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around 1070–1079 CE

Khayyam's Al-jabr

Exact solution procedure for cubic equations

Omar Khayyam's Maqalah fi al-jabr wa-al muqabalah (On the Proofs of the Problems of Algebra and Muqabala) was most likely written between the years 1070–1079 CE. It considers several types of algebraic problems, but is best known for geometric solutions to six classes of cubic equations. This treatment represents the first systematic study of—as well as the first exact solution procedure for—general classes of cubic equations.

Khayyam's Al-jabr

While Khayyam is best known in the Western world as the author of the collection of poems known as the Rubáiyát, he was also a mathematician and worked as an astronomer for the court of Sultan Malik-Shah I (1055–1092). His work Al-jabr was composed in Samarkand under the patronage of Samarkand's governor, Abu Tahir Abd al-Rahman ibn 'Alaq.

Artifact dimensions

6.1 in. × 9.6 in.

Artifact origin

Samarkand, Uzbekistan

Current artifact location

Columbia University in the City of New York Library

Catalog number

Smith Oriental MS 45


Algebra timeline Babylonian Metric Algebra Problems Tablet Berlin Pythagorean Theorem Papyrus Rhind Papyrus Al-Khwārizmī's Al-Jabr Khayyam's Al-jabr Cardano's Ars Magna Recorde's Whetstone of Witte Faulhaber's Academia Algebrae Wallis's Treatise of Algebra Emerson's Treatise of Algebra Hermes's Suitcase of Göttingen

Interactive Content

Computational Explanation

Additional Reading

  • Berggren, J. L. Episodes in the Mathematics of Medieval Islam. New York: Springer-Verlag, 1986.
  • Berggren, J. L. "The Algebra of Omar Khayyām." In The Mathematics of Egypt, Mesopotamia, China, India, and Islam: A Sourcebook (Ed. V. J. Katz). Princeton, NJ: Princeton University Press, pp. 556–560, 2007.
  • Grattan-Guinness, I. (Ed.) Companion Encyclopedia on the History and Philosophy of the Mathematical Science, Vol. 1. London: Routledge, p. 76, 1994.
  • Kasir, D. S. The Algebra of Omar Khayyam. New York: Columbia University, 1932.
  • Katz, V. J. A History of Mathematics. Reading, MA: Addison-Wesley, 1998.
  • Mardia, K. V. "Omar Khayyam, René Descartes and Solutions to Algebraic Equations." Paper presented to the Omar Khayyam Club, London, 19 November 1999. [link]
  • Merzbach, U. C. and Boyer, C. B. "Omar Khayyam." In A History of Mathematics, 3rd ed. Hoboken, NJ: Wiley, pp. 218–220, 2011.
  • van der Waerden, B. L. "Omar Khayyam." Ch. 1, Part C in A History of Algebra: From al-Khwārizmī to Emmy Noether. Berlin: Springer-Verlag, pp. 24–31, 1985.
  • Woepke. F. L'algèbre d'Omar Alkhayyami. Paris: Benjamin Duprat, 1851.