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.
I don't think you ever really know what all you're doing, so you have to act on faith.
All that I have said up to now has merely been words._x000D_ When people come to see me, I have to say something._x000D_ But it is best not to speak about these matters too much._x000D_ Better to begin practice without delay. _x000D_ I am like a good friend inviting you to go somewhere._x000D_ Do not hesitate, just get going. You won't regret it.
Let go of your ego's need to be right. When you're in the middle of an argument, ask yourself: Do I want to be right or be happy? When you choose the joyous, loving, spiritual mode, your connection to intention is strengthened.
It ain't what you don't know that gets you into trouble. It's what you know for sure that just ain't so.
In everything one must consider the end.
Nothing can be done except little by little.
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