Beauty in Proofs: Kant on Aesthetics in Mathematics by Angela Breitenbach

http://www.phil.cam.ac.uk/people/teaching-research-pages/breitenbach/breitenbach-beautyproofs.pdf

This is a wonderful paper – a rigorous exploration of the nature of the aesthetic experience of mathematics and whether it can be called a Kantian beauty. The answer is yes, probably, if it’s a proof we’re talking about. It’s based on this offhand comment of Kant’s:

[o]ne could rather call a demonstration of such properties beautiful, since by means of this the understanding, as the faculty of concepts, and the imagination, as the faculty for exhibiting them a priori, feel strengthened (which together with the precision which is introduced by reason, is called its elegance): for here at least the satisfaction,  although its ground lies in concepts, is subjective, whereas perfection is accompanied with an objective satisfaction (CJ, V 366)
Exactly where this subjectivity comes in is the subject of the paper, and how the role of intuition in Kant’s a priori synthetic understanding of mathematics makes admiration – and beauty – possible.
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