The Origin and Transformations of Old Babylonian Algebra

  • Jens Høyrup
Part of the Sources and Studies in the History of Mathematics and Physical Sciences book series (SHMP)


Several offhand references were made in the preceding chapters to “riddles”, to “practitioners”, and to “lay surveyors”. In order to make these considerations meaningful and fruitful, a somewhat more systematic discussion may be needed.[431] The following applies to the situation as it looked (with a few exceptions, mostly regarding the Islamic world) until the seventeenth century, that is, to a situation where the knowledge system of a practical profession or craft was much more autonomous than today. As is well known, the relation between theoreticians’ and practitioners’ knowledge began to change in the late Renaissance, and was wholly transformed by the nineteenth-century advent of the modern engineers’ professions; in consequence, today a large part of the practitioner’s knowledge (though still far from all of it) is applied theory, which complicates the relation between the two types of knowledge without wholly abolishing their distinctive characteristics.


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  1. 431.
    With some changes, these reflections draw on ideas first presented coherently in [Heyrup 1990a] (slightly revised reprint in [Hoyrup 1994: 23–43]).Google Scholar
  2. 432.
    Metaphysica 982a1 [ed. Tredennick 1933: I,3].Google Scholar
  3. 433.
    Mahâvira, Ganita-stira-sangraha VI.242–243 [trans. Ra ngâcârya 1912: 157].Google Scholar
  4. 434.
    From the German translation in [Suter 1910: 101]. The phrases “and so on” and “or more or less” refer to the existence of other variants.Google Scholar
  5. 435.
    Propositiones ad acuendos iuvenes,52 (version ii) [ed. Folkerts 1978: 74].Google Scholar
  6. 436.
    Book of Rarities in Calculation; from the German translation in [Suter 1910: 100].Google Scholar
  7. 437.
    See, for instance, [Ong 1982: 43ff and passim]. Google Scholar
  8. 438.
    to find out, not without exceptional amazement of the ignorant, how many penning, creutzer, or other coin somebody possesses“, in Christoph Rudolff’s words [1540]. In the pre-Modern world, indeed, subscientific knowledge was neither ”folk“ nor ”popular“ knowledge, but a possession of the few to a significantly higher degree than scientific knowledge today.Google Scholar
  9. 439.
    There is another point in the term “sub-scientific” which I shall not pursue here, namely, that the subscientific knowledge systems have served as inspiration in the development of “scientific” mathematics.Google Scholar
  10. 487.
    Thus in Liber mensurationum #49–50 [ed. Busard 1968: 97f], and in Fibonacci’s Pratica geometrie [ed. Boncompagni 1862: 70f].Google Scholar

Copyright information

© Springer Science+Business Media New York 2002

Authors and Affiliations

  • Jens Høyrup
    • 1
  1. 1.Section for Philosophy ans Sciences StudiesUniversity of RoskildeRoskildeDenmark

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