Al-Khwārizmī (780?-850?), Arab mathematician. Muhammad ibn Mūsā al-Khwārizmī was born in Khwārizm (now Khiva, Uzbekistan). He was librarian at the court of Caliph al-Mamun and astronomer at the Baghdād observatory. His works on algebra, arithmetic, and astronomical tables greatly advanced mathematical thought, and he was the first to use for mathematical purposes the expression al jabr, from which the English word algebra is derived. The Latin version, by the Italian translator Gerard of Cremona, of his treatise on algebra (based on a Hindu work) was responsible for much of the mathematical knowledge of medieval Europe. His work on algorithm, a term derived from his name, introduced the method of calculating by use of Arabic numerals and decimal notation.