The Algorithmic-Device View of Informal Rigorous Mathematical Proof

Jody Azzouni ()
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Jody Azzouni: Tufts University, Department of Philosophy

A chapter in Handbook of the History and Philosophy of Mathematical Practice, 2024, pp 2179-2260 from Springer

Abstract: Abstract A new approach to informal rigorous mathematical proof is offered. To this end, algorithmic devices are characterized and their central role in mathematical proof delineated. It is then shown how all the puzzling aspects of mathematical proof, including its peculiar capacity to convince its practitioners, are explained by algorithmic devices. Diagrammatic reasoning is also characterized in terms of algorithmic devices, and the algorithmic device view of mathematical proof is compared to alternative construals of informal proof to show its superiority.

Keywords: Informal mathematical proof; Diagrams; Turing computability; Algorithms; Euclidean geometry; Venn diagrams; Formalization; Conceptual engineering; Games (search for similar items in EconPapers)
Date: 2024
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-031-40846-5_4

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DOI: 10.1007/978-3-031-40846-5_4

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