Heuristics and Mathematical Practice

Otávio Bueno ()
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Otávio Bueno: University of Miami, Department of Philosophy

A chapter in Handbook of the History and Philosophy of Mathematical Practice, 2024, pp 431-442 from Springer

Abstract: Abstract Proofs are central to mathematical practice in large part due to the heuristic role that some of them play. Not only do they help establish a result, but often provide new avenues of mathematical research. Jody Azzouni has argued that underlying the practice of creating mathematical proofs there is a very specific norm: to each proof there should be a corresponding algorithmic derivation, a derivation in an algorithmic system. Here a framework is provided to classify and assess mathematical proofs. It is argued that there is a plurality of kinds of proofs in mathematics and a plurality of roles these proofs play. In the end, mathematical practice is far less unified in this respect than it may seem to be.

Keywords: Proofs; Explanation; Unification; Set theory (search for similar items in EconPapers)
Date: 2024
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DOI: 10.1007/978-3-031-40846-5_42

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