Education which is not modern share the fate of all organic things which are kept too long.

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.

There are two principles inherent in the very nature of things, recurring in some particular embodiments whatever field we explore - the spirit of change, and the spirit of conservation. There can be nothing real without both. Mere change without conservation is a passage from nothing to nothing. . . . Mere conservation without change cannot conserve. For after all, there is a flux of circumstance, and the freshness of being evaporates under mere repetition.

The point about zero is that we do not need to use it in the operations of daily life. No one goes out to buy zero fish. It is in a way the most civilised of all the cardinals, and its use is only forced on us by the needs of cultivated modes of thought.

One main factor in the upward trend of animal life has been the power of wandering.

The art of progress is to preserve order amid change, and to preserve change amid order. Life refuses to be embalmed alive. The more prolonged the halt in some unrelieved system of order, the greater the crash of the dead society.

The importance of an individual thinker owes something to chance. For it depends upon the fate of his ideas in the minds of his successors.