The human race may well become extinct before the end of the century. Speaking as a mathematician, I should say the odds are about three to one against survival.

The demand for certainty is one which is natural to man, but is nevertheless an intellectual vice. If you take your children for a picnic on a doubtful day, they will demand a dogmatic answer as to whether it will be fine or wet, and be disappointed in you when you cannot be sure.

Of these austerer virtues the love of truth is the chief, and in mathematics, more than elsewhere, the love of truth may find encouragement for waning faith. Every great study is not only an end in itself, but also a means of creating and sustaining a lofty habit of mind; and this purpose should be kept always in view throughout the teaching and learning of mathematics.

That Plato's Republic should have been admired, on its political side, by decent people, is perhaps the most astonishing example of literary snobbery in all history.

He will see himself and life and the world as truly as our human limitations will permit; realizing the brevity and minuteness of human life, he will realize also that in individual minds is concentrated whatever of value the known universe contains. And he will see that the man whose mind mirrors the world becomes in a sense as great as the world. In emancipation from the fears that beset the slave of circumstance he will experience a profound joy, and through all the vicissitudes of his outward life he will remain in the depths of his being a happy man.

Philosophers, for the most part, are constitutionally timid, and dislike the unexpected. Few of them would be genuinely happy as pirates or burglars. Accordingly they invent systems which make the future calculable, at least in its main outlines.

The wise man thinks about his troubles only when there is some purpose in doing so; at other times he thinks about other things, or, if it is night, about nothing at all.