The best way to learn is to do; the worst way to teach is to talk.

Mathematics - this may surprise or shock some - is never deductive in creation.

...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.

... 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."

The author discusses valueless measures in pointless spaces.

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.

The only way to learn mathematics is to do mathematics.