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.
Exposition, criticism, appreciation, is work for second-rate minds.
Interpretation
What this quote means
G. H. Hardy suggests that true intellectual work goes beyond mere analysis and requires creativity and original thought.
In this quote, G. H. Hardy emphasizes the distinction between superficial analyses of work and the deeper, original contributions of great minds. He implies that those who are limited to exposition, criticism, and appreciation lack the originality required to create real advancements in thought or art. For Hardy, the highest form of intellectual engagement is not just about understanding or evaluating previous work, but also about creating something new and valuable.
Themes
In practice
Example use cases
In a speech about innovation, one might quote Hardy to emphasize the importance of originality over imitation.
More from G. H. Hardy
All quotes βMathematics 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.
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.
Similar quotes
Hinduism is a living organism. One and indivisible at the root, it has grown into a vast tree with innumerable branches. Knowledge is limitless and so also the application of truth. Everyday we add to our knowledge of the power of Atman (soul) and we shall keep on doing so.
Godβs purpose is βto bring to pass the immortality and eternal life of man.β2 That is fundamental to all we do. Sometimes we get so wrapped up in things that we find fascinating or become so consumed by mundane responsibilities that we lose sight of Godβs objectives. As you consistently focus your life on the most basic principles, you will gain an understanding of what you are to do, and you will produce more fruit for the Lord and more happiness for yourself.
The philosopher is not a citizen of any community of ideas, that is what makes him a philosopher.
The destructive character lives from the feeling, not that life is worth living, but that suicide is not worth the trouble.
What is freedom? Freedom is the right to choose: the right to create for oneself the alternatives of choice.
I enjoy the simplistic training and life in marathon. You run, eat, sleep, walk around - that's how life is. You don't get complicated. The moment you get complicated it distracts your mind.