Abu Ja'far Muhammad ibn Musa al-Khwarizmi was a Persian, astronomer, astrologer and geographer. He was born around 780 in Khwārizm(in ancient Persia, now Khiva, Uzbekistan) and died around 850 in Baghdad, Iraq. He worked most of his life as a scholar in the House of Wisdom in Baghdad.
He wrote mathematical books that collected and arranged the discoveries of earlier mathematicians and achievements of herself. His Al-Kitab al-mukhtasar fi hisab al-jabr wa'l-muqabala ("The Compendious Book on Calculation by Completion and Balancing") is a compilation of rules for solving linear and quadratic equations, as well as problems of geometry and proportion. Its translation into Latin in the 12th century provided the link between the great Hindu and Arab mathematicians and European scholars. A corruption of the book's title resulted in the word algebra; a corruption of the author's own name resulted in the term algorithm.(Britannica)
Al-Khwarizmi's other main surviving works are a treatise on the Hindu system of numerals and a treatise on geography. The Hindu number system, with its epoch-making innovations, for example the incorporation of a symbol for zero, was introduced to Europe via a Latin translation (De numero indorum; On the Hindu Art of Reckoning) of al-Khwarizmi's work.(Oxford University Press)
Of great importance also was al-Khwarizmi's contribution to medieval geography. His improvement upon Ptolemy's work is entitled Surat al-Ard (The Shape of the Earth). The text exists in a manuscript; the maps have unfortunately not been preserved, although modern scholars have been able to reconstruct them from al-Khwarizmi's descriptions.(Answers)
Al-Khwārizmī wrote several other works including a treatise on the Hebrew calendar (Risāla fi istikhrāj ta , rīkh al-yahūd "Extraction of the Jewish Era"). It describes the 19-year intercalation cycle, the rules for determining on what day of the week the first day of the month Tishrī shall fall; calculates the interval between the Jewish era (creation of Adam) and the Seleucid era; and gives rules for determining the mean longitude of the sun and the moon using the Jewish calendar.(Wikipedia)
In The Universal History of Numbers, Georges Ifrah sums up Khwarizmi's contribution to the modern world:
Unbeknown to him, al-Khwarizmi privided the name for a fundamental branch of modern mathamatics, and gave his own name to the science of algorithms, the basis for one of the practical and theoretical activities of computing. What more can be said about this great scholar's influence?