Calculus required continuity, and continuity was supposed to require the infinitely little; but nobody could discover what the infinitely little might be.

Moreover, the attitude that one ought to believe such and such a proposition, independently of the question whether there is evidence in its favor, is an attitude which produces hostility to evidence and causes us to close our minds to every fact that does not suit our prejudices.

If you question any candid person who is no longer young, he is very likely to tell you that, having tasted life in this world, he has no wish to begin again as a "new boy" in another.

But I simply can't stand a view limited to this earth, I feel life is so small unless it has windows into other worlds...I like mathematics largely because it is not human.

I believe that the abolition of private ownership of land and capital is a necessary step toward any world in which the nations are to live at peace with one another.

If the youth is content to abandon his previous associates and to throw in his lot whole-heartedly with the rulers, he may, after suitable tests, be promoted, but if he shows any regrettable solidarity with his previous associates, the rulers will reluctantly conclude that there is nothing to be done with him except to send him to the lethal chamber before his ill-disciplined intelligence has had time to spread revolt. This will be a painful duty to the rulers, but I think they will not shrink from performing it.

Philosophy, for Plato, is a kind of vision, the 'vision of truth'...Everyone who has done any kind of creative work has experienced, in a greater or less degree, the state of mind in which, after long labour, truth or beauty appears, or seems to appear, in a sudden glory - it may only be about some small matter, or it may be about the universe. I think that most of the best creative work, in art, in science, in literature, and in philosophy, has been a result of just such a moment.