What is mathematical beauty? An experimental philosophical investigation into mathematicians’ aesthetic judgements

Mathematicians often make judgements about mathematical beauty when evaluating equations or proofs. But what do they mean by mathematical beauty? Is it an objective feature of certain mathematical proofs, equations, ideas etc.? Or is it entirely relative to each individual mathematician's judgement? To what extent do mathematicians agree when they make judgements about mathematical beauty? If they do agree, what could explain their agreement? Can we understand their aesthetic agreement in a literal sense of being about beauty, or can it only be explained by non-aesthetic properties? These questions are derived from two ongoing philosophical disputes regarding the nature of mathematical beauty: (i) literal versus non-literal aesthetic standpoints, and (ii) aesthetic realism versus non-realism.

This thesis engages with these philosophical disputes by conducting a series of empirical studies that measure mathematicians’ and undergraduates’ aesthetic judgements. It employs novel methods that have not yet been used in measuring mathematicians’ aesthetic and epistemic judgements. It also presents a philosophical account that combines epistemic goods and functional beauty in understanding mathematicians’ aesthetic judgements. Chapter 2 argues for a pluralistic functional account of mathematical beauty. Chapters 3, 4 and 5 use the method of comparative judgement to measure mathematicians’ and undergraduates’ level of consensus in their aesthetic and epistemic judgements. Chapter 6 adopts a method from experimental philosophy to measure mathematicians’ opinions about the relationship between aesthetic and epistemic judgements. The central findings of this thesis are that mathematicians and undergraduates generally agree in their aesthetic judgements about mathematical objects, but they seem to disagree over what criteria constitute the notion of mathematical beauty.