


Medieval Muslims
made invaluable contributions to the study of mathematics, and their key
role is clear from the many terms derived from Arabic. Perhaps the most
famous mathematician was Muhammad ibn Musa alKhwarizmi (ca. 800ca. 847),
author of several treatises of earthshattering importance. His book On
the Calculation with Hindu Numerals, written about 825, was principally
responsible for the diffusion of the Indian system of numeration (Arabic
numerals) in the Islamic lands and the West.
Traditional systems
had used different letters of the alphabet to represent numbers or cumbersome
Roman numerals, and the new system was far superior, for it allowed people
to multiply and divide easily and check their work. The merchant Leonardo
Fibonacci of Pisa, who had learned about Arabic numerals in Tunis, wrote
a treatise rejecting the abacus in favor of the Arab method of reckoning,
and as a result, the system of HinduArabic numeration caught on quickly
in Central Italy. By the fourteenth century, Italian merchants and bankers
had abandoned the abacus and were doing their calculations using pen and
paper, in much the same way we do today.
In addition to
his treatise on numerals, alKhwarizmi also wrote a revolutionary book
on resolving quadratic equations. These were given either as geometric
demonstrations or as numerical proofs in an entirely new mode of expression.
The book was soon translated into Latin, and the word in its title, aljabr,
or transposition, gave the entire process its name in European languages,
algebra, understood today as the generalization of arithmetic in which
symbols, usually letters of the alphabet such as A, B, and C, represent
numbers. AlKhwarizmi had used the Arabic word for "thing" (shay)
to refer to the quantity sought, the unknown. When alKhwarizmi's work
was translated in Spain, the Arabic word shay was transcribed as xay,
since the letter x was pronounced as sh in Spain. In time this word was
abbreviated as x, the universal algebraic symbol for the unknown.
Robert of Chester's
translation of alKhwarzmi's treatise on algebra opens with the words
dixit Algorithmi, "Algorithmi says." In time, the mathematician's
epithet of his Central Asian origin, alKhwarizmi, came in the West to
denote first the new process of reckoning with HinduArabic numerals,
algorithmus, and then the entire stepbystep process of solving
mathematical problems, algorithm.
