The study of mathematics is, if an unprofitable, a perfectly harmless and innocent occupation.

No mathematician should ever allow himself to forget that mathematics, more than any other art or science, is a young man's game

The theory of numbers, more than any other branch of mathematics, began by being an experimental science. Its most famous theorems have all been conjectured, sometimes a hundred years or more before they were proved; and they have been suggested by the evidence of a mass of computations.

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.

It is rather astonishing how little practical value scientific knowledge has for ordinary men, how dull and commonplace such of it as has value is, and how its value seems almost to vary inversely to its reputed utility.

If intellectual curiosity, professional pride, and ambition are the dominant incentives to research, then assuredly no one has a fairer chance of gratifying them than a mathematician.

317 is a prime, not because we think so, or because our minds are shaped in one way rather than another, but because it is so, because mathematical reality is built that way.