The Beauty of Mathematical Proofs in Kant’s Critical Philosophy

Abstract

This article examines the question – never systematically addressed by Kant – of the beauty of mathematics. In the Critique of the Power of Judgment, Kant repeatedly claims that numbers and geometrical figures, insofar as they are mere exhibitions of determinate concepts and subject to strict conformity to rules (Steif-Regelmäßigkeit), cannot constitute objects of aesthetic judgment. In §62, however, he opens up the possibility of considering a proof as “beautiful.” This paper attempts to reconstruct and clarify this ambiguous position, also contextualizing it in light of the Critique of Pure Reason. The interpretation proposed here is that mathematics regards numbers and geometrical figures not as given entities, but as rules of their construction, and thus already as schemata—standing in opposition to the free schematism that Kant identifies as the basis of judgments of taste. A proof, by contrast, depends on an ability that cannot be learned, namely, the capacity to employ rules without being rigidly bound to a schema. In this way, it enables the “free play” of imagination and understanding, together with the pleasure characteristic of aesthetic experience.