Back Mohammed ibn Moesa al-Chwarizmi Afrikaans Al-Chwarizmi ALS አል-ሗሪዝሚ Amharic Muhammad ibn Mūsā al-Khwārizmī AN محمد بن موسى الخوارزمي Arabic الخوارزمي ARY الخوارزمى ARZ Muhammad ibn Musa al-Khwarizmi AST अल-ख्वारिज्मी AWA Əl-Xarəzmi Azerbaijani

Al-Khwarizmi

For other uses, see Al-Khwarizmi (disambiguation).
Muḥammad ibn Mūsā al-Khwārizmī
محمد بن موسى الخوارزمي‎
Woodcut panel depicting al-Khwarizmi, 20th century
Bornc. 780
Khwarazm, Abbasid Caliphate
Diedc. 850[2][3] (aged ~70)
Abbasid Caliphate
NationalityPersian
OccupationHead of the House of Wisdom in Baghdad (appt. c. 820)
Academic work
EraIslamic Golden Age
Main interests
Notable works
Notable ideasTreatises on algebra and the Hindu–Arabic numeral system
InfluencedAbu Kamil of Egypt[1]

Muhammad ibn Musa al-Khwarizmi[note 1] (Arabic: محمد بن موسى الخوارزمي; c. 780 – c. 850), often referred to as simply al-Khwarizmi, was a Persian polymath who produced vastly influential Arabic-language works in mathematics, astronomy, and geography. Hailing from Khwarazm, he was appointed as the astronomer and head of the House of Wisdom in the city of Baghdad around 820 CE.

His popularizing treatise on algebra, compiled between 813–33 as Al-Jabr (The Compendious Book on Calculation by Completion and Balancing),[6]: 171  presented the first systematic solution of linear and quadratic equations. One of his achievements in algebra was his demonstration of how to solve quadratic equations by completing the square, for which he provided geometric justifications.[7]: 14  Because al-Khwarizmi was the first person to treat algebra as an independent discipline and introduced the methods of "reduction" and "balancing" (the transposition of subtracted terms to the other side of an equation, that is, the cancellation of like terms on opposite sides of the equation),[8] he has been described as the father[9][10][11] or founder[12][13] of algebra. The English term algebra comes from the short-hand title of his aforementioned treatise (الجبر Al-Jabr, transl. "completion" or "rejoining").[14] His name gave rise to the English terms algorism and algorithm; the Spanish, Italian, and Portuguese terms algoritmo; and the Spanish term guarismo[15] and Portuguese term algarismo, both meaning "digit".[16]

In the 12th century, Latin-language translations of al-Khwarizmi's textbook on Indian arithmetic (Algorithmo de Numero Indorum), which codified the various Indian numerals, introduced the decimal-based positional number system to the Western world.[17] Likewise, Al-Jabr, translated into Latin by the English scholar Robert of Chester in 1145, was used until the 16th century as the principal mathematical textbook of European universities.[18][19][20][21]

Al-Khwarizmi revised Geography, the 2nd-century Greek-language treatise by the Roman polymath Claudius Ptolemy, listing the longitudes and latitudes of cities and localities.[22]: 9  He further produced a set of astronomical tables and wrote about calendric works, as well as the astrolabe and the sundial.[23] Al-Khwarizmi made important contributions to trigonometry, producing accurate sine and cosine tables and the first table of tangents.

  1. ^ O'Connor, John J.; Robertson, Edmund F., "Abū Kāmil Shujā' ibn Aslam" Archived 11 December 2013 at the Wayback Machine, MacTutor History of Mathematics archive, University of St Andrews.
  2. ^ Toomer, Gerald J. (1970–1980). "al-Khuwārizmī, Abu Ja'far Muḥammad ibn Mūsā". In Gillispie, Charles Coulston (ed.). Dictionary of Scientific Biography. Vol. VII. pp. 358–365. ISBN 978-0-684-16966-8.
  3. ^ Vernet, Juan (1960–2005). "Al-Khwārizmī". In Gibb, H. A. R.; Kramers, J. H.; Lévi-Provençal, E.; Schacht, J. (eds.). The Encyclopaedia of Islam. Vol. IV (2nd ed.). Leiden: Brill. pp. 1070–1071. OCLC 399624.
  4. ^ Ibn Khaldūn, The Muqaddimah: An introduction to history Archived 17 September 2016 at the Wayback Machine, Translated from the Arabic by Franz Rosenthal, New York: Princeton (1958), Chapter VI:19.
  5. ^ Knuth, Donald (1997). "Basic Concepts". The Art of Computer Programming. Vol. 1 (3rd ed.). Addison-Wesley. p. 1. ISBN 978-0-201-89683-1.
  6. ^ Oaks, J. (2009), "Polynomials and Equations in Arabic Algebra", Archive for History of Exact Sciences, 63(2), 169–203.
  7. ^ Cite error: The named reference Maher was invoked but never defined (see the help page).
  8. ^ (Boyer 1991, "The Arabic Hegemony" p. 229) "It is not certain just what the terms al-jabr and muqabalah mean, but the usual interpretation is similar to that implied in the translation above. The word al-jabr presumably meant something like "restoration" or "completion" and seems to refer to the transposition of subtracted terms to the other side of an equation; the word muqabalah is said to refer to "reduction" or "balancing" – that is, the cancellation of like terms on opposite sides of the equation."
  9. ^ Corbin, Henry (1998). The Voyage and the Messenger: Iran and Philosophy. North Atlantic Books. p. 44. ISBN 978-1-55643-269-9. Archived from the original on 28 March 2023. Retrieved 19 October 2020.
  10. ^ Boyer, Carl B., 1985. A History of Mathematics, p. 252. Princeton University Press. "Diophantus sometimes is called the father of algebra, but this title more appropriately belongs to al-Khowarizmi...", "...the Al-jabr comes closer to the elementary algebra of today than the works of either Diophantus or Brahmagupta..."
  11. ^ Gandz, Solomon, The sources of al-Khwarizmi's algebra, Osiris, i (1936), 263–277, "Al-Khwarizmi's algebra is regarded as the foundation and cornerstone of the sciences. In a sense, al-Khwarizmi is more entitled to be called "the father of algebra" than Diophantus because al-Khwarizmi is the first to teach algebra in an elementary form and for its own sake, Diophantus is primarily concerned with the theory of numbers."
  12. ^ Katz, Victor J. "Stages in the History of Algebra with Implications for Teaching" (PDF). VICTOR J.KATZ, University of the District of Columbia Washington DC, USA: 190. Archived from the original (PDF) on 27 March 2019. Retrieved 7 October 2017 – via University of the District of Columbia Washington DC, USA. The first true algebra text which is still extant is the work on al-jabr and al-muqabala by Mohammad ibn Musa al-Khwarizmi, written in Baghdad around 825.
  13. ^ Esposito, John L. (6 April 2000). The Oxford History of Islam. Oxford University Press. p. 188. ISBN 978-0-19-988041-6. Archived from the original on 28 March 2023. Retrieved 29 September 2020. Al-Khwarizmi is often considered the founder of algebra, and his name gave rise to the term algorithm.
  14. ^ Brentjes, Sonja (1 June 2007). "Algebra". Encyclopaedia of Islam, THREE. Archived from the original on 22 December 2019. Retrieved 5 June 2019.
  15. ^ Knuth, Donald (1979). Algorithms in Modern Mathematics and Computer Science (PDF). Springer-Verlag. ISBN 978-0-387-11157-5. Archived from the original (PDF) on 7 November 2006.
  16. ^ Gandz, Solomon (1926). "The Origin of the Term "Algebra"". The American Mathematical Monthly. 33 (9): 437–440. doi:10.2307/2299605. ISSN 0002-9890. JSTOR 2299605.
  17. ^ Struik 1987, p. 93
  18. ^ Philip Khuri Hitti (2002). History of the Arabs. Palgrave Macmillan. p. 379. ISBN 978-1-137-03982-8. Archived from the original on 20 December 2019.
  19. ^ Fred James Hill, Nicholas Awde (2003). A History of the Islamic World. Hippocrene Books. p. 55. ISBN 978-0-7818-1015-9. "The Compendious Book on Calculation by Completion and Balancing" (Hisab al-Jabr wa H-Muqabala) on the development of the subject cannot be underestimated. Translated into Latin during the twelfth century, it remained the principal mathematics textbook in European universities until the sixteenth century
  20. ^ Shawn Overbay; Jimmy Schorer; Heather Conger. "Al-Khwarizmi". University of Kentucky. Archived from the original on 12 December 2013.
  21. ^ "Islam Spain and the history of technology". www.sjsu.edu. Archived from the original on 11 October 2018. Retrieved 24 January 2018.
  22. ^ van der Waerden, Bartel Leendert (1985). A History of Algebra: From al–Khwarizmi to Emmy Noether. Berlin: Springer-Verlag.
  23. ^ Arndt 1983, p. 669


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