Since this research doesn't mention some hard to quantify ties, it missed on the painting the picture of the most interesting actual family in mathematics: the Bernoullis. Brothers Jacob and Johann sprung up seemingly out of nowhere to continue Leibnitz's work in Basel as some of Europe's greatest mathematicians of their time.
The most remarkable part is how Johann tutored the son of a local pastor, a friend of the family. After noticing his talent, he convinced the father to let the young boy focus on mathematics instead of joining the clergy. That young boy was Euler, and when we add Johann's son Daniel into consideration (who turned out to be a mathematician of similar caliber to his father) I'd venture to say that there is an actual family at the core of modern mathematics that would by itself be an object of study.
Off the top of my head, Euler, Gauss, Newton, Leibniz, Euclid pretty much cover an undergraduate curriculum and all the math most people would know, and those are just five people. Expanding to the fullness of the discipline and 24 families does not seem surprising at all. It's probably more about how much of a long tail of subjects the field has.
(As I said, this is off the top of my head and some obviously build on predecessors work. Descartes and to a lesser extent Fermat are also relevant here, no doubt others that made contributions the people I listed built on - Cardano?)
> Off the top of my head, Euler, Gauss, Newton, Leibniz, Euclid pretty much cover an undergraduate curriculum and all the math most people would know, and those are just five people.
Who just happened to be around at the right time to a certain extent. The fact that these particular people are the famous ones may be an accident of history and someone else would have come along and and produce the same results.
Newton and Leibniz (and de Fermat, etc) famously both invented/discovered calculus at the same time:
At least when it comes to mathematics, and perhaps 'mechanical' discoveries/inventions; lots of folks fiddling around with boiling water over the course of history, for example:
Other aspects of human thought may be different: I think Aristotle (and later Thomas Aquinas) were unique and we'd be in a very different place, world-view-wise, if they hadn't been around.
I suspect that this is true for any field. Not just mathematics. Think computer science. Think physics. The reality is that only a tiny percentage of people move a field/humankind forward. For every Einstein there are millions of people with zero long term impact.
> The reality is that only a tiny percentage of people move a field/humankind forward.
We just happen to remember the ones that got more press, or perhaps published first. As one example, multiple folks came up with calculus at just about the same time:
I don’t think that’s true at all. Sure, some folks have outsized impact, but that doesn’t mean that,e.g., only Turing Award winners are have contributed to computer science. In fact, an outsized percentage of work put into projects led by these research “celebrities” is done by oft-forgotten grad students.
Also, the article literally shows the opposite: these lineages contain many illustrious mathematicians, and it does them a disservice to classify them all as, e.g., “gauss’s line”
Yeah, this doesn't surprise me at all, and I think you'd be likely to see similar relationships in any "niche" pursuits that take tons of expertise, e.g. classical musicians, ballet dancers, archeologists, successful startup companies, etc. etc.
[+] [-] mihaic|3 years ago|reply
The most remarkable part is how Johann tutored the son of a local pastor, a friend of the family. After noticing his talent, he convinced the father to let the young boy focus on mathematics instead of joining the clergy. That young boy was Euler, and when we add Johann's son Daniel into consideration (who turned out to be a mathematician of similar caliber to his father) I'd venture to say that there is an actual family at the core of modern mathematics that would by itself be an object of study.
[+] [-] huachimingo|3 years ago|reply
[+] [-] version_five|3 years ago|reply
(As I said, this is off the top of my head and some obviously build on predecessors work. Descartes and to a lesser extent Fermat are also relevant here, no doubt others that made contributions the people I listed built on - Cardano?)
[+] [-] sudosysgen|3 years ago|reply
There are a lot of small but inaccessible results that are necessary and left out if you only consider sheer amount.
[+] [-] throw0101a|3 years ago|reply
Who just happened to be around at the right time to a certain extent. The fact that these particular people are the famous ones may be an accident of history and someone else would have come along and and produce the same results.
Newton and Leibniz (and de Fermat, etc) famously both invented/discovered calculus at the same time:
* https://en.wikipedia.org/wiki/List_of_multiple_discoveries#1...
* https://en.wikipedia.org/wiki/Multiple_discovery
At least when it comes to mathematics, and perhaps 'mechanical' discoveries/inventions; lots of folks fiddling around with boiling water over the course of history, for example:
* https://en.wikipedia.org/wiki/History_of_the_steam_engine
Other aspects of human thought may be different: I think Aristotle (and later Thomas Aquinas) were unique and we'd be in a very different place, world-view-wise, if they hadn't been around.
[+] [-] ncmncm|3 years ago|reply
[+] [-] mbrodersen|3 years ago|reply
[+] [-] throw0101a|3 years ago|reply
We just happen to remember the ones that got more press, or perhaps published first. As one example, multiple folks came up with calculus at just about the same time:
* https://en.wikipedia.org/wiki/List_of_multiple_discoveries#1...
Everyone knows Newton, some folks know about Leibniz, but how many now about de Fermat, etc?
Bell is know for the telephone, but what about Elisha Gray?
* https://en.wikipedia.org/wiki/Elisha_Gray_and_Alexander_Bell...
Also Edison and the light bulb versus Swan (and others):
* https://en.wikipedia.org/wiki/Incandescent_light_bulb
[+] [-] Ar-Curunir|3 years ago|reply
Also, the article literally shows the opposite: these lineages contain many illustrious mathematicians, and it does them a disservice to classify them all as, e.g., “gauss’s line”
[+] [-] PragmaticPulp|3 years ago|reply
[+] [-] hn_throwaway_99|3 years ago|reply
[+] [-] bombcar|3 years ago|reply
[+] [-] rob_c|3 years ago|reply
If this wasn't nature.com I would give it a free pass and shrug that "huh, everyone else is doing it", but really....
'C'MON!!!
[+] [-] adventured|3 years ago|reply
[+] [-] ncmncm|3 years ago|reply
You need something about the Fields Medal.
[+] [-] sva_|3 years ago|reply
United Kingdom — 138
Germany — 111
France — 71
Sweden — 32 (tie)
Russia — 32 (tie)
Japan — 29
Canada — 28
Switzerland — 27
Austria — 22 (tie)
Netherlands — 22 (tie)
https://worldpopulationreview.com/country-rankings/nobel-pri...
Doesn't seem so