A Muslim mathematician, astronomer, and geographer, who wrote on Hindu-Arabic numerals and was among the first to use zero as a place holder in positional base notation. The word algorithm derives from his name. His algebra treatise Hisab al-jabr w'al-muqabala gives us the word algebra and can be considered as the first book to be written on algebra. He was born around 780 in Khwārizm (now Khiva, Uzbekistan) and died around 850. He worked most of his life as a scholar in the House of Wisdom in Baghdad.
His Kitab fi 'l-jabr wa-'l-muqabala (Book on algebra and in opposition) was the first book on the systematic solution of linear and quadratic equations. Consequently he is considered to be the father of algebra. Latin translations of his Arithmetic, on the Indian numerals, introduced the decimal positional number system to the Western world in the 12th century.
See for a biography and review of al-Khwarizmi's mathematical contribution: Full MacTutor biography. See also "Al-Khwarizmi, Abdu'l-Hamid Ibn Turk and the Place of Central Asia in the History of Science".