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.
Do not feel safe. The poet remembers._x000D_ You can kill one, but another is born._x000D_ The words are written down, the deed, the date.
If Charlie Parker were a Gunslinger, There'd be a Whole Lot of Dead Copycats
I can't say what people use the experience of listening to songs for, but I would never tell somebody what it is supposed to mean. That defeats the purpose of making it. Hopefully, whoever connects with it connects with it in their own way, and it can mean whatever it is supposed to mean to them.
The writer must earn money in order to be able to live and to write, but he must by no means live and write for the purpose of making money.
Yes, every venture is always filled with apprehensions. But if we were to conduct ourselves continuously on that aspect, then we would lose the most important reason to be in this profession: to challenge the art of and be part of what is commonly known as our creative instincts.
The really magical things are the ones that happen right in front of you. A lot of the time you keep looking for beauty, but it is already there. And if you look with a bit more intention, you see it.
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