From mathematical axioms to mathematical rules of proof: recent developments in proof analysis

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A short text in the hand of David Hilbert, discovered in Gottingen a century after it was written, shows that Hilbert had considered adding a 24th problem to his famous list of mathematical problems of the year 1900. The problem he had in mind was to find criteria for the simplicity of proofs and to develop a general theory of methods of proof in mathematics. In this paper, it is discussed to what extent proof theory has achieved the second of these aims.

This article is part of the theme issue 'The notion of 'simple proof' - Hilbert's 24th problem'.

Original languageEnglish
Article number20180037
JournalProceedings of the Royal Society. A . Mathematical, physical and engineering sciences
Issue number2140
Number of pages10
Publication statusPublished - 11 Mar 2019
MoE publication typeA1 Journal article-refereed

Fields of Science

  • 611 Philosophy
  • Hilbert's 24th problem
  • proof analysis
  • proof theory

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