[kdwikzncba]

> I've come to the conclusion that convex functions are functions that are trivial to optimize

I think a lot of maths is created like this. I'm trying to solve problem P in domain D. I couldn't do that, but I've noticed that I could do it in subset D1 of the domain. If problem P was important enough and D1 large enough, I become very famous within mathematics and people start studying D1 by itself, without connection to P. After a generation or more a lot of experts in D1 might not know the original reason why someone decided to study it. Eventually some historians of science re-discover the original motivation and publish it as a curiosity.

[xanderlewis]

Very true, combined with the fact that deep understanding of D1 turns out, centuries later, to be of practical use in building some sort of physical machinery.