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, …

- Paul Halmos

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 reas…

- Paul Halmos

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.

- Paul Halmos

The heart of mathematics consists of concrete examples and concrete problems. Big general theories are usually afterthoughts based on small but profo…

- Paul Halmos

The library is the mathematician's laboratory.

- Paul Halmos

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

- 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.

- Paul Halmos

[Mathematics] is security. Certainty. Truth. Beauty. Insight. Structure. Architecture. I see mathematics, the part of human knowledge that I call mat…

- Paul Halmos

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

- Paul Halmos