Rob just told me--
There's something about going through the math classes that gives you a sense of when there are holes in someone's argument. You may not know exactly where the holes are, but you know that you're not totally convinced.
The classes themselves may not give me the most pertinent knowledge-- some of the math I'm doing right now, I will never use. But he's right-- I am learning when to say "Wait a minute, something's fishy." And that's what's fundamental to scientific reasoning and discussion.
It's somewhat astonishing how my ability to find these holes has improved over the past few years. Just ask my study buddies-- I have a bad reputation for destroying their ideas that they were done with the homework...
