There is no greater hindrance to the progress of thought than an attitude of irritated party-spirit.

Art flourishes where there is a sense of adventure.

There is no more common error than to assume that, because prolonged and accurate mathematical calculations have been made, the application of the result to some fact of nature is absolutely certain.

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.

Art heightens the sense of humanity. It gives an elation to feeling which is supernatural...A million sunsets will not spur us on towards civilization. It requires Art to evoke into consciousness the finite perfections which lie ready for human achievement.

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.

If a dog jumps into your lap, it is because he is fond of you; but if a cat does the same thing, it is because your lap is warmer.