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.
The economists will have to revise their theories of value.
For Dawkins, evolution is a battle among genes, each seeking to make more copies of itself. Bodies are merely the places where genes aggregate for a time.
Unlike science, creationism cannot predict anything, and it cannot provide satisfactory answers about the past.
I love science, and it pains me to think that so many are terrified of the subject or feel that choosing science means you cannot also choose compassion, or the arts, or be awed by nature. Science is not meant to cure us of mystery, but to reinvent and reinvigorate it.
Artificial selection turned the wolf into the shepherd, and the wild grasses into wheat and corn. In fact, almost every plant and animal that we eat today was bred from a wild, less edible ancestor. If artificial selection can work such profound changes in only ten or fifteen thousand years, what can natural selection do operating over billions of years? The answer is all the beauty and diversity of life.
Among other things, neuroplasticity means that emotions such as happiness and compassion can be cultivated in much the same way that a person can learn through repetition to play golf and basketball or master a musical instrument, and that such practice changes the activity and physical aspects of specific brain areas.
Subscribe for the occasional hand-picked quote. No noise.