I've been giving this lecture to first-year classes for over twenty-five years. You'd think they would begin to understand it by now.

We come finally, however, to the relation of the ideal theory to real world, or "real" probability. If he is consistent a man of the mathematical school washes his hands of applications. To someone who wants them he would say that the ideal system runs parallel to the usual theory: "If this is what you want, try it: it is not my business to justify application of the system; that can only be done by philosophizing; I am a mathematician". In practice he is apt to say: "try this; if it works that will justify it".

I constantly meet people who are doubtful, generally without due reason, about their potential capacity [as mathematicians]. The first test is whether you got anything out of geometry. To have disliked or failed to get on with other [mathematical] subjects need mean nothing; much drill and drudgery is unavoidable before they can get started, and bad teaching can make them unintelligible even to a born mathematician.

The surprising thing about this paper is that a man who could write it would.

Mathematics is a dangerous profession; an appreciable proportion of us go mad.

The first test of potential in mathematics is whether you can get anything out of geometry.

I've been giving this lecture to first-year classes for over twenty-five years. You'd think they would begin to understand it by now.