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.
No one may have the guts to say this, but if we could make better human beings by knowing how to add genes, why shouldn't we?
The first mission to Mars did not expect to find craters and river valleys, and yet they did. The first mission to Jupiter didn't expect to find ocean worlds and volcano worlds, but they did.
Well, biology today as I see it has an amiable look - quite different from the 19th-century view that the whole arrangement of nature is hostile, 'red in tooth and claw.' That came about because people misread Darwin's 'survival of the fittest.'
The heart of the matter, as I see it, is the stark fact that world poverty is primarily a problem of two million villages, and thus a problem of two thousand million villagers.
My experiments proved that the radiation of uranium compounds can be measured with precision under determined conditions and that this radiation is an atomic property of the element of uranium.
Imagine being able to predict and prevent cancer before it starts. If we gather the world's talent and expertise in a committed, targeted effort, great progress is possible.
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