The mathematician is entirely free, within the limits of the imagination, to construct what worlds he pleases.

The hypothesis that life has developed from inorganic matter is, at present, still an article of faith.

... it is certain that the real function of art is to increase our self-consciousness

It is certain that the real function of art is to increase our self-consciousness to make us more aware of what we are, and therefore of what the universe in which we live really is. And since mathematics, in its own way, also performs this function, it is not only aesthetically charming but profoundly significant. It is an art, and a great art.

To be willing to suffer in order to create is one thing to realize that one's creation necessitates one's suffering, that suffering is one of the greatest of God's gifts, is almost to reach a mystical solution of the problem of evil.

We have reached one of the great stages in the adventure of thought … We are required to see the universe with new eyes, and it is because it makes such demands and also holds out the promise of realizing them, that the study of science is so supremely worth while.