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 saved a man's life once," said Granny. "Special medicine, twice a day. Boiled water with a bit of berry juice in it. Told him I'd bought it from the dwarves. That's the biggest part of doct'rin, really. Most people'll get over most things if they put their minds to it, you just have to give them an interest.
We should take care not to make the intellect our god; it has, of course, powerful muscles, but no personality.
It's easy to pretend expertise when there's no data to contradict you.
Basically, there are two paths you can walk: faith or fear. It's impossible to simultaneously trust God and not trust God.
I just write stuff down and pile it up, and when I get enough stuff, I spread it out and look at it and figure out how to use it.
Whatever he says, let his inner resolution be not to bear whatever comes to him, but to bear it 'for a reasonable period'--and let the reasonable period be shorter than the trial is likely to last. It need not be much shorter; in attacks on patience, chastity, and fortitude, the fun is to make the man yield just when (had he but known it) relief was almost in sight.
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