The difference between ancients and moderns is that the ancients asked what have we experienced, and moderns asked what can we experience.

I am sure that one secret of a successful teacher is that he has formulated quite clearly in his mind what the pupil has got to know in precise fashion. He will then cease from half-hearted attempts to worry his pupils with memorizing a lot of irrelevant stuff of inferior importance.

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.

It is not paradox to say that in our most theoretical moods we may be nearest to our most practical applications.

When success turns a man's head he faces failure

Every really new idea looks crazy at first.

Dogmatism is the anti-Christ of learning.