Purity and explanation: a systematic case study

This paper systematically studies the connections between purity and explanation of mathematical proofs. We consider a well-known proof of Pythagoras’s Theorem which is considered explanatory, and Euclid’s proof of the Infinitude of Primes which is considered pure. We apply the best-known models of purity to the former proof, and the best-known models of explanation to the latter proof. Results show that, contrary to an illustrious tradition going back to Aristotle where purity and explanation are deeply interconnected, most contemporary approaches separate purity and explanation. We conclude the paper by analysing a recent approach to explanation where explanation and purity reunite.