Etymology

Algorithm

Every algorithm running on every device traces its name to a ninth-century Persian mathematician.

Arabic · 9th century
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Arabic
al-Khwārizmī
Medieval Latin
Algoritmi
English
algorithm

The word algorithm derives from the Latinized name of Muhammad ibn Musa al-Khwarizmi, a Persian mathematician and astronomer who worked at the House of Wisdom in Baghdad around 820 CE.1 The epithet al-Khwarizmi means "the native of Khwarazm," a region in what is now Uzbekistan and Turkmenistan. When his book on Hindu-Arabic numerals was translated into Latin in the twelfth century, it appeared under the title Algoritmi de numero Indorum, and the Latinized version of his name became the word for the method he described.

Al-Khwarizmi's most influential work, Al-Kitab al-mukhtasar fi hisab al-jabr wa'l-muqabala (The Compendious Book on Calculation by Completion and Balancing), gave the world a second foundational word. Al-jabr, meaning "restoration" or "completion," became algebra.2 The book presented the first systematic methods for solving linear and quadratic equations.

For several centuries, algorism referred specifically to the rules for performing arithmetic with Hindu-Arabic numerals, the system al-Khwarizmi had popularized.3 The broader meaning, a finite set of step-by-step instructions for solving a problem, emerged in the early twentieth century. Alan Turing's theoretical work in the 1930s formalized the concept, establishing that a machine could follow algorithmic instructions to solve complex mathematical problems.4

A ninth-century scholar working in a Baghdad library gave his name to the governing logic of search engines, social media feeds, and AI-assisted work tools.

c. 820
Al-Khwarizmi works at the House of Wisdom in Baghdad, writing on algebra and Hindu-Arabic numerals.
12th century
Latin translations of al-Khwarizmi's work introduce Algoritmi to Europe.
1930s
Alan Turing formalizes the concept of an algorithm as a set of machine-executable instructions.
1 J.L. Berggren, Episodes in the Mathematics of Medieval Islam (New York: Springer, 2003).
2 Encyclopaedia Britannica, "al-Khwarizmi."
3 Douglas Harper, "Algorithm," Online Etymology Dictionary.
4 Donald E. Knuth, "Algorithms in Modern Mathematics and Computer Science," Stanford University Department of Computer Science (1980).
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