The infinitely competent can be uncreative.

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

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 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.

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

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