Elements of Purity
by
Andrew Arana
Book Details
Format
Paperback / Softback
Book Series
Elements in the Philosophy of Mathematics
ISBN-10
1009055895
ISBN-13
9781009055895
Publisher
Cambridge University Press
Imprint
Cambridge University Press
Country of Manufacture
GB
Country of Publication
GB
Publication Date
Jan 16th, 2025
Print length
84 Pages
Weight
144 grams
Dimensions
22.80 x 15.20 x 0.70 cms
Product Classification:
Philosophy
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This Element explores the preference for pure proofs in mathematics since antiquity, focusing on geometry and number theory. It discusses different types of purity, reasons for preferring pure proofs, and the importance of local purity. It also touches on translation issues and the relationship between purity and local considerations.
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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