Try a hard problem. You may not solve it, but you will prove something else.

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

It is possible for a mathematician to be "too strong" for a given occasion. He forces through, where another might be driven to a different, and possible more fruitful, approach. (So a rock climber might force a dreadful crack, instead of finding a subtle and delicate route.)

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."

In passing, I firmly believe that research should be offset by a certain amount of teaching, if only as a change from the agony of research. The trouble, however, I freely admit, is that in practice you get either no teaching, or else far too much.

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".

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