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Mathematical Method and Proof

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Abstract

On a traditional view, the primary role of a mathematical proof is to warrant the truth of the resulting theorem. This view fails to explain why it is very often the case that a new proof of a theorem is deemed important. Three case studies from elementary arithmetic show, informally, that there are many criteria by which ordinary proofs are valued. I argue that at least some of these criteria depend on the methods of inference the proofs employ, and that standard models of formal deduction are not well-equipped to support such evaluations. I discuss a model of proof that is used in the automated deduction community, and show that this model does better in that respect.

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  1. Department of Philosophy, Carnegie Mellon University, Baker Hall 135, Pittsburgh, PA, 15213, US

    Jeremy Avigad

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Avigad, J. Mathematical Method and Proof. Synthese 153, 105–159 (2006). https://doi.org/10.1007/s11229-005-4064-5

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