“Imaginary’ universes are so much more beautiful than this stupidly constructed ‘real’ one; and most of the finest products of an applied mathematician’s fancy must be rejected, as soon as they have been created, for the brutal but sufficient reason that they do not fit the facts.”

“What is the proper justification of a mathematician’s life? My answers will be, for the most part, such as are expected from a mathematician: I think that it is worthwhile, that there is ample justification. But I should say at once that my defense of mathematics will be a defense of myself, and that my apology is bound to be to some extent egotistical. I should not think it worth while to apologize for my subject if I regarded myself as one of its failures. Some egotism of this sort is inevitable, and I do not feel that it really needs justification. Good work is no done by "humble" men. It is one of the first duties of a professor, for example, in any subject, to exaggerate a little both the importance of his subject and his own importance in it. A man who is always asking "Is what I do worth while?" and "Am I the right person to do it?" will always be ineffective himself and a discouragement to others. He must shut his eyes a little and think a little more of his subject and himself than they deserve. This is not too difficult: it is harder not to make his subject and himself ridiculous by shutting his eyes too tightly.”

“There is no scorn more profound, or on the whole more justifiable, than that of the men who make for the men who explain.”

“We must not allow the clock and the calendar to blind us to the fact that each moment of life is a miracle and mystery.”

“The clock struck the solemn hour of one, that hour when fancy stalks outside reason, and malignant possibilities stand rock-firm as facts.”

“the social moulds civilization fits us into have no more relation to our actual shapes than the conventional shapes of the constellations have to the real star-patterns.”

“The only true measure of success is the ratio between what we might have done and what we might have been on the one hand, and the thing we have made and the things we have made of ourselves on the other.”