Muhammad ibn Musa al-Khwarizmi

Al-Khwarizmi gave algebra its name and the algorithm its name. Born around 780, probably in Khwarazm in Central Asia, he worked at the House of Wisdom in Baghdad under the caliph al-Ma'mun, the research and translation institution that gathered Greek, Persian and Indian learning. His book on calculation by completion and balancing, written around 820, gives systematic methods for solving linear and quadratic equations. Its Arabic title contains al-jabr, meaning the restoration of a subtracted quantity to the other side of an equation, and the Latin transliteration of that word became algebra. The work matters because of what it does rather than what it solves. Earlier mathematicians had handled particular problems; al-Khwarizmi set out general procedures, expressed in words rather than symbols, and gave geometric proofs that they work. Algebra becomes a discipline rather than a collection of tricks. He also wrote a treatise on the Indian numerals, introducing the decimal positional system and the use of zero to the Arabic-speaking world and, through a twelfth-century Latin translation beginning Dixit Algorizmi, to Europe. The word algorithm comes from that rendering of his name. He revised Ptolemy's Geography, correcting the length of the Mediterranean and the coordinates of hundreds of places, and worked on a project to measure the earth's circumference. He wrote on the astrolabe, the sundial and the Jewish calendar, and produced astronomical tables that were used for centuries. His concerns were practical as well as theoretical: he framed the algebra as useful for inheritance division, legacies, partition, lawsuits and trade. He probably died around 850.

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