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

Those who have never known the deep intimacy and the intense companionship of happy mutual love have missed the best thing that life has to give.

Adventurous men enjoy shipwrecks, mutinies, earthquakes, conflagrations, and all kinds of unpleasant experiences. They say to themselves, for example, 'So this is what an earthquake is like,' and it gives them pleasure to have their knowledge of the world increased by this new item.

... the word "theory" ... was originally an Orphic word, which Cornford interprets as "passionate sympathetic contemplation" ... For Pythagoras, the "passionate sympathetic contemplation" was intellectual, and issued in mathematical knowledge ... To those who have reluctantly learnt a little mathematics in school this may seem strange; but to those who have experienced the intoxicating delight of sudden understanding that mathematics gives, from time to time, to those who love it, the Pythagorean view will seem completely natural.

Every advance in civilization has been denounced as unnatural while it was recent

When a man acts in ways that annoy us we wish to think him wicked, and we refuse to face the fact that his annoying behavior is the result of antecedent causes which, if you follow them long enough, will take you beyond the moment of his birth, and therefore to events for which he cannot be held responsible by any stretch of imagination... When a motorcar fails to start, we do not attribute its annoying behavior to sin, we do not say, you are a wicked motorcar, and you shall not have any more gasoline until you go.

The sentiments of an adult are compounded of a kernel of instinct surrounded by a vast husk of education.