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.

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.)

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

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

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.

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