“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.”

“It takes two or three generations to do what I tried to do in one; and my impulses--affections--vices perhaps they should be called-- were too strong not to hamper a man without advantages; who should be as cold-blooded as a fish and as selfish as a pig to have a really good chance of being one of his country's worthies. You may ridicule me--I am quite willing that you should-- I am a fit subject, no doubt. But I think if you knew what I have gone through these last few years you would rather pity me. And if they knew"--he nodded towards the college at which the dons were severally arriving--"it is just possible they would do the same.”

“I had better say something here about this question of age, since it is particularly important for mathematicians. No mathematician should ever allow himself to forget that mathematics, more than any other art or science, is a young man's game. To take a simple illustration at a comparatively humble level, the average age of election to the Royal Society is lowest in mathematics. We can naturally find much more striking illustrations. We may consider, for example, the career of a man who was certainly one of the world's three greatest mathematicians. Newton gave up mathematics at fifty, and had lost his enthusiasm long before; he had recognized no doubt by the time he was forty that his greatest creative days were over. His greatest idea of all, fluxions and the law of gravitation, came to him about 1666 , when he was twentyfour—'in those days I was in the prime of my age for invention, and minded mathematics and philosophy more than at any time since'. He made big discoveries until he was nearly forty (the 'elliptic orbit' at thirty-seven), but after that he did little but polish and perfect.Galois died at twenty-one, Abel at twenty-seven, Ramanujan at thirty-three, Riemann at forty. There have been men who have done great work a good deal later; Gauss's great memoir on differential geometry was published when he was fifty (though he had had the fundamental ideas ten years before). I do not know an instance of a major mathematical advance initiated by a man past fifty. If a man of mature age loses interest in and abandons mathematics, the loss is not likely to be very serious either for mathematics or for himself.”

“You both think I know not what,' said I. 'Have the goodness to make me as little the subject of your mutual talk and thoughts as possible. I have my own sort of life apart from yours.”

“whether to follow uncritically the track he finds himself in, without considering his aptness for it, or to consider what his aptness or bent may be, and reshape his course accordingly. I tried to do the latter, and I failed. But I don't admit that my failure proved my view to be a wrong one, or that my success would have made it a right one; though that's how we appraise such attempts nowadays.”

“Not long since, a strolling Indian went to sell baskets at the house of a well-known lawyer in my neighborhood. “Do you wish to buy any baskets?” he asked. “No, we do not want any,” was the reply. “What!” exclaimed the Indian as he went out the gate, “do you mean to starve us?” Having seen his industrious white neighbors so well off—that the lawyer had only to weave arguments, and, by some magic, wealth and standing followed—he had said to himself: I will go into business; I will weave baskets; it is a thing which I can do. Thinking that when he had made the baskets he would have done his part, and then it would be the white man’s to buy them. He had not discovered that it was necessary for him to make it worth the other’s while to buy them, or at least make him think that it was so, or to make something else which it would be worth his while to buy.I too had woven a kind of basket of a delicate texture, but I had not made it worth any one’s while to buy them. Yet not the less, in my case, did I think it worth my while to weave them, and instead of studying how to make it worth men’s while to buy my baskets, I studied rather how to avoid the necessity of selling them. The life which men praise and regard as successful is but one kind. Why should we exaggerate any one kind at the expense of the others?”

“I have no right to say or do anything that diminishes a man in his own eyes. What matters is not what I think of him but what he thinks of himself. Hurting a man in his dignity is a crime.”