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.

The Axiom of Choice is necessary to select a set from an infinite number of socks, but not an infinite number of shoes.

You find this curious fact, that the more intense has been the religion of any period and more profound has been the dogmatic belief, the greater has been the cruelty and the worse has been the state of affairs. In the so called age of faith, when men really did believe the Christian religion in all its completeness, there was the Inquisition, with its tortures; there were millions of unfortunate women burnt as witches; and there was every kind of cruelty practised upon all sorts of people in the name of religion.

I cannot favour laws such as that of Idaho, which allows sterilization of 'mental defectives, epileptics, habitual criminals, moral degenerates, and sex perverts.' The last two categories here are very vague . . . The law of Idaho would have justified the sterilization of Socrates, Plato, Julius Caesar, and St. Paul.

As soon as we abandon our own reason, and are content to rely upon authority, there is no end to our troubles.

To discover a system for the avoidance of war is a vital need of our civilisation.

Righteousness cannot be born until self-righteousness is dead.