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.
So we find that the three possible solutions of the great problem of increasing human energy are answered by the three words: food, peace, work... Their scientific meaning and purpose now clear to me: food to increase the mass, peace to diminish the retarding force, and work to increase the force accelerating human movement.
The nuclear industry has this amazing record, even equipment from generations one and two. But nuclear mishaps tend to come in these big events - Chernobyl, Three Mile Island, and now Fukushima - so it's more visible.
Our great struggle in medicine these days is not just with ignorance and uncertainty. It's also with complexity: how much you have to make sure you have in your head and think about. There are a thousand ways things can go wrong.
What a deep faith in the rationality of the structure of the world and what a longing to understand even a small glimpse of the reason revealed in the world there must have been in Kepler and Newton to enable them to unravel the mechanism of the heavens in long years of lonely work!
The mineral world is a much more supple and mobile world than could be imagined by the science of the ancients. Vaguely analogous to the metamorphoses of living creatures, there occurs in the most solid rocks, as we now know, perpetual transformation of a mineral species.
I don't believe that the ultimate theory will come by steady work along existing lines. We need something new. We can't predict what that will be or when we will find it because if we knew that, we would have found it already!
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