Algorithm

A precise, finite procedure for solving a class of problems. The word itself descends from the name of Muhammad ibn Musa al-Khwarizmi, the ninth century mathematician of the House of Wisdom in Baghdad: a Latin translation of his arithmetic treatise circulated as Algoritmi de numero Indorum, and the Latinized form of his name, algorismus, became the medieval European word for the Hindu-Arabic method of calculation it taught, from which algorithm descends. His algebra treatise, Hisab al-jabr wal-muqabala, separately gave mathematics the word algebra. The modern, fully formal definition of an algorithm waited until 1936, when Alan Turing's paper On Computable Numbers, with an Application to the Entscheidungsproblem described an abstract machine that moves between a finite table of states reading and writing symbols on a tape, what Alonzo Church that same year named the Turing machine, and proved the existence of a universal machine able to carry out the work of any other by reading suitable instructions from its own tape. A computable number, in Turing's definition, is a real number whose decimal expansion such a machine can produce, and this became the standard modern account of what an algorithm is.