A man really writes for an audience of about ten persons. Of course if others like it, that is clear gain. But if those ten are satisfied, he is content.

Mathematics, in its widest significance, is the development of all types of formal, necessary, deductive reasoning.

Imagination is not to be divorced from the facts. It is a way of illuminating the facts.

Education should turn out the pupil with something he knows well and something he can do well.

Education with inert ideas is not only useless; it is above all things harmful.

Not ignorance, but ignorance of ignorance, is the death of knowledge.

The point of mathematics is that in it we have always got rid of the particular instance, and even of any particular sorts of entities. So that for example, no mathematical truths apply merely to fish, or merely to stones, or merely to colours. So long as you are dealing with pure mathematics, you are in the realm of complete and absolute abstraction. . . . Mathematics is thought moving in the sphere of complete abstraction from any particular instance of what it is talking about.