Artistic proofs: a Kantian approach to aesthetics in mathematics

This paper explores the nature of mathematical beauty from a Kantian perspective. According to Kant’s Critique of the Power of Judgment, satisfaction in beauty is subjective and non-conceptual, yet a proof can be beautiful even though it relies on concepts. I propose that, much like art creation, the formulation and study of a complex demonstration involves multiple and progressive interactions between the freely original imagination and taste (that is, the aesthetic power of judgement). Such a proof is artistic insofar as it is guided by beauty, namely, the mere feeling about the imagination’s free lawfulness. The beauty in a proof’s process and the perfection in its completion together facilitate a transition from subjective to objective purposiveness, a transition that Kant himself does not address in the third Critique.