Elements of purity:

A proof of a theorem can be said to be pure if it draws only on what is 'close' or 'intrinsic' to that theorem. In this Element we will investigate the apparent preference for pure proofs that has persisted in mathematics since antiquity, alongside a competing preference for impu...

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Bibliographic Details
Main Author: Arana, Andrew Peter (Author)
Format: Electronic eBook
Language:English
Published: Cambridge Cambridge University Press 2024
Series:Cambridge elements
Subjects:
Online Access:DE-12
DE-634
DE-92
DE-473
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Summary:A proof of a theorem can be said to be pure if it draws only on what is 'close' or 'intrinsic' to that theorem. In this Element we will investigate the apparent preference for pure proofs that has persisted in mathematics since antiquity, alongside a competing preference for impurity. In Section 1, we present two examples of purity, from geometry and number theory. In Section 2, we give a brief history of purity in mathematics. In Section 3, we discuss several different types of purity, based on different measures of distance between theorem and proof. In Section 4 we discuss reasons for preferring pure proofs, for the varieties of purity constraints presented in Section 3. In Section 5 we conclude by reflecting briefly on purity as a preference for the local and how issues of translation intersect with the considerations we have raised throughout this work
Item Description:Title from publisher's bibliographic system (viewed on 05 Dec 2024)
Physical Description:1 Online-Ressource (77 Seiten)
ISBN:9781009052719
DOI:10.1017/9781009052719

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