John

“I believe that mathematical reality lies outside us, that our function is to discover or observe it, and that the theorems which we prove, and which we describe grandiloquently as our "creations," are simply our notes of our observations. This view has been held, in one form or another, by many philosophers of high reputation from Plato onwards, and I shall use the language which is natural to a man who holds it.”
― G.H. Hardy, A Mathematician's Apology

“A mathematical proof should resemble a simple and clear-cut constellation, not a scattered cluster in the Milky Way.”
― G.H. Hardy, A Mathematician's Apology

“Real mathematics must be justified as art if it can be justified at all.”
― G.H. Hardy, A Mathematician's Apology

“No mathematician should ever allow him to forget that mathematics, more than any other art or science, is a young man's game. … Galois died at twenty-one, Abel at twenty-seven, Ramanujan at thirty-three, Riemann at forty. There have been men who have done great work later; … [but] I do not know of a single instance of a major mathematical advance initiated by a man past fifty. … A mathematician may still be competent enough at sixty, but it is useless to expect him to have original ideas.”
― G.H. Hardy, A Mathematician's Apology