The infinitely competent can be uncreative.

The infinitely competent can be uncreative.

In H. Eves
Mathematical Circles
Squared, Boston:
Prindle, Weber and
Schmidt, 1972.

I constantly meet people who are doubtful, generally without due reason, about their potential capacity [as mathematicians]. The first test is whether you got anything out of geometry. To have disliked or failed to get on with other [mathematical] subjects need mean nothing; much drill and drudgery is unavoidable before they can get started, and bad teaching can make them unintelligible even to a born mathematician.

A Mathematician's
Miscellany, Methuen
and Co., 1953.

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 possibly more fruitful, approach. (So a rock climber might force a dreadful crack, instead of finding a subtle and delicate route.)

A Mathematician's
Miscellany, Methuen
and Co., 1953.

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.

"The Mathematician's
Art of Work" in Bela
Bollobas (ed.)
Littlewood's
Miscellany,
Cambridge: Cambridge
University Press,
1986.

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 Mathematician's
Miscellany, Methuen
and Co., 1953.

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

A Mathematician's
Miscellany, Methuen
and Co., 1953.

It is true that I should have been surprised in the past to learn that Professor Hardy had joined the Oxford Group. But one could not say the adverse chance was 1:10. Mathematics is a dangerous profession; an appreciable proportion of us go mad, and then this particular event would be quite likely.

A Mathematician's
Miscellany, Methuen
and Co., 1953.

Who has not been amazed to learn that the function y = e^x , like a phoenix rising again from its own ashes, is its own derivative?

Great Currents of
Mathematical
Thought, Vol. 1, New
York: Dover
Publications.

[On the Gaussian curve, remarked to Poincare:]

Experimentalists think that it is a mathematical theorem while the mathematicians believe it to be an experimental fact.

In D'Arcy Thompson,
On Growth and Form,
1917.

I have often noticed that when people come to understand a mathematical proposition in some other way than that of the ordinary demonstration, they promptly say, "Oh, I see. That's how it must be." This is a sign that they explain it to themselves from within their own system.