This is a soft question.
It's extremely commonplace for mathematician's to refer to work as "elegant," "beautiful," and I've seen many compare the process of doing mathematics to painting, or playing music. I think that for the most part, I can understand how certain theorems, formula, or general theory can be evocative, surprising, or maybe just confounding.
However, what is less clear is how far the analogy of art can be extended. Art, as much as it makes one elated or excited, also has the capacity to elicit feelings of sadness or melancholy (or any further scope.) I was wondering if this is the case for mathematics as well. I know certainly some people have cited the proof for the four-color theorem as "disappointing," (although I don't have a suitable background to have a stake in this) but this doesn't seem to have quite the same flavor as a musical masterpiece that makes one feel negatively.
I cannot think of such an experience that I have had, and I'm curious to see if maybe there are some examples that others feel strongly about.
Here are some non-examples:
Freshman's Dream: I'm not really interested in the feeling of something you'd hope works, but winds up being false because of an error
Math that's too difficult for you to understand.
edit: I was surprised to see such a decidedly negative response to my question. Maybe I have it all wrong, in which case, I'd also like to be corrected with a convincing argument.
When I first learned that equations of degree five or higher may not be solved using an equation similar to the infamous quadratic formula, I felt a great amount of despair.