The word “algorithm”? is quite interesting; at first glance it may look as though someone intended to write “logarithm” but jumble up the first four letters. The word did not appear in Webster’s New World Dictionary as late as 1975; we found only the older form “algorism” with this ancient meaning, the process of doing arithmetic using Arabic numerals. During the Middle Ages, abacists computed on the abacus and algorists computed by algorism. By the time of the Renaissance, the origin of this word was in doubt, and early linguists attempted to guess at its derivation by making combinations like algiros [painful]+arithmos [number]; others said no, the word comes from “King Algor of Castile.” Finally, historians of mathematics found the true origin of the word algorism: It comes from the name of a famous Persian textbook author, Abu Abd Allah Muhammad ibn Musa al-Khawarizmi — literally, “Father of Abdullah, Mohammed, son of Moses, native of Khawarizm.” The Aral sea in Central Asia was once known as Lake Khawarizm, and the Khawarizm region is located in the Amu River basin just south of that sea. Al-Khawarizmi wrote the celebrated Arabic text Kitab al-jabr wa’l-muqabala (“Rules of restoring and equating”); another word, “algebra,” stems from the title of that book, which was a systematic study of the solution of linear and quadratic equations. [For notes on al-Khwarizmi's life and work, see H. Zemanek, Lecture in Computer Science 122 (1981, 1-81.]
Gradually the form and meaning of algorism became corrupted; as explained by the Oxford English Dictionary, the word “passed through many pseudo-etymological perversions, including a recent algorithm, in which it is learnedly confused” with Greek root of the word arithmetic. This change from “algorism” to “algorithm” is not hard to understand in view of the fact that people had forgotten the original derivation of the word. An early German mathematical dictionary, Vollstandiges mathematisches Lexicon: “(Leipzig: 1774), gave the following definition for the word Algorithmus: “Under this designation are combined the notions of the four types of arithmetic calculations, namely addition, multiplication, substraction, and division.” The Latin phrase algorithmus infinitesimalis was at that time used to denote “ways of calculation with infinitely small quantities, as invented by Leibniz.
By 1950, the word algorithm was most frequently associated with Euclid’s algorithm, a process for finding the greatest common divisor of two numbers that appears in Euclid’s Elements (Book 7, Propositions 1 and 2).
[Donald Knuth, The Art of Computer Programming, volume 1, 2007]
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