The heart of mathematics consists of concrete examples and concrete problems. Big general theories are usually afterthoughts based on small but profound insights; the insights themselves come from concrete special cases.

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 library is the mathematician's laboratory.

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

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

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.

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