When taking mathematics classes in university I always noticed an enormous gap between what I thought I understood compared to how confusing the problems were.

When taking mathematics classes in university I always noticed an enormous gap between what I thought I understood compared to how confusing the problems were. I am glad the author mentions that phenomenon. For (the few) students who actually understood the subject the problems are just busywork, for those who didn't it is the most important part of the learning process. There is exactly one way to understand mathematics, which is actually doing it. This can be many things, but actually solving problems is an important part. I believe that problems should be interesting, but repeated recall definitely is important as well.