Hehehe. James is right, I do have a fondness for Nietzsche. :) He's not someone I agree with completely on everything, but he does have his very valid points, and I love his sense of humor. My favorite thing about him though, is the fact that, at least in the stuff I've read, Nietzsche doesn't merely state his own ideas for the reader to reject or accept, very often he puts them forth in a way that really allows the reader to draw their own conclusions from what he's saying. He gives you the setup, but what you pull from it is sort of up to you and how much you want to think about what he's saying, and in what context. This is extremely appealing to my math-wired mind, as it's similar to being given a puzzle, but not its solution(s).
I'm familiar with the Feynman video you speak of, too, and that was indeed one of my favorite parts of it. I really do see the world very much in the way I described, and the alchemy of physics, math, and philosophy playing off each other in mind makes for a life in which boredom must be a willful decision. :)