When is the solution to a mathematical problem “elegant”?

It’s hard to say so universally. Certainly, a rather short proof is rather something that you would call elegant, but this is often accompanied by the fact that many results have already been raised with the others already proved executable.

You can also find elegant when you get something from axiomen.

Elegant can mean everything.

Examples:

one can prove in a two-liner, taking the riemannian guess, the prime number set from the algebra, which otherwise needed a lot of preparation.

One can also say a proof of the whole thing about school mathematics is elegant. Thus, 11 students can prove the phrase of Pythagoras.

Also interesting Cohen has invented his own mathematical method (forcing) to prove a fundamental set of logic. You can call it elegant or the opposite at the same time