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Al-Khwārizmī and algebra

al-Khwārizmī

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For everyone

Al-Khwārizmī, working at the House of Wisdom in Baghdad, gave the word "algebra" its name with his book on solving equations systematically. The word "algorithm" also comes from the Latin form of his name. Historians debate whether the "father" of algebra is al-Khwārizmī or the earlier Diophantus of Alexandria.

For specialists

Al-Kitāb al-mukhtaṣar fī ḥisāb al-jabr wa'l-muqābala classifies linear and quadratic equations into six canonical types and supports each solution with a geometric proof (completing the square). It is rhetorical, not symbolic, algebra. Diophantus' Arithmetica uses abbreviated (syncopated) notation and focuses on rational solutions of indeterminate equations. Al-Khwārizmī's treatise on calculation with Indian numerals spread the decimal system in Europe through its Latin translation (Algoritmi de numero Indorum).

Claims

Positions

View crediting al-Khwārizmī as founder of algebra
Al-Khwārizmī was the first to establish algebra as a discipline in its own right, with general methods of solution and proofs.[1]
View emphasising Diophantus
Diophantus' Arithmetica (c. 250 CE) contains notation for unknowns and solutions of equations, and is older.[2]

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Mathematics

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Zero as a number

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Sources

  1. BookRashed, R. (2009). Al-Khwārizmī: The Beginnings of Algebra. Saqi Books, London
  2. BookHeath, T. L. (1910). Diophantus of Alexandria: A Study in the History of Greek Algebra. Cambridge University Press, 2nd edition
  3. WebAbu Ja'far Muhammad ibn Musa Al-Khwarizmi (biography). MacTutor History of Mathematics, University of St Andrewsmathshistory.st-andrews.ac.ukarchive

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APA

Athena contributors. (2026). Al-Khwārizmī and algebra. Athena: The tree of human knowledge. Retrieved November 1, 2026, from https://latifkedi.github.io/athena/en/d/harezmi/

BibTeX
@misc{athena_harezmi,
  title        = {Al-Khwārizmī and algebra},
  author       = {{Athena contributors}},
  year         = {2026},
  howpublished = {\url{https://latifkedi.github.io/athena/en/d/harezmi/}},
  note         = {Athena: The tree of human knowledge. Accessed: 2026-11-01}
}

Added: September 27, 2026 · Last changed: September 28, 2026 · Page history

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