When success turns a man's head he faces failure

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.

There is only one subject matter for education, and that is Life in all its manifestations

Algebra reverses the relative importance of the factors in ordinary language. It is essentially a written language, and it endeavors to exemplify in its written structures the patterns which it is its purpose to convey. The pattern of the marks on paper is a particular instance of the pattern to be conveyed to thought. The algebraic method is our best approach to the expression of necessity, by reason of its reduction of accident to the ghostlike character of the real variable.

A race preserves its vigor so long as it harbors a real contrast between what has been and what may be; and so long as it is nerved by the vigor to adventure beyond the safeties of the past. Without adventure civilization is in full decay.

You cannot evade quantity. You may fly to poetry and music, and quantity and number will face you in your rhythms and your octaves.

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