
Elements of Purity
Andrew Arana(Author)
Cambridge University Press
Published on 16. January 2025
Book
Hardback
84 pages
978-1-009-53970-8 (ISBN)
Description
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.
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Series
Language
English
Place of publication
Cambridge
United Kingdom
Illustrations
Worked examples or Exercises
Dimensions
Height: 235 mm
Width: 157 mm
Thickness: 10 mm
Weight
289 gr
ISBN-13
978-1-009-53970-8 (9781009539708)
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Andrew Arana
Elements of Purity
Book
01/2025
Cambridge University Press
€26.70
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Content
1. Purity in practice; 2. A brief history of purity; 3. Types of purity; 4. Values of purity; 5. Conclusions; References.