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Series:   Elements in the Philosophy of Mathematics

Mathematical Rigour and Informal Proof

Published online by Cambridge University Press:  01 March 2024

Fenner Stanley Tanswell
Fenner Stanley Tanswell
Affiliation:
Loughborough University

Summary

This Element looks at the contemporary debate on the nature of mathematical rigour and informal proofs as found in mathematical practice. The central argument is for rigour pluralism: that multiple different models of informal proof are good at accounting for different features and functions of the concept of rigour. To illustrate this pluralism, the Element surveys some of the main options in the literature: the 'standard view' that rigour is just formal, logical rigour; the models of proofs as arguments and dialogues; the recipe model of proofs as guiding actions and activities; and the idea of mathematical rigour as an intellectual virtue. The strengths and weaknesses of each are assessed, thereby providing an accessible and empirically-informed introduction to the key issues and ideas found in the current discussion.
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Keywords

mathematical rigourinformal proofmathematical practiceformalisationepistemology of mathematics
Type
Element
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Series: Elements in the Philosophy of Mathematics
Online ISBN: 9781009325110
Publisher: Cambridge University Press
Print publication: 28 March 2024

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