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Axiomatics—Euclid’s and Hilbert’s: From Material to Formal

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Turning Points in the History of Mathematics

Part of the book series: Compact Textbooks in Mathematics ((CTM))

Abstract

The axiomatic method is, without doubt, the single most important contribution of ancient Greece to mathematics. The explicit recognition that mathematics deals with abstractions, and that proof by deductive reasoning from explicitly stated postulates offers a foundation for mathematics, was indeed an extraordinary development. When, how, and why this came about is open to conjecture.

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Authors and Affiliations

  1. Department of Mathematics and Statistics, York University, Toronto, Ontario, Canada

    Hardy Grant & Israel Kleiner

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  1. Hardy Grant
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  2. Israel Kleiner
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Correspondence to Hardy Grant .

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Grant, H., Kleiner, I. (2015). Axiomatics—Euclid’s and Hilbert’s: From Material to Formal. In: Turning Points in the History of Mathematics. Compact Textbooks in Mathematics. Birkhäuser, New York, NY. https://doi.org/10.1007/978-1-4939-3264-1_1

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