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?)
And while the list already includes Newton and Leibniz, nobody is proving calculus without Cauchy. There's no calculus without limits -- well, not unless you consider infinitesimal calculus, but that wasn't formalized until the mid-20th century.
> 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:
A lot of calculus is intuitively obvious IMO. People make way too big a deal over who "invented" it. Half the people here probably figured integrals out on their own writing video games in their teens.
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.
Exactly - the smallest ones often go through teacher/pupil, and since almost all PhD mathematicians studied under a PhD it makes for a relatively small group.
I'm pretty critical of click-bait headlines in what are supposed to be more academic journals, but I don't get the frustration with this one. 'Families' is written in quotations, which tells me right from the jump that the author is probably not speaking about literal family units, and the use of "family" or "family tree" nomenclature in discussing matters of genesis and inheritance is pretty commonplace.
Unfortunately if you do enough outreach it's not long until you encounter some nitwit who claims all "religion of science" is controlled by them (be they lizards, moonmen or voldermort). And articles structured like this don't help trying to people like that.
and leading with "Evolution of mathematics traced using unusually comprehensive genealogy database" ?
anyway, the more interesting aspect seems to be the drop-off after the top five, they don't even bother naming the others- see the first graph on the page
I think they name them all in Figure 10 in the actual paper [1]. But it doesn't seem to contain a rank ordering of the mathematicians that is easy to recover.
Also, it appears there is data duplication with the first four names appearing twice in the list (first four and last four).
Abel prize, and Turing Award. And to an extent the Sveriges Riksbank Prize in Economic Sciences in Memory of Alfred Nobel. All same payout, which really matters to give it dignity.
> Nobel Prizes (including the SRPESMAN) have been awarded 609 times to a total of 943 people and 25 organizations
Using the number of 943 people, a majority of Nobel Laureates (meaning more than 50%) would be more than 472 people. US + UK is 538 people which puts them above that threshold of being a majority.
I guess if you put it that way, the statement might be correct. But the disparity between US and UK being so big, I feel like the argument is a bit weaker. Using the average on such a small set doesn't seem to be so useful if there is such an outlier.
I guess you could also look at laureates by country born, considering many people went to the US in WW2. But I imagine it'd just devolve into senseless nationalism.
Comparing the US against any other Western country (and most others) using absolute numbers is usually an exercise in https://xkcd.com/1138/. It's physically bigger (except maybe similar to Canada and Australia, both of which have big uninhabited areas) and has more people.
Based on this page, 110 out of 400 were born elsewhere (I searched for number of "born" entries) I can see some cases where they immigrated to the US at a young age so all their education was in the US. So another way to look at it would be where they got their college degree.
There are a couple other non-American or dual citizenship people there, for example there are some marked with "Japanese citizenship" like Osamu Shimomura https://en.wikipedia.org/wiki/Osamu_Shimomura
Certainly this is the only reason Germany is behind the UK. They were somehow the centre of the scientific world despite their less-than-ideal political conditions and then they ran their own talent out of their country. (And then they lost the war and the superpowers came and took the remaining talent, which was still formidable)
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.