When reading mathematical books written for a general audience, or even searching questions on this site, the adjective beautiful is often used to describe mathematics. My question is whether there has been scholarly work on the semantics of the word beautiful as used in this sense.
More precisely, what do mathematicians find beautiful, and why do they choose this word to describe math? Have any authors focused on how the idea of "beauty" in mathematics may have changed over time, or how mathematicians may find different ideas beautiful depending on their social/cultural influences?
To clarify, I am not looking for examples of why mathematics is "beautiful". I am also not looking for quotes or aphorisms from famous mathematicians about the beauty of math. My personal opinion is that mathematicians often use beautiful when they could instead choose words such as simple, elegant, or clever to describe proofs or theorems. I am interested in why they choose to use 'beauty', and the implications of this choice in mathematics exposition. References that investigate the success (or failure!) of efforts to show mathematical beauty in education would also be welcomed.