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"Algorithm": A Word from the 9th Century

Zusammenfassung

The word “algorithm” derives from the name of Muhammad ibn Musa al-Khwarizmi, a 9th-century Persian mathematician who worked at the House of Wisdom in Baghdad. When his book on arithmetic was translated into Latin in the 12th century, “al-Khwarizmi” became “Algoritmi” in Latin transliteration, and “Algoritmi dixit” (al-Khwarizmi says) became the title-like phrase introducing his methods. “Algorithm” — a procedure for solving a problem by a defined sequence of steps — carries the name of a man who died around 850 CE into every computer science course, textbook, and technical discussion in the world.

Al-Khwarizmi and the House of Wisdom

Muhammad ibn Musa al-Khwarizmi (c. 780–850 CE) worked at the Bayt al-Ḥikma (House of Wisdom) in Baghdad during the Islamic Golden Age under the Abbasid caliphs al-Maʾmūn and al-Mutawakkil. The House of Wisdom was the premier intellectual institution of the medieval world — a library, translation center, and research institution where scholars from across the Islamic world translated and extended Greek, Indian, and Persian scientific and mathematical works.

Al-Khwarizmi wrote two works that transformed European mathematics:

  1. Kitāb al-mukhtaṣar fī ḥisāb al-jabr wa-l-muqābala (The Compendious Book on Calculation by Completion and Balancing, c. 820 CE): A systematic treatment of linear and quadratic equations. The word “al-jabr” in the title gave European mathematicians the word “algebra”.

  2. Kitāb al-ḥisāb al-hindī (Book on Hindu Arithmetic, c. 825 CE): An explanation of the Indian positional decimal numeral system — the system we now call Hindu-Arabic numerals, using digits 0–9 with positional value. This book, when translated into Latin in the 12th century, introduced the decimal place-value system to Europe.

The Latin Translation and “Algorismus”

Al-Khwarizmi’s arithmetic book was translated into Latin in the 12th century, possibly by Adelard of Bath. The translator began the text with a phrase in the convention of the era: Dixit Algoritmi — “Al-Khwarizmi says” — using a Latin transliteration of the author’s name. “Algoritmi” (a genitive form, “of al-Khwarizmi”) became attached to the procedures described in the book.

European scholars began using “algorismus” (later “algorism”) to mean the system of arithmetic using Hindu-Arabic numerals with place value — as opposed to calculation using Roman numerals or an abacus. “Algorism” meant specifically: calculation by the new positional number system that al-Khwarizmi had described.

The word’s meaning drifted over centuries: from al-Khwarizmi’s specific numeral system, to any systematic calculation procedure, to the modern computer science definition: a finite sequence of unambiguous instructions for solving a class of problems.

The Mathematical Concept Before the Word

The concept of an algorithm — a defined procedure for solving a problem, guaranteed to terminate in a correct answer — is older than the word. The Algorithm as a Concept traces its history through Euclid’s algorithm for finding the greatest common divisor (c. 300 BCE), Hindu astronomical calculation procedures, and medieval arithmetic. Al-Khwarizmi’s contribution was not the invention of the concept but the systematic codification and transmission of specific algorithmic methods to European mathematics.

The formal definition of what an algorithm is — the question of what is and is not computable — was not settled until Alan Turing’s 1936 paper on computable numbers and Alonzo Church’s lambda calculus. The word “algorithm” is ancient; the theory of algorithms is 20th-century mathematics.

Algebra from the Same Author

The title of al-Khwarizmi’s algebra book — al-jabr wa-l-muqābala — contained two technical terms. Al-jabr meant “completion” or “restoration” — the operation of moving a subtracted quantity to the other side of an equation (e.g., converting x - 2 = 5 to x = 7 by “restoring” the 2). This word, when the text was translated into Latin and Spanish, became “algebra” in European languages.

Al-Khwarizmi’s name thus gave two fundamental mathematical terms to modern science: “algorithm” from his name itself, and “algebra” from the title of one of his books. The history of mathematics and the history of computing share a linguistic debt to a mathematician who died twelve centuries ago.

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