Khwarizmi, Muhammad Ibn Musa al-

Ninth-century Uzbek mathematician and astronomer. Born in Khiva.

Al-Khwarizmi was the author of a treatise on arithmetic that was translated from Arabic into Latin in the 12th century and that acquainted Europe with the Hindu positional numeration system. His work Kitab al-jabr wa’l muqabala (Book of Redintegration and Comparison) provided the first treatment of algebra as a distinct branch of mathematics; it presented rules for operations with algebraic quantities and for the solution of linear and quadratic equations. A 12th-century Latin translation of the work was long the main handbook on algebra in Europe.

The word “algebra” derives from al-Khwarizmi’s expression al-jabr, which refers to transposition—that is, the moving of terms from one member of an equation to the other, with a change of sign. The name “al-Khwarizmi,” latinized to “Algorithmi,” evolved into the designation of arithmetic operations using arabic numerals and later the general term for a system of computations that are carried out according to strictly defined rules (seeALGORITHM).

Al-Khwarizmi also wrote works on astronomy, sundials, and astrolabes and compiled astronomical tables. A manuscript on geography, Description of the Earth, was discovered in 1878.