Except for aesthetics. Beauty, value, and sentiment, have all been mentioned and discussed informally with respect to mathematics. Among the many things G.H. Hardy is famous for is his 'Mathematician's Apology' which seems to be the first historical appearance of a matter of fact of close similarities between a mathematician and a poet. I call this a 'matter of fact' because to most non-mathematicians, math is unquestionably all rigid formality. Since Hardy, there has been much talk about how the practice of creating new mathematics is an art, engenders feelings of beauty. Lots of academic mathematicians have written about mathematical aesthetics; every other article in the Mathematical Intelligencer tends to have an aesthetic character. But there has been little (or no) academic, philosophical study of aesthetics by aestheticians if that's not a word, it's a word now) or mathematicians themselves.
I'm not about to presume to fill that gap in any depth. How about I'll presume to outline what kinds of topics might be pursued academically, rather than to stop at what has been done only informally.
- in what way is mathematics like poetry, painting? (artifice)
- beauty and ugliness in mathematics
- what do people find beautiful in a proof? Surprise, symmetry, simplicity
- correspondence between a picture (which might be beautiful)
- account for universals and differences in appreciation of mathematical concepts
- examples
- theorems
- proofs
- objects
- theories (collections of theorems and definitions and objects)
- deep vs. beautiful vs. useful (many applications)
- mathematical measures of aesthetic judgments (a calculus of beauty; math in the service of non-mathematical aesthetics)
