The beauty (?) of mathematical proofs

Catarina Dutilh Novaes (University of Groningen)

Abstract

Mathematicians often use aesthetic vocabulary to describe mathematical proofs: they can be beautiful, elegant, ugly etc. In recent years, philosophers of mathematics have been asking themselves what these descriptions in fact mean: should we take them literally, as tracking truly aesthetic properties of mathematical proofs, or are these terms being used as proxy for non-aesthetic properties, in particular epistemic properties? Starting from the idea that one of the main functions of mathematical proofs is to explain and persuade an interlocutor, I develop an account of the beauty (or ugliness) of mathematical proofs that seems to allow for a reconciliation of these apparently opposed accounts of aesthetic judgments in mathematics. I do so by discussing the role of affective responses and emotions in the practice of mathematical proofs, thus arguing that the aesthetic and the epistemic are intrinsically related (while not entirely coinciding) in mathematical proofs.