Exactly! Writing something that is both meaningful and interesting is like solving a puzzle.

Thank goodness someone mentioned Tom Lehrer. He's "exhibit A" in the case for funny mathematicians. I wish there were a Youtube clip of Tom performing "New Math", but this is close:

http://www.youtube.com/watch?v=oHuRcDnJOAQ

Absolutely true. I am a songwriter who happens to know how to program. Equivalences abound.