Quotes from Paul Halmos

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

The only way to learn mathematics is to do mathematics.

Mathematics is not a deductive science - that's a cliché... What you do is trial and error, experimentation, guesswork.

If the NSF had never existed, if the government had never funded American mathematics, we would have half as many mathematicians as we now have, and I don't see anything wrong with that.

A smooth lecture... may be pleasant; a good teacher challenges, asks, irritates and maintains high standards - all that is generally not pleasant.

It is the duty of all teachers, and of teachers of mathematics in particular, to expose their students to problems much more than to facts.

A good stack of examples, as large as possible, is indispensable for a thorough understanding of any concept,and when I want to learn something new, I make it my first job to build one.

To be a scholar of mathematics you must be born with talent, insight, concentration, taste, luck, drive and the ability to visualize and guess.

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

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

When a student comes and asks, Should I become a mathematician? the answer should be no. If you have to ask, you shouldn't even ask.

In other words, general set theory is pretty trivial stuff really, but, if you want to be a mathematician, you need some and here it is; read it, absorb it, and forget it.

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

... 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 computer is important, but not to mathematics.