Paul Halmos Quotes

The only way to learn mathematics is to do mathematics.

The author discusses valueless measures in pointless spaces.

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

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

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

The beginner should not be discouraged if he finds he does not have the prerequisites for reading the prerequisites.

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.

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.

Applied mathematics will always need pure mathematics just as anteaters will always need ants.

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

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

The heart of mathematics is its problems.

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

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.

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

You are allowed to lie a little, but you must never mislead.

It saddens me that educated people don't even know that my subject exists.

The library is the mathematician's laboratory.

... 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.

The mathematical fraternity is a little like a self-perpetuating priesthood. The mathematicians of today teach the mathematicians of tomorrow and, in effect, decide whom to admit to the priesthood.

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.

I read once that the true mark of a pro - at anything - is that he understands, loves, and is good at even the drudgery of his profession.

A clever graduate student could teach Fourier something new, but surely no one claims that he could teach Archimedes to reason better.