I have never done anything 'useful'. No discovery of mine has made, or is likely to make, directly or indirectly, for good or ill, the least difference to the amenity of the world... Judged by all practical standards, the value of my mathematical life is nil; and outside mathematics it is trivial anyhow. I have just one chance of escaping a verdict of complete triviality, that I may be judged to have created something worth creating. And that I have created something is undeniable: the question is about its value.

A mathematician, like a painter or a poet, is a maker of patterns.

A mathematician, like a painter or poet, is a maker of patterns. If his patterns are more permanent than theirs, it is because they are made with ideas.

It is not worth an intelligent man's time to be in the majority. By definition, there are already enough people to do that.

The primes are the raw material out of which we have to build arithmetic, and Euclid's theorem assures us that we have plenty of material for the task.

A man who sets out to justify his existence and his activities has to distinguish two different questions. The first is whether the work which he does is worth doing; and the second is why he does it (whatever its value may be).

Cricket is the only game where you are playing against eleven of the other side and ten of your own.