As history proves abundantly, mathematical achievement, whatever its intrinsic worth, is the most enduring of all.
Interpretation
Mathematics has long-lasting value and significance in history.
G. H. Hardy highlights the idea that mathematical accomplishments, regardless of their immediate significance or application, hold a timeless quality that surpasses other achievements. Throughout history, mathematical discoveries have provided foundational insights that continue to influence various fields, showcasing their enduring relevance and importance in understanding the world.
In practice
During a lecture on the importance of STEM education, one might state this quote to emphasize mathematics's lasting impact.
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.
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.
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.
In the development of antibiotics, the soil microbiological population has contributed more than its share. It is to the soil that the microbiologists came in search of new antibacterial agents.
We find, therefore, under this orderly arrangement, a wonderful symmetry in the universe, and a definite relation of harmony in the motion and magnitude of the orbs, of a kind that is not possible to obtain in any other way.
I suppose the one quality in an astronaut more powerful than any other is curiosity. They have to get some place nobody's ever been.
Low socioeconomic status carries with it an enormously increased risk of a broad range of diseases, and this gradient cannot be fully explained by factors such as health-care access.
The cross pollination of disciplines is fundamental to truly revolutionary advances in our culture.
Man does not limit himself to seeing; he thinks and insists on learning the meaning of phenomena whose existence has been revealed to him by observation. So he reasons, compares facts, puts questions to them, and by the answers which he extracts, tests one by another. This sort of control, by means of reasoning and facts, is what constitutes experiment, properly speaking; and it is the only process that we have for teaching ourselves about the nature of things outside us.
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