The real history does not get written, because it is not in people's brains but in their nerves and vitals.

Now in creative thought common sense is a bad master. Its sole criterion for judgement is that the new ideas shall look like the old ones. In other words it can only work by suppressing originality.

The importance of an individual thinker owes something to chance. For it depends upon the fate of his ideas in the minds of his successors.

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.

Almost all new ideas have a certain aspect of foolishness when they are first produced.

No man of science wants merely to know. He acquires knowledge to appease his passion for discovery. He does not discover in order to know, he knows in order to discover.

By relieving the brain of all unnecessary work, a good notation sets it free to concentrate on more advanced problems, and in effect increases the mental power of the race.