I've always been curious if I'd like the exploratory nature of 'pure math' where proofs of very difficult problem solutions are discovered. I imagine it being sort of like designing very complex software systems used in life-sustaining (?) applications such as on airplanes or manned space missions. As a software engineer working on these systems, you have to essentially prove that the software is fault-tolerant, essentially bug-free. There has to be a lot of internal consistency in such a system.
In my mind, it's really too bad so many people hate math or think they're not good at it. That has to do with the way math (and every other topic) is taught in school. Kids shouldn't be expected to solve problems from day one until they graduate high-school. They need to learn how to think. And that applies to all of the other subjects they're taught as well. I really like interdisciplinary and exploratory approaches. Some teachers (and certainly many school administrators) are afraid of allowing kids to explore beyond a little controlled discussion.
Paul Graham, eminent computer science scholar, just published an interesting essey online entitled What You'll Wish You'd Known where he presents his approach to the high-school commencement-style address to graduates but directed at students way before they finish high-school. Good reading!