# Purity as an Ideal of Proof

# Purity as an Ideal of Proof

This chapter sketches the development of purity as an ideal of mathematical proof from antiquity through the 20th century. The basic thought behind this ideal is that a proof of a proposition ought not to have to appeal to notions other than those contained in the proposition in order to justify it. A proof that does appeal to such extraneous notions thus strays at points from its proper topic and is not in all its parts relevant. Attention is also given to the common idea that the discipline of seeking purity in proofs has intervenient benefits for those who practice it.

*Keywords:*
purity, topical purity, prime number theorem, intermediate value theorem

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