Many mathematicians often equate mathematics to art and find a deep beauty in its method, results, and ideas. The classic example of this romanticism is captured by G.H. Hardy's A Mathematician's Apology, for instance. However, it seems like the aesthetics of mathematics are much less studied than the aesthetics of more traditional conceptions of art. For example, in his 1938 Modes of Thought, Whitehead writes:
Also the feeling, widespread among mathematicians, that some proofs are more beautiful than others, should excite the attention of philosophers.
I suggest to you that the analogy between aesthetics and logic is one of the undeveloped topics of philosophy.
Has this changed significantly since Whitehead's time? Are there any standard reference for the philosophical study of aesthetics in math, or particularly relevant articles/books? If the field has developed enough to have different schools then I would also appreciate a brief summary of the schools with a representative reference to the ideas typical of said schools.
Note that I am asking for the philosophical discussions of why math is (found to be) beautiful, and why some features of mathematics are (perceived to be) more beautiful than others. I am less interested in works by mathematicians describing the specific things they find beautiful (otherwise I would have asked on math.SE), unless they also advance a philosophy along with their personal tastes.