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.
Interpretation
Mathematics requires creativity and active engagement, rather than mere contemplation.
G. H. Hardy emphasizes that mathematics is fundamentally a creative endeavor, suggesting that true understanding and appreciation come from the act of creation rather than passive observation. He laments that when a mathematician loses the desire or ability to create, they become less relevant, highlighting the importance of creativity in the field of mathematics.
In practice
This quote can be used in a speech about the value of creativity in education.
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.
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.
No man is able to make progress when he is wavering between opposite things.
Good questions work on us, we don't work on them. They are not a project to be completed but a doorway opening onto greater depth of understanding, actions that will take us into being more fully alive.
Good character is not formed in a week or a month. It is created little by little, day by day. Protracted and patient effort is needed to develop good character.
We are all in the gutter, but some of us are looking at the stars.
The years after 50 can be a time of great productivity, meaningful work, pleasure, creativity, and innovation. It's a huge opportunity.
Perhaps our originality manifests itself most strikingly in what we do with that which we did not originate. To discover something wholly new can be a matter of chance, of idle tinkering, or even of the chronic dissatisfaction of the untalented.
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