The Online Encyclopedia and Dictionary







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".



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 mentions the word Al-majusi when describing him, which gives credit to some claims that he was initially 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. 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.

He is also responsible for the use of Arabic numerals in mathematics: In the 12th century a second work by al-Khwarizmi introduced Hindu-Arabic numerals and their arithmetic to the West. It is preserved only in a Latin translation, Algoritmi de numero Indorum. From the name of the author, rendered in Latin as algoritmi, originated the term algorithm.

While his major contributions were the result of original research, he also did much to synthesize the existing knowledge in these fields from Greek, Indian, and other sources. He appropriated the place-marker symbol of zero, which originated in India.

Al-Khwarizmi systematized and corrected Ptolemy's research in geography and astronomy/astrology, using his own original findings. 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, his influence made an indelible mark on the development of science in the West: his algebra book introduced that discipline to Europe and became the standard mathematical text at European universities until the 16th century. 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

  • Al-Jabr wa-al-Muqabilah from whose title came the name "Algebra"
  • Kitab al-Jam'a wal-Tafreeq bil Hisab al-Hindi (on Arithmetic, which survived in a Latin translation but was lost in the original Arabic)
  • Kitab Surat-al-Ard (on geography)
  • Istikhraj Tarikh al-Yahud (about the Jewish calendar)
  • Kitab al-Tarikh
  • Kitab al-Rukhmat (about sun-dials)

See also

Sources for writing this article

(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 Encyclopædia 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 arithmétique et algèbre: Recherches sur l'histoire des mathématiques 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 premières oeuvres latines issues de l'arithmétique 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 cxÛ + 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, Über eine frühe 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 Viète : 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

Last updated: 09-12-2005 02:39:13