Mathematical Aesthetic Judgements

Abstract

This chapters discusses how the aesthetic as process theory accounts for mathematical aesthetic judgements and also presents a review of the most relevant insights afforded by the aesthetic-as-process theory. The question ‘what do mathematicians mean when they talk about beauty?’ is answered in a simple way: mathematicians employ aesthetic terms in a literal sense, but their use is closer to the way aesthetic terms are used by specialists, critics or artists, rather than by an average person. Appreciation depends profoundly on a great deal of background mathematical knowledge. Our goal of literally interpreting aesthetic judgements in mathematics is achieved with the following interpretation: mathematical aesthetic judgements are articulated expressions of subjective states which result from an affective engagement of our attention to a mathematical item. The affective reaction reflects our preferences and values, which in turn are modulated by our natural tendencies and cultural influences.