A precisian professor had the habit of saying: "... quartic polynomial ax^4+bx^3+cx^2+dx+e , where e need not be the base of the natural logarithms."

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 read in the proof sheets of Hardy on Ramanujan: "As someone said, each of the positive integers was one of his personal friends." My reaction was, "I wonder who said that; I wish I had." In the next proof-sheets I read (what now stands), "It was Littlewood who said..."

A heavy warning used to be given that pictures are not rigorous; this has never had its bluff called and has permanently frightened its victims into playing for safety.

The higher mental activities are pretty tough and resilient, but it is a devastating experience if the drive does stop. Some people lose it in their forties and can only stop. In England they are a source of Vice-Chancellors.

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.

A good mathematical joke is better, and better mathematics, than a dozen mediocre papers.