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

Sara Negri | Zendy; Jan von Plato | Zendy

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

Author(s) -

Sara Negri,

Jan von Plato

Publication year - 2019

Publication title -

philosophical transactions of the royal society a mathematical physical and engineering sciences

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 1.074

H-Index - 169

eISSN - 1471-2962

pISSN - 1364-503X

DOI - 10.1098/rsta.2018.0037

Subject(s) - mathematical proof , axiom , simplicity , proof theory , simple (philosophy) , structural proof theory , analytic proof , formal proof , calculus (dental) , mathematics , computer science , mathematical theory , proof assistant , computer assisted proof , algebra over a field , pure mathematics , epistemology , philosophy , medicine , physics , geometry , dentistry , quantum mechanics

A short text in the hand of David Hilbert, discovered in Göttingen 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’.

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