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.

The factor in human life provocative of a noble discontent is the gradual emergence of a sense of criticism, founded upon appreciation of beauty, and of intellectual distinction, and of duty.

Through and through the world is infested with quantity: To talk sense is to talk quantities. It is no use saying the nation is large. . . . How large? It is no use saying the radium is scarce. . . . How scarce? You cannot evade quantity. You may fly to poetry and music, and quantity and number will face you in your rhythms and your octaves.

In a certain sense, everything is everywhere at all times. For every location involves an aspect of itself in every other location. Thus every spatio-temporal standpoint mirrors the world

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

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.

Philosophy is the product of wonder.