When you take a course in Euclidean geometry is not the teacher putting a... learning program into you? ...You enter the course and cannot do problem… - Richard Hamming

A central problem in teaching mathematics is to communicate a reasonable sense of taste—meaning often when to, or not to, generalize, abstract, or extend something you have just done.

I must address the topic of whether the effort required for excellence worth it. I believe it is — the chief gain is in the effort to change yourself, in the struggle with yourself, and it is less in the winning than you might expect. Yes, it is nice to end up where you wanted to be, but the person you are when you get there is far more important. I believe a life in which you do not try to extend yourself regularly is not worth living — but it is up to you to pick the goals you believe are worth striving for.

Theorems... record more complex patterns of thinking that once shown to be valid need not be repeated every time they are needed.