A linguist would be shocked to learn that if a set is not closed this does not mean that it is open, or again that "E is dense in E" does not mean the same thing as "E is dense in itself".

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.

I recall once saying that when I had given the same lecture several times I couldn't help feeling that they really ought to know it by now.

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.

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

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".