N. Akmal Ayyubi in Muslim Heritage:
One of the greatest minds of the early mathematical production in Arabic was Abu Abdullah Muhammad ibn Musa al-Khwarizmi (b. before 800, d. after 847 in Baghdad) who was a mathematician and astronomer as well as a geographer and a historian. It is said that he is the author in Arabic of one of the oldest astronomical tables, of one the oldest works on arithmetic and the oldest work on algebra; some of his scientific contributions were translated into Latin and were used until the 16th century as the principal mathematical textbooks in European universities. Originally he belonged to Khwârazm (modern Khiwa) situated in Turkistan but he carried on his scientific career in Baghdad and all his works are in Arabic.
He was summoned to Baghdad by Abbasid Caliph Al-Ma’mun (213-833), who was a patron of knowledge and learning. Al-Ma’mun established the famous Bayt al-Hikma (House of Wisdom) which worked on the model of a library and a research academy. It had a large and rich library (Khizânat Kutub al-Hikma) and distinguished scholars of various faiths were assembled to produce scientific masterpieces as well as to translate faithfully nearly all the great and important ancient works of Greek, Sanskrit, Pahlavi and of other languages into Arabic. Muhammad al-Khwarizmi, according to Ibn al-Nadîm  and Ibn al-Qiftî  (and as it is quoted by the late Aydin Sayili) , was attached to (or devoted himself entirely to) Khizânat al-Hikma. It is also said that he was appointed court astronomer of Caliph Al-Ma’mun who also commissioned him to prepare abstracts from one of the Indian books entitled Surya Siddhanta which was called al-Sindhind  in Arabic . Al-Khwarizmi’s name is linked to the translation into Arabic of certain Greek works  and he also produced his own scholarly works not only on astronomy and mathematics but also in geography and history. It was for Caliph al-Ma’mun that Al-Khwarizmi composed his astronomical treatise and dedicated his book on Algebra.
…It is worth remarking that the term al-jabr, in the Latinized form of algebra, has found its way into the modern languages, whilst the old mathematical term algorism is a distortion of al-Khwarizmi’s name.