I feel life is so small unless it has windows into other worlds.

Mathematics is only the art of saying the same thing in different words.

But as the work proceeded I was continually reminded of the fable about the elephant and the tortoise. Having constructed an elephant upon which the mathematical world could rest, I found the elephant tottering, and proceeded to construct a tortoise to keep the elephant from falling. But the tortoise was not more secure than the elephant, and after some twenty years of very arduous toil, I came to the conclusion that there was nothing more that I could do in the way of making mathematical knowledge indubitable.

Change is scientific; progress is ethical; change is indubitable, whereas progress is a matter of controversy.

The satisfaction to be derived from success in a great constructive enterprise is one of the most massive that life has to offer.

There lies before us, if we choose, continual progress in happiness, knowledge and wisdom. Shall we instead choose death, because we cannot forget our quarrels? I appeal as a human being to human beings; remember your humanity, and forget the rest.

Even if the open windows of science at first make us shiver after the cozy indoor warmth of traditional humanizing myths, in the end the fresh air brings vigor, and the great spaces have a splendor of their own.