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.
The way to stop financial joyriding is to arrest the chauffeur, not the automobile.
The wisdom of the appearance of the spirit in the body is this: the human spirit is a Divine Trust, and it must traverse all conditions, for its passage and movement through the conditions of existence will be the means of its acquiring perfections.
A power struggle collapses when you withdraw your energy from it. Power struggles become uninteresting to you when you change your intention from winning to learning about yourself.
When fate hands us a lemon, let's try to make lemonade.
An expert is a man who has made all the mistakes which can be made, in a narrow field.
What matters is how quickly you do what your soul directs.
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