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.

The infinitely competent can be uncreative.

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

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.

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.)

I listen only to Bach, Beethoven or Mozart. Life is too short to waste on other composers.

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...

The first lecture of each new year renews for most people a light stage fright.

The referee said it was not acceptable, but the Press considered they could not refuse to publish a book by a professor of the university.

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.

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.