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 make no manner of doubt that you threw a very diamond of truth at me, though you see it hit me so directly in the face that it wasn't exactly appreciated, at first.
You can try, but you seem cleverer than Fudge, so I'd have thought you'd have learned from his mistakes. He tried intervening at Hogwarts. You might have noticed he's not Minister anymore, but Dumbledore's still headmaster. I'd leave Dumbledore alone, if I were you.
Hath any wounded thee with injuries? Meet them with patience. Hasty words rankle the wound; soft language dresses it.
He who speaks without modesty will find it difficult to make his words good.
God will never reveal more truth about himself until you have obeyed what you know already
Twenty-four hours a day one looks for contentment in eight different directions but one must also explore the ninth place, which is to their own body and contemplate within. Within the body are the nine treasures of the Name of the Lord—seek the depths of these virtues. Those blessed with the karma of good actions praise the Lord and become true devotees
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