In pure math, the journey is the reward; in applied math, the destination is, and how you get there is unimportant.
That, IMO, is why applied math rarely is beautiful. Pure math often is because no sane person would spend time doing ugly work that doesn't even lead to useful results.
Computational proofs such as that of the four color theorem have changed that a bit. That may be the reason some mathematicians don't accept them as proofs.
Similarly, "publish or perish" may have led to more proofs in pure mathematics that are more hard work than inspiration, and of course, zillions of hours have been spent looking for counterexamples of theorems in pure mathematics.
That, IMO, is why applied math rarely is beautiful. Pure math often is because no sane person would spend time doing ugly work that doesn't even lead to useful results.
Computational proofs such as that of the four color theorem have changed that a bit. That may be the reason some mathematicians don't accept them as proofs.
Similarly, "publish or perish" may have led to more proofs in pure mathematics that are more hard work than inspiration, and of course, zillions of hours have been spent looking for counterexamples of theorems in pure mathematics.