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.

The mathematician is entirely free, within the limits of his imagination, to construct what worlds he pleases. What he is to imagine is a matter for his own caprice; he is not thereby discovering the fundamental principles of the universe nor becoming acquainted with the ideas of God.

... 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.

It is only in exceptional moods that we realize how wonderful are the commonest experiences of life. It seems to me sometimes that these experiences have an "inner" side, as well as the outer side we normally perceive. At such moments one suddenly sees everything with new eyes; one feels on the brink of some great revelation. It is as if we caught a glimpse of some incredibly beautiful world that lies silently about us all the time.

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