A lot of this sounds reasonably applicable to applied math, but it sounds very out-of-place for describing pure math. The point of a proof (at least one that i

A lot of this sounds reasonably applicable to applied math, but it sounds very out-of-place for describing pure math. The point of a proof (at least one that isn't a terribly contrived homework problem) is that there is no "correct tool" to solve it. You're developing the theory that creates (or demonstrates the validity of) the "correct tool." It's a very good training for a research mindset (research is similarly notorious for causing frustration, among many other similarities) and that's evidenced by the premium that great school admissions programs put on students with a track record of pure math success.