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Soviet postage stamp commemorating the 1200th anniversary of Muhammad al‑Khwarizmi in 1983.

Abu Abdullah Muhammad bin Musa al-Khwarizmi (خوارزمی in Persian, أبو عبد الله محمد بن موسى الخوارزمي in Arabic), also spelled Muhammad ibn-Musa al-Khwarizmi, Muhammad ibn-Musa al-Khowarizmi, Mohammad Bin Musa Al-Khawarizmi, and Abu Ja'Far Muhammad ibn-Musa Al-Khowarizmi, was a Persian scientist, mathematician, astronomer/astrologer, and author. He was probably born in 780, or around 800; and probably died in 845, or around 840.

He is often cited as "the father of algebra", which was named after a part of the title of his book, Hisab al-jabr w'al-muqabala, along with the algorism number system.



Khwarizmi was born in the town of Khwarizm (now Khiva), in Khorasan province of Persia (now in Uzbekistan). The name al-Khwarizmi means the person from Khwarizm. His family moved soon afterward, to a place near Baghdad, where he accomplished most of his work in the period between 813 and 833. There are various guesses at his native languages, including Persian or more probably Khwarezmian (an extinct Iranian language). Like all scientists in the House of Wisdom, Al-Khwarizmi wrote his works in Arabic. The historian Al-Tabari however applies the epithet Al-Majusi ("the magus") when describing him, which gives credit to claims that he was a Zoroastrian.

Mathematical historian Gandz gives this opinion of al-Khwarizmi's algebra:

"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." (1)

and Mohammad Kahn, says:

"In the foremost rank of mathematicians of all time stands Al-Khwarizmi. He composed the oldest works on arithmetic and algebra. They were the principal source of mathematical knowledge for centuries to come in the East and the West. The work on arithmetic first introduced the Hindu numbers to Europe, as the very name algorism signifies; and the work on algebra ... gave the name to this important branch of mathematics in the European world..."(2)


He made major contributions to the fields of algebra, trigonometry, astronomy/astrology, geography and cartography by translating important works from Sanskrit and other languages. His systematic and logical approach to solving linear and quadratic equations gave shape to the discipline of algebra, a word that is derived from the name of his 830 book on the subject, al-Kitab al-mukhtasar fi hisab al-jabr wa'l-muqabala (حساب الجبر و المقابلة) or: "The Compendious Book on Calculation by Completion and Balancing". The book was first translated into Latin in the 12th century, from which the title and term Algebra derives.

His book On the Calculation with Hindu Numerals written about 825, was principally responsible for the diffusion of the Indian system of numeration in the Middle-East and then Europe. The book was translated into Latin in the 12th century as Algoritmi de numero Indorum. From the name of the author, rendered in Latin as algoritmi, originated the term algorithm.

Much of his contributions were based on the original research of the Hindus in Astronomy and Greek, and other sources. He appropriated the place-marker symbol of zero, which originated in India.

Al-Khwarizmi systematized and corrected Ptolemy's data in geography as regards to Africa and the Middle east. Another major book was his Kitab surat al-ard ("The Image of the Earth"; translated as Geography), which presented the coordinates of localities in the known world based, ultimately, on those in the Geography of Ptolemy but with improved values for the length of the Mediterranean Sea and the location of cities in Asia and Africa.

He also assisted in the construction of a world map for the caliph al-Ma'mun and participated in a project to determine the circumference of the Earth, supervising the work of 70 geographers to create the map of the then "known world".(3)

When his work became known in Europe through Latin translations, it made a significant contribution to the advancement of mathematics in Europe. He also wrote on mechanical devices like the clock, astrolabe, and sundial. His other contributions include tables of trigonometric functions, refinements in the geometric representation of conic sections, and aspects of the calculus of two errors.

Famous works

See also


(1): S Gandz, The sources of al-Khwarizmi's algebra, Osiris, i (1936), 263-77.

(2): A A al'Daffa, The Muslim contribution to mathematics (London, 1978).

(3): From his biography in Encyclopdia Britannica.

Other sources to use


  1. Biography in Dictionary of Scientific Biography (New York 1970-1990).
  2. J N Crossley, The emergence of number (Singapore, 1980).
  3. A F Faizullaev, The scientific heritage of Muhammad al-Khwarizmi (Russian) (Tashkent, 1983).
  4. S Gandz (ed.), The geometry of al-Khwarizmi (Berlin, 1932).
  5. E Grant (ed.), A source book in medieval science (Cambridge, 1974).
  6. O Neugebauer, The exact sciences in Antiquity (New York, 1969).
  7. R Rashed, The development of Arabic mathematics : between arithmetic and algebra (London, 1994).
  8. R Rashed, Entre arithmtique et algbre: Recherches sur l'histoire des mathmatiques arabes (Paris, 1984).
  9. F Rosen (trs.), Muhammad ibn Musa Al-Khwarizmi : Algebra (London, 1831).


  1. K F Abdulla-Zade, al-Khwarizmi and the Baghdad astronomers (Russian), in The great medieval scientist al-Khwarizmi (Tashkent, 1985), 178-183.
  2. M Abdullaev, al-Khwarizmi and scientific thought in Daghestan (Russian), in The great medieval scientist al-Khwarizmi (Tashkent, 1985), 228-232.
  3. A Abdurakhmanov, al-Khwarizmi : great mathematician (Russian), in The great medieval scientist al-Khwarizmi (Tashkent, 1985), 149-151.
  4. M A Akhadova, The mathematics of India and al-Khwarizmi (Russian), in The great medieval scientist al-Khwarizmi (Tashkent, 1985), 238-240.
  5. S al-Khalidi, al-Khwarizmi : scholar of astronomical and mathematical geography (Arabic), in Proceedings of the Seventh Annual Conference on the History of Arabic Science (Arabic) (Aleppo, 1986), 55-63.
  6. A Allard, La diffusion en occident des premires oeuvres latines issues de l'arithmtique perdue d'al-Khwarizmi, J. Hist. Arabic Sci. 9 (1-2) (1991), 101-105.
  7. P G Bulgakov, al-Biruni and al-Khwarizmi (Russian), in Mathematics and astronomy in the works of scientists of the medieval East (Tashkent, 1977), 117-122, 140.
  8. J N Crossley and A S Henry, Thus spake al-Khwarizmi : a translation of the text of Cambridge University Library ms., Historia Math. 17 (2) (1990), 103-131.
  9. Y Dold-Samplonius, Developments in the solution to the equation cx + bx = a from al-Khwarizmi to Fibonacci, in From deferent to equant (New York, 1987), 71-87.
  10. R Z Du, al-Khwarizmi and his algebraic treatise (Chinese), Math. Practice Theory (1) (1987), 79-85.
  11. K Fogel, How al-Khwarizmi became known in Germany (Russian), in The great medieval scientist al-Khwarizmi (Tashkent, 1985), 85-91.
  12. J P Hogendijk, al-Khwarizmi's table of the "sine of the hours" and the underlying sine table, Historia Sci. 42 (1991), 1-12.
  13. B B Hughes, Robert of Chester's Latin translation of al-Khwarizmi's 'al-Jabr', Boethius : Texts and Essays on the History of the Exact Sciences XIV (Stuttgart, 1989).
  14. D K Ibadov, The work of al-Khwarizmi in the estimation of Eastern encyclopedic scholars of the 10th - 16th centuries (Russian), in The great medieval scientist al-Khwarizmi (Tashkent, 1985), 265-268.
  15. W Kaunzner, ber eine frhe lateinische Bearbeitung der Algebra al-Khwarizmis in MS Lyell 52 der Bodleian Library Oxford, Arch. Hist. Exact Sci. 32 (1) (1985), 1-16.
  16. E S Kennedy, Al-Khwarizmi on the Jewish calendar, Scripta Math. 27 (1964), 55-59.
  17. A S Kennedy and W Ukashah, al-Khwarizmi's planetary latitude tables, Centaurus 14 (1969), 86-96.
  18. M M Khairullaev, al-Khwarizmi and his era (Russian), Voprosy Istor. Estestvoznan. i Tekhn. (3) (1983), 121-127.
  19. P Kunitzsch, al-Khwarizmi as a source for the 'Sententie astrolabii', in From deferent to equant (New York, 1987), 227-236.
  20. G P Matvievskaya, The algebraic treatise of al-Khwarizmi (Russian), in On the history of medieval Eastern mathematics and astronomy (Tashkent, 1983), 3-22.
  21. G P Matvievskaya, History of the study of the scientific work of al-Khwarizmi (Russian),, in The great medieval scientist al-Khwarizmi (Tashkent, 1985), 72-82.
  22. C A Nallino, Al'Khuwarizimi e il suo rifacimento della Geografia di Tolomeo, Raccolta di scritti editie inediti V (Rome, 1944), 458-532.
  23. K H Parshall, The art of algebra from al-Khwarizmi to Vite : a study in the natural selection of ideas, Hist. of Sci. 26 (72, 2) (1988), 129-164.
  24. M A Pathan, Al-Khwarizmi, Math. Ed. 6 (2) (1989), 92-94.
  25. D Pingree, al-Khwarizmi in Samaria, Arch. Internat. Hist. Sci. 33 (110) (1983), 15-21.
  26. B A Rosenfeld, 'Geometric trigonometry' in treatises of al-Khwarizmi, al-Mahani and ibn al-Haytham, in Vestigia mathematica (Amsterdam, 1993), 305-308.
  27. B A Rozenfeld, al-Khwarizmi's spherical trigonometry (Russian), Istor.-Mat. Issled. 32-33 (1990), 325-339.
  28. B A Rozenfeld, Number theory, geometry and astronomy in al-Khwarizmi's 'Book of Indian arithmetic' (Russian), in The great medieval scientist al-Khwarizmi (Tashkent, 1985), 66-72.
  29. B A Rozenfeld and N D Sergeeva, The astronomical treatises of al-Khwarizmi (Russian), Istor.-Astronom. Issled. 13 (1977), 201-218.
  30. M M Rozhanskaya, The historical-astronomical value of al-Khwarizmi's "zij" (Russian), in The great medieval scientist al-Khwarizmi (Tashkent, 1985), 158-165.
  31. A S Sadykov, al-Khwarizmi : his era, life and work (Russian), in The great medieval scientist al-Khwarizmi (Tashkent, 1985), 8-13.
  32. M Sani, The life and work of al-Khwarizmi, Menemui Mat. 4 (1) (1982), 1-9.
  33. K S Siddikov, Muhammad al-Khwarizmi : creator of algebra (Russian), in The great medieval scientist al-Khwarizmi (Tashkent, 1985), 152-154.
  34. S Kh Sirazhdinov and G P Matvievskaya, Muhammad ibn Musa al-Khwarizmi and his contribution to the history of science (Russian), Voprosy Istor. Estestvoznan. i Tekhn. (1) (1983), 108-119.
  35. Z K Sokolovskaya, The "pretelescopic" period of the history of astronomical instruments. al-Khwarizmi in the development of precision instruments in the Near and Middle East (Russian), in The great medieval scientist al-Khwarizmi (Tashkent, 1985), 165-178.
  36. B van Dalen, Al'Khwarizmi's astronomical tables revisited : analysis of the equation of time, in From Baghdad to Barcelona (Barcelona, 1996), 195-252.
  37. K Vogel, Wie wurden al-Khwarizmi s mathematische Schriften in Deutschland bekannt?, Sudhoffs Arch. 68 (2) (1984), 230-234.
  38. A I Volodarskii, al-Khwarizmi and Indian mathematics (Russian), in The great medieval scientist al-Khwarizmi (Tashkent, 1985), 232-238.
  39. E Yu Yusupov and M M Kharullaev, The creative legacy of al-Khwarizmi and his place in the history of science (Russian), Voprosy Filos. (8) (1983), 140-146, 174.
  40. Kh Zemanek, Manuscripts of al-Khwarizmi's works (Russian), in The great medieval scientist al-Khwarizmi (Tashkent, 1985), 115-121.
  41. V K Zharov, Instrumental counting in al-Khwarizmi's arithmetical treatise (Russian), in The great medieval scientist al-Khwarizmi (Tashkent, 1985), 154-157.

External links

de:Al-Chwarizmi es:Abu Yafar Mohamed Ben Musa Al Juarism eo:Al-Ĥorezmi fr:Abou Abdallah Muḥammad Ben Mūsa ʾal-Khuwārizmī gl:Al-Khwarizmi id:Abu Abdullah Muhammad Ibn Musa al-Khawarizmi is:Al-Khwarizmi it:Al-Khwarizmi he:אבו ג'עפר מוחמד אל חואריזמי hu:Al-Kvrizmi ms:Abu Abdullah Mohammad Ibn Musa al-Khawarizmi nl:Al-Chwarizmi pl:Muhammed ibn Musa Alchwarizmi ru:Абу Абд Аллах Мухаммед ибн Мусса аль-Хорезми sk:Muhammad al-Chorezm sl:Al-Hvarizmi fi:Al-Khwarizmi sv:Muhammad ibn Musa al-Khwarizmi tr:Harezmi zh:花拉子密


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