Vigorous societies harbour a certain extravagance of objectives.

The misconception which has haunted philosophic literature throughout the centuries is the notion of 'independent existence.' There is no such mode of existence; every entity is to be understood in terms of the way it is interwoven with the rest of the universe.

I will not go so far as to say that to construct a history of thought without profound study of the mathematical ideas of successive epochs is like omitting Hamlet from the play which is named after him. That would be claiming too much. But it is certainly analogous to cutting out the part of Ophelia. This simile is singularly exact. For Ophelia is quite essential to the play, she is very charming . . . and a little mad.

Inventive genius requires pleasurable mental activity as a condition for its vigorous exercise

In the history of the world the prize has not gone to those species which specialized in methods of violence, or even in defensive armor. In fact, nature began with producing animals encased in hard shells for defense against the ill of life. But smaller animals, without external armor, warm-blooded, sensitive, alert, have cleared those monsters off the face of the earth.

Religion is the reaction of human nature to its search for God.

By relieving the brain of all unnecessary work, a good notation sets it free to concentrate on more advanced problems, and in effect increases the mental power of the race.