A month's intelligent instruction in the theory of numbes ought to be twice as instructive, twice as useful, and at least 10 times as entertaining as the same amount of 'calculus for engineers'.

They [formulae 1.10 - 1.12 of Ramanujan] must be true because, if they were not true, no one would have had the imagination to invent them.

Young men should prove theorems, old men should write books.

Most people can do nothing at all well

I remember once going to see him [Ramanujan] when he was lying ill at Putney. I had ridden in taxi-cab No. 1729, and remarked that the number seemed to me rather a dull one, and that I hoped it was not an unfavourable omen. "No," he replied, "it is a very interesting number; it is the smallest number expressible as a sum of two cubes in two different ways."

I count Maxwell and Einstein, Eddington and Dirac, among "real" mathematicians. The great modern achievements of applied mathematics have been in relativity and quantum mechanics, and these subjects are at present at any rate, almost as "useless" as the theory of numbers.

Mathematics is not a contemplative but a creative subject; no one can draw much consolation from it when he has lost the power or the desire to create; and that is apt to happen to a mathematician rather soon. It is a pity, but in that case he does not matter a great deal anyhow, and it would be silly to bother about him.