Aesthetic Preferences in Mathematics: a Case Study

Although mathematicians often use it, mathematical beauty is a philosophically challenging concept. How can abstract objects be evaluated as beautiful? Is this related to the way we visualise them? Using a case study from graph theory (the highly symmetric Petersen graph), this paper tries to analyse aesthetic preferences in mathematical practice and to distinguish genuine aesthetic from epistemic or practical judgements. It argues that, in making aesthetic judgements, mathematicians may be responding to a combination of perceptual properties of visual representations and mathematical properties of abstract structures; the latter seem to carry greater weight. Mathematical beauty thus primarily involves mathematicians' sensitivity to aesthetics of the abstract