The notion of fit as a mathematical value

Abstract

Many judgments are made about mathematical proofs, and among these we find the claim that a certain proof is beautiful or not. Beauty in mathematics is rarely denied, but it is also rarely explained. What is meant by the term, what criteria are needed for a proof to be beautiful, could there be objective qualities of a mathematical proof that map more or less onto the subjective experiences we might have when we read and understand it? While the concept of beauty itself is nebulous, the claim in this paper is that it might be related to a slightly more tractable quality of fit. We will discuss how fit arises in mathematics by looking at contrasting examples of proofs commonly held to be beautiful or not. We then take up the question about whether fit is a value, arguing that like justice and beauty, fit describes meaningful relationships and coherence, which make it a candidate for something to be valued not only in our mathematics classrooms, but also in the world at large.