I've always wondered about this question. I've taken university math courses and gotten A+'s. But then years later, if I never used topics in that course again, I realize how much I have forgotten. A math professor who does research in, say, number theory would essentially never use, say, the Gauss-Bonnet Theorem that he had learned many years ago in Differential Geometry. Would the number theorist be able to pick a textbook problem in the Gauss-Bonnet chapter and solve it from the top of his head? Are math professors so mentally powerful that the phrase "if you don't use it, you lose it" does not apply to them? Do they remember every math topic they have learned as much as they did just before walking into their final exam many years ago? For example, how many math professors reading this post can prove the Inverse Function Theorem of second year calculus from scratch?