Mathematics is only the art of saying the same thing in different words.

Change is one thing, progress is another.

It seems to us unwise to have insisted on teaching geometry to the younger Dionysius, tyrant of Syracuse, in order to make him a good king, but from Plato's point of view it was essential. He was sufficiently Pythagorean to think that without mathematics no true wisdom is possible.

A man who has once perceived, however temporarily and however briefly, what makes greatness of soul, can no longer be happy if he allows himself to be petty, self-seeking, troubled by trivial misfortunes, dreading what fate may have in store for him. The man capable of greatness of soul will open wide the windows of his mind, letting the winds blow freely upon it from every portion of the universe.

If there were in the world today any large number of people who desired their own happiness more than they desired the unhappiness of others, we could have a paradise in a few years.

From the height of their disillusionment they look down upon those whom they despise as simple souls. For my part I have no sympathy with this outlook. All disenchantment is to me a malady, which, it is true, certain circumstances may render inevitable, but which none the less, when it occurs, is to be cured as soon as possible, not to be regarded as a higher form of wisdom.

Belief in God and a future life makes it possible to go through life with less of stoic courage than is needed by skeptics.