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.

中文翻译：

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艺术证明：数学美学的康德方法

本文从康德的角度探讨了数学美的本质。根据康德对判断力的批判，对美的满足是主观的和非概念的，尽管证据依赖于概念，但它仍然可以是美丽的。我建议，就像艺术创作一样，复杂演示的制定和研究涉及自由的原始想象力和品味（即判断的美学力量）之间的多重渐进式相互作用。就美感而言，这种证明是艺术性的，即对想象力自由合法性的单纯感觉。证明过程中的美感和完成过程中的完美性共同促进了从主观目的向客观目的的转变，康德本人在第三次批判中并未解决这一转变。