Affiliation:
1. Inria, Palaiseau, France
Abstract
In this short overview article, I will discuss the problem of proof identity and explain how it is related to Hilbert's 24th problem. I will also argue that not knowing when two proofs are ‘the same’ has embarrassing consequences not only for proof theory but also for certain areas of computer science where formal proofs play a fundamental role, in particular, the formal verification of software. Then I will formulate a set of four objectives that a satisfactory notion of proof identity should obey. And finally, I discuss Hughes'
combinatorial proofs
and argue that they can be seen as a first step towards a possible solution to the problem of proof identity.
This article is part of the theme issue ‘The notion of ‘simple proof’ - Hilbert's 24th problem’.
Subject
General Physics and Astronomy,General Engineering,General Mathematics
Reference78 articles.
1. Mathematische Probleme;Hilbert D;Nachrichten der Königlichen Gesellschaft der Wissenschaften zu Göttingen, mathematisch-physikalische Klasse,1900
2. Hilbert's Twenty-Fourth Problem
3. Hilbert D. Mathematische Notizbücher. Niedersächsische Staats- und Universitätbibliothek Cod. Ms. D. Hilbert 600:3 S.25.
4. Hales TC. 2005 Introduction to the Flyspeck Project. In Mathematics algorithms proofs (eds T Coquand H Lombardi M-F Roy). Dagstuhl Seminar Proc. vol. 05021. Wadern Germany: Internationales Begegnungs- und Forschungszentrum für Informatik (IBFI) Schloss Dagstuhl Germany.
5. Gonthier G. 2007 The four colour theorem: engineering of a formal proof. In 8th Asian Symp. Computer Mathematics (ed. D Kapur). Lecture Notes in Computer Science vol. 5081 p. 333. Berlin Germany: Springer.
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