Are aesthetic judgements purely aesthetic? Testing the social conformity account

Abstract

Many of the methods commonly used to research mathematical practice, such as analyses of historical episodes or individual cases, are particularly well-suited to generating causal hypotheses, but less well-suited to testing causal hypotheses. In this paper we reflect on the contribution that the so-called hypothetico-deductive method, with a particular focus on experimental studies, can make to our understanding of mathematical practice. By way of illustration, we report an experiment that investigated how mathematicians attribute aesthetic properties to mathematical proofs. We demonstrate that perceptions of the aesthetic properties of mathematical proofs are, in some cases at least, subject to social influence. Specifically, we show that mathematicians' aesthetic judgements tend to conform to the judgements made by others. Pedagogical implications are discussed.

The Beauty (?) of Mathematical Proofs

“…Notice also that Mancosu himself (Hafner and Mancosu, 2005) is sympathetic to the idea of non-homogeneous phenomena as the objects of study for philosophical accounts of mathematics and mathematical practice. 13 In recent work, Inglis and Aberdein (2017) have been tackling some of these concerns. See also (Larvor, 2016).…”

Do Mathematicians Agree about Mathematical Beauty?

“…On social influence, Inglis and Aberdein (2020) replicated their 2016 study, this time with the manipulation that half of their 203 mathematician participants were told the proof's source, Aigner and Ziegler's (2010) attempt to produce a version of Erdős's 'The Book'. Pure mathematicians who were given the source rated the proof more highly than those who were not, but applied mathematicians did not show such an effect.…”