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.
I'm a person that works off of music. I let the music dictate the direction.
The actual world, not some fantastic structure that has nothing to do with reality, must provide the material for modern poetry.
One day, I will be a poet. Water will depend on my visions.
A writer's definitive death is when no one reads his books anymore. That's the final death.
To wake the soul by tender strokes of art, To raise the genius, and to mend the heart
My sole inspiration is a telephone call from a director. ... (when asked who wrote 'Some Enchanted Evening') Rodgers and Hammerstein, if you can imagine it taking two men to write one song. ... Good authors, too, who once knew better words now use only four-letter words writing prose. ... Brush up your Shakespeare and they'll all kowtow.
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