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.
Interpretation
Hardy argues that while chess problems are mathematically interesting, they lack significance compared to more profound mathematical discoveries.
G. H. Hardy draws a distinction between chess problems and what he considers true mathematics. He acknowledges the ingenuity and complexity of chess problems but emphasizes that they ultimately lack importance in the grander scheme of mathematics. For Hardy, the value of mathematics lies in its seriousness and beauty, drawing a clear line between playful puzzles and the deeper significance found in serious mathematical inquiry.
In practice
This quote can be used in a lecture on the philosophy of mathematics to emphasize the depth of mathematical thinking.
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.
Real mathematics must be justified as art if it can be justified at all.
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.
The transfinite numbers are in a sense the new irrationalities [ ... they] stand or fall with the finite irrational numbers.
Pure mathematics is, in its way, the poetry of logical ideas.
We must say that there are as many squares as there are numbers.
Why learn a number like pi to so many decimal places? The answer I gave then as I do now is that pi is for me an extremely beautiful and utterly unique thing. Like the Mona Lisa or a Mozart symphony, pi is its own reason for loving it.
I would certainly end up forever crying the blues into a coffee cup in a park for old men playing chess or silly games of some sort.
Self-confidence is very important. If you don't think you can win, you will take cowardly decisions in the crucial moments, out of sheer respect for your opponent. You see the opportunity but also greater limitations than you should. I have always believed in what I do on the chessboard, even when I had no objective reason to. It is better to overestimate your prospects than underestimate them.
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