Does understanding moderate aesthetic appraisals of proofs?

Abstract

The relationship between understanding and aesthetic appraisal in mathematics is an open question, with implications for both the philosophy of mathematics and mathematics education. In this study, we investigated how undergraduate students’ understanding of a mathematical proof relates to their perception of its aesthetic value. Participants were asked to evaluate the proof’s aesthetics and to complete three different assessments of their understanding. The results reveal that self-reported understanding was moderately associated with aesthetic appraisals, while two performance-based measures of understanding showed close-to-zero relationships. These findings challenge the view that aesthetic judgements in mathematics are merely disguised epistemic judgements, and suggest that future research should focus on exploring the non-epistemic factors that shape aesthetic judgements. We conclude by discussing the implications of these results for educational practices that seek to promote aesthetic experiences.