Algebra, Surveyors'

  • Jens Høyrup
Reference work entry

Around 1930, a mathematical technique very close to later second‐degree algebra was discovered in Babylonian cuneiform tablets, most of them dating from the early second and a few from the late first millennium BCE (the “Old Babylonian” and “Seleucid” periods, respectively). Although the texts did not say so in any way, it was supposed that the technique was purely arithmetical, and that its “lengths,” “widths,” and “areas” were metaphors designating numerical unknowns and their products. The geometry of Euclid's Elements II was then believed to represent a Greek geometrical reinterpretation of the arithmetical results of the Babylonians, necessitated by the discovery of irrationality.

A more sophisticated analysis of the Old Babylonian texts shows that the arithmetical interpretation does not hold water. For instance, the texts distinguish sharply between two different concepts that had been understood as one and the same “addition”; two different “subtractions”; two different...
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  1. The surveyors’ tradition and its relations to the written mathematical traditions is treated in: Høyrup, Jens, On a Collection of Geometrical Riddles and Their Role in the Shaping of Four to Six “Algebras.” Science in Context 14 (2001): 85–131.Google Scholar
  2. The most thorough argument for the naive‐geometric character of Old Babylonian “algebra” is: Høyrup, Jens, 2002. Lengths, Widths, Surfaces: A Portrait of Old Babylonian Algebra and Its Kin (Studies and Sources in the History of Mathematics and Physical Sciences). New York: Springer, 2002.Google Scholar
  3. The innovations of the Seleucid are treated at depth in: Høyrup, Jens, Seleucid Innovations in the Babylonian “Algebraic” Tradition and Their Kin Abroad. Ed. Yvonne Dold‐Samplonius et al. From China to Paris: 2000 Years Transmission of Mathematical Ideas (Boethius, 46). Stuttgart: Steiner, 2002. 9–29.Google Scholar
  4. The influence of the Near Eastern tradition on Mahāvīra's Gaṇita‐sāra‐saṅgraha is the theme of Høyrup, Jens, Mahāvīra's Geometrical Problems: Traces of Unknown Links between Jaina and Mediterranean Mathematics in the Classical Ages. Ed. Ivor Grattan‐Guinness and B. S. Yadav. History of the Mathematical Sciences. New Delhi: Hindustan Book Agency. 2004. 83–95.Google Scholar

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© Springer-Verlag Berlin Heidelberg New York 2008

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  • Jens Høyrup

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