The Story of the Discovery of Incommensurability, Revisited

  • David H. Fowler
Part of the Boston Studies in the Philosophy of Science book series (BSPS, volume 151)


I take as my opening text the kind of thing my colleagues — certainly the mathematicians and often the historians of mathematics — might say about the beginnings of Greek mathematics. Something like this:

The early Pythagoreans based their theory of proportion on commensurable magnitudes (or on the rational numbers, or on common fractions m/n), but their discovery of the phenomenon of incommensurability (or the irrationality of √2) showed that this was inadequate. This provoked problems in the foundation of mathematics that were not resolved before the discovery of the proportion theory that we find in Elements V.


Common Fraction Decimal Fraction Late Antiquity Greek Mathematic Explicit Evidence 
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Copyright information

© Springer Science+Business Media Dordrecht 1994

Authors and Affiliations

  • David H. Fowler
    • 1
  1. 1.University of WarwickUK

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