Like a stool which needs three legs to be stable, mathematics education needs three components: good problems, with many of them being multi-step ones, a lot of technical skill, and then a broader view which contains the abstract nature of mathematics and proofs. One does not get all of these at once, but a good mathematics program has them as goals and makes incremental steps toward them at all levels.

We are often raised as dependents then given over to teachers. It's experience and exploration that can transform us and lead to mastery.

Sometimes, looking at the many books I have at home, I feel I shall die before I come to the end of them, yet I cannot resist the temptation of buying new books. Whenever I walk into a bookstore and find a book on one of my hobbies — for example, Old English or Old Norse poetry — I say to myself, “What a pity I can’t buy that book, for I already have a copy at home.

You need, as a historian, essential triangulation from your subject and the only way you get that triangulation is through time.

School is about learning to wait your turn, however long it takes to come, if ever. And how to submit with a show of enthusiasm to the judgment of strangers, even if they are wrong, even if your enthusiasm is phony.

It is good for a student to be poor. Getting and spending, the typical American college student lays waste his powers. Work and contemplation don't mix, and university days ought to be days of contemplation.