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Book Synopsis
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.

Elements of Purity

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    A Paperback by Andrew Arana

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      Book details

      Publisher Cambridge University Press
      Published 1/16/2025
      ISBN-13 9781009055895
      978-1009055895
      ISBN-10 1009055895
      Also in:
      Philosophy

      Description

      Book Synopsis
      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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