Abstract
AbstractIt is a common thought that mathematics can be not only true but also beautiful, and many of the greatest mathematicians have attached central importance to the aesthetic merit of their theorems, proofs and theories. But how, exactly, should we conceive of the character of beauty in mathematics? In this paper I suggest thatKant's philosophy provides the resources for a compelling answer to this question. Focusing on §62 of the ‘Critique of Aesthetic Judgment’, I argue against the common view thatKant's aesthetics leaves no room for beauty in mathematics. More specifically, I show that on theKantian account beauty in mathematics is a non‐conceptual response felt in light of our own creative activities involved in the process of mathematical reasoning. TheKantian proposal I thus develop provides a promising alternative toPlatonist accounts of beauty widespread among mathematicians. While on thePlatonist conception the experience of mathematical beauty consists in an intellectual insight into the fundamental structures of the universe, according to theKantian proposal the experience of beauty in mathematics is grounded in our felt awareness of the imaginative processes that lead to mathematical knowledge. TheKantian accountIdevelop thus offers to elucidate the connection between aesthetic reflection, creative imagination and mathematical cognition.
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