...and this is also generally true in the physical sciences. Oh, sure, there is a base of knowledge, but ideally, it's about using familiar tools to DO unfamiliar things. Or to find answers to questions, I suppose.

Math is a foreign language. Some people need to be fluent in some dialects (statistics, vector calculus) more than in others. What's really, really COOL, though, is that math is truly an international language throughout most of the world.

Schrödinger's cat walks into a bar. And doesn't.