The only way to learn mathematics is to do mathematics. That tenet is the foundation of the do-it-yourself, Socratic, or Texas method.

Mathematics is not a deductive science - that's a cliché. When you try to prove a theorem, you don't just list the hypotheses, and then start to reason. What you do is trial and error, experimentation, guesswork.

Don't just read it; fight it! Ask your own question, look for your own examples, discover your own proofs. Is the hypothesis necessary? Is the converse true? ... Where does the proof use the hypothesis?

... the student skit at Christmas contained a plaintive line: "Give us Master's exams that our faculty can pass, or give us a faculty that can pass our Master's exams."

Feller was an ebullient man, who would rather be wrong than undecided.

The only way to learn mathematics is to do mathematics. That tenet is the foundation of the do-it-yourself, Socratic, or Texas method.

...the source of all great mathematics is the special case, the concrete example. It is frequent in mathematics that every instance of a concept of seemingly generality is, in essence, the same as a small and concrete special case.