Who are the greatest modern polymaths
Polymaths exist today. For example, the (late) Clifford Truesdell, Roger Penrose, etc.
Fred Hoyle, Paul Dirac's student, on everything from physics to science fiction, economics to astronomy. Eddington was engaged in philosophy.
William Clifford, although he died in his thirties, wrote on almost every subject. William Strutt, Lord Raleigh too. James Hutton too.
Carl (von) Menger, the economist, father of the famous mathematician Karl Menger, had a library with over 30,000 books.
Condillac wrote over forty volumes. Wolff too. Cauchy was a master of anything and everything except economics and history.
Waterston gave the modern kinetic theory of heat in a book on an explanation of the brain via neural networks (in the 1840s!) Before publishing it in the Philosophical Journal and submitting his work on physics and thermodynamics to other journals and presentation in royal society .
I suspect the real problem is pretty basic.
Today's physics takes a lot of time to learn. On the other hand, we have better tools. On ten pages, with the help of fiber bundles and groups and modern integration methods, dynamic stories can be discussed more precisely and in greater detail than a thousand pages in the 19th century. It is not true that if you are a (mathematical) biologist, for example, you cannot know physics, or that a physicist cannot know biology and economics.
We learn so much more, in depth and breadth. and in relation to empirical knowledge alongside mathematical concepts. However, our larger human capital makes the process a lot easier. We easily solve problems that would require months of correspondence and effort a hundred years ago.
Compare the vast literature prior to the 1930s on specific functions made unusable by advances in basic analysis methods, including the use of operators.
Although there is more to be known in each area, access to literature is much easier and faster than ever before, where one had to spend huge sums of money several times a year to get rare monographs, often by pre-subscription or by chance purchase.
During his lifetime, only about 60 copies of one of Euler's most important calculus books were sold. Within fifty years all continental mathematics was being taught using his methods.
No, the problem is elsewhere.
1) There is a general lack of respect for a scientist, at least for the past in Western Europe.
As Truesdell once wrote, people who became scientists in the past gained tremendously in social "rank", status, and income when they succeeded. This is no longer the case. Scientists were very rare and interesting people with whom the nobility liked to meet. Do you remember how the King of England invited and met George, Lichtenberg, Gauss's teacher.
Today, several orders of magnitude more people are scientists, engineers, and most of them, as statistically necessary, are not, per se, extraordinary individuals. Hence, everyone is less valuable to the public unless the public can understand what exactly one can do that another cannot.
2) There are far more opportunities to do other things today than in the past, so LESS people devote MUCH of their time to studying and writing, even though our population is much larger. In the past it was partly done to be self-sufficient, today it is partly work compared to other things to do.
Consider the following: the missed opportunities, the cost of spending as much time as EULER. Science, for example, is much bigger today.
(This also applies to the cost of children, by the way, as it means less time is spent working or using all modern recreational goods, which is why people have three children, not thirteen.)
To make their lives interesting, the polymaths of the past would sit around reading and reading and writing, writing, studying, studying and corresponding, and sometimes they rarely met. There was no television, no internet, no fast travel, no many shops or even many restaurants, and social gatherings took place in private homes or on the farm. There were few products. Few books were easy to come by. Few industries were willing to pay them to work on challenging, well-paid problems. They filled their entire day of study. Of course, they knew everything that was known and could also contribute. They have dedicated their entire lives to knowledge for their own sake. Very few people nowadays are willing to do this, even within a profession. It's too expensive unless you really enjoy reading and writing.
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