If you have had your attention directed to the novelties in thought in your own lifetime, you will have observed that almost all really new ideas have a certain aspect of foolishness when they are first produced, and almost any idea which jogs you out of your current abstractions may be better than nothing.

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.

Peace is self-control at its widest-at the width where the "self" has been lost, and interest has been transferred to coordinations wider than personality.

There is a technique, a knack, for thinking, just as there is for doing other things. You are not wholly at the mercy of your thoughts, any more than they are you. They are a machine you can learn to operate.

War can protect; it cannot create.

Knowledge shrinks as wisdom grows.

An open mind is all very well in its way, but it ought not to be so open that there is no keeping anything in or out of it.