like Al Kindi, Al Sarakhsi, the three sons of Shakir Ibn Musa (the Banu Musa), Alhazen (Ibn al Haitham), and the Brethren of Purity (Ikhwan ul Safa), etc.
In line with Muslims scholars’ emphasis in the applied side, they were the first to develop trigonometry in its post-Greek form. They were the first to use the Sine and Co-sine in their work in Astronomy. They also wrote on spherical trigonometry. Their works on Trigonometry of tangents were not known in Europe until five centuries later. During the thirteenth century, trigonometrical progress was entirely due to Muslim efforts.69
The achievements of Islamic mathematics can be summarized as follows: the Muslims developed Numerical theory in both its mathematical and metaphysical aspects. They generalized numerical studies beyond what was known to the Greeks and devised new methods of numerical computation reaching their height with Al Kashani in the eighth/fifteenth centuries. They also dealt with numerical series, decimal fractions and similar branches of mathematics connected with numbers.
(…to be continued in the next e-newsletter – part 5)