Real mathematics must be justified as art if it can be justified at all.
Interpretation
Mathematics is an artistic endeavor that requires justification beyond mere practicality.
In this quote, G. H. Hardy emphasizes the view that mathematics transcends utility and becomes an art form in its own right. He advocates for the appreciation of mathematics as something beautiful and creative, suggesting that its value lies not only in its application to science but also in its aesthetic and philosophical dimensions.
In practice
In a lecture about the aesthetics of mathematics, one could use this quote to illustrate how mathematical concepts can be seen as artistic.
A chess problem is genuine mathematics, but it is in some way "trivial" mathematics. However, ingenious and intricate, however original and surprising the moves, there is something essential lacking. Chess problems are unimportant. The best mathematics is serious as well as beautiful-"important" if you like, but the word is very ambiguous, and "serious" expresses what I mean much better.
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.
Exposition, criticism, appreciation, is work for second-rate minds.
It is hardly possible to maintain seriously that the evil done by science is not altogether outweighed by the good. For example, if ten million lives were lost in every war, the net effect of science would still have been to increase the average length of life.
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.
There is no scorn more profound, or on the whole more justifiable, than that of the men who make for the men who explain. Exposition, criticism, appreciation, is work for second-rate minds.
In the best of all possible worlds, directors would obsess about the quality of their storytelling, and not the details of their technical methods.
The reason we go to poetry is not for wisdom, but for the dismantling of wisdom
I have desired, like every artist, to create a little world out of the beautiful, pleasant, and significant things of this marred and clumsy world, and to show in a vision something of the face of Ireland to any of my own people who would look where I bid them. I have therefore written down accurately and candidly much that I have heard and seen, and, except by way of commentary, nothing that I have merely imagined.
In no other sport is the connection between performer and observer so intimate, so frequently painful, so unresolved
I agree with Balzac and 19th-century writers, black and white, who say, 'I write for money.' Yes, I think everybody should be paid handsomely; I insist on it, and I pay people who work for me, or with me, handsomely.
The more the technocrats programme it down to the smallest detail, the more the powerful manipulate it, football continues to be the art of the unforeseeable. When you least expect it, the impossible occurs: the dwarf teaches the giant a lesson, and a scraggy, bow-legged black man makes an athlete sculpted in Greece look ridiculous.
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