16
" 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.
The case for my life, then, or for that of any one else who has been a mathematician in the same sense in which I have been one, is this: that I have added something to knowledge, and helped others to add more; and that these somethings have a value which differs in degree only, and not in kind, from that of the creations of the great mathematicians, or of any of the other artists, great or small, who have left some kind of memorial behind them. "
― G.H. Hardy , A Mathematician's Apology
18
" I spoke of the 'real' mathematics of Fermat and other great mathematicians, the mathematics which has permanent aesthetic value, as for example the best Greek mathematics has, the mathematics which is eternal because the best of it may, like the best literature, continue to cause intense emotional satisfaction to thousands of people after thousands of years. These men were all primarily pure mathematicians; but I was not thinking only of pure mathematics. 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. It is the dull and elementary parts of applied mathematics, as it is the dull and elementary parts of pure mathematics, that work for good or ill. "
― G.H. Hardy , A Mathematician's Apology
20
" The mathematician is in much more direct contact with reality. This may seem a paradox, since it is the physicist who deals with the subject-matter usually described as 'real' ... A chair may be a collection of whirling electrons, or an idea in the mind of God : each of these accounts of it may have its merits, but neither conforms at all closely to the suggestions of common sense. ... neither physicists nor philosophers have ever given any convincing account of what 'physical reality' is, or of how the physicist passes, from the confused mass of fact or sensation with which he starts, to the construction of the objects which he calls 'real'.
A mathematician, on the other hand, is working with his own mathematical reality. ... mathematical objects are so much more what they seem. ... 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. "
― G.H. Hardy , A Mathematician's Apology