The study of mathematics is apt to commence in disappointment... We are told that by its aid the stars are weighed and the billions of molecules in a drop of water are counted. Yet, like the ghost of Hamlet's father, this great science eludes the efforts of our mental weapons to grasp it.

Algebra reverses the relative importance of the factors in ordinary language.

Art is the imposing of a pattern on experience, and our aesthetic enjoyment is recognition of the pattern.

Seek simplicity, then distrust.

Learning is often spoken of as if we are watching the open pages of all the books which we have ever read, and then, when occasion arises, we select the right page to read aloud to the universe.

The only use of a knowledge of the past is to equip us for the present. The present contains all that there is. It is holy ground; for it is the past, and it is the future.

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.