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What is a proof?

Alan Bundy·Mateja Jamnik·Andrew Fugard
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Abstract

To those brought up in a logic-based tradition there seems to be a simple and clear definition of proof. But this is largely a twentieth century invention; many earlier proofs had a different nature. We will look particularly at the faulty proof of Euler's Theorem and Lakatos' rational reconstruction of the history of this proof. We will ask: how is it possible for the errors in a faulty proof to remain undetected for several years-even when counter-examples to it are known? How is it possible to have a proof about concepts that are only partially defined? And can we give a logic-based account of such phenomena? We introduce the concept of schematic proofs and argue that they offer a possible cognitive model for the human construction of proofs in mathematics. In particular, we show how they can account for persistent errors in proofs.

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AlgorithmsCultureMathematical ComputingModels, TheoreticalNumerical Analysis, Computer-AssistedSoftwareSoftware ValidationJournal ArticleResearch Support, Non-U.S. Gov't

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Alan Bundy, Mateja Jamnik, Andrew Fugard. 2005-10-15. What is a proof?. https://doi.org/10.1098/rsta.2005.1651

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