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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:

  1. 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

  2. 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.

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closed as off-topic by Ivo Terek, zz20s, user223391, user299912, Austin Mohr Jul 26 '16 at 23:20

This question appears to be off-topic. The users who voted to close gave this specific reason:

  • "This question is not about mathematics, within the scope defined in the help center." – Community, MathematicsStudent1122, Austin Mohr
If this question can be reworded to fit the rules in the help center, please edit the question.

  • $\begingroup$ Proving a result via brute force checking multiple cases is often frowned upon, and a search for a more elegant proof is desired. For extreme example, seeing someone prove that $x^2+x+1$ is odd for every integer $x$ between $0$ and $1000$ by simply plugging in every value and checking its parity would make me facepalm quite strongly. $\endgroup$ – JMoravitz Jul 26 '16 at 23:19
  • $\begingroup$ I didn't realize that this question would be so controversial (or unanimously disliked.) A lot of people speak of mathematics as an art form, I just figured it should also reflect a greater array of sentiments... $\endgroup$ – Andres Mejia Jul 26 '16 at 23:25
  • $\begingroup$ @JMoravitz Yes, I see your point there. But that question is different because it immediately suggests a finite number of cases to check. Similarly, the method is not extendable, whereas the other methods reduced the problem to finitely many computations. $\endgroup$ – Andres Mejia Jul 26 '16 at 23:26
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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.

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  • $\begingroup$ I noticed that you both answered and voted to close. Can you tell me why, so that I can do a better job asking these sorts of questions in the future? Or is it that this is an inappropriate place for such questions? $\endgroup$ – Andres Mejia Aug 2 '16 at 3:52

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