Majority of mathematicians hail from just 24 scientific ‘families’ (2016) | Hacker News Reader

Majority of mathematicians hail from just 24 scientific ‘families’ (2016)

nature.com

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.

I've always wondered why today we dont have people like them. Is science stagnating (aka Law of diminishing returns)?

The fruits are hanging higher up nowadays.

Each field has folks like these, you just don’t hear of them because fields are super specialized.

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?)

You would also need Cantor and Riemann, as well as Pythagoras, Bernoulli, Al-Kashi and Al-Khawarizmi, Yang Hui maybe also Lebesgue, Cayley, etc...

There are a lot of small but inaccessible results that are necessary and left out if you only consider sheer amount.

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.

> nobody is proving calculus without Cauchy

Unless you are Heine?

Cauchy was also a pioneer in complex analysis, which is taught in undergrad.

Riemann and Cantor are both in Gauss’s family.

I learned the expression "grandstudent" when I met a number theorist who had studied under a student of Andrew Weil.

> 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:

* 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.

Hey don't forget that Archimedes also invented calculus.

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.

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”

> 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:

* 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

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.

To be clear, this refers to teacher-pupil relationships, not actual familial heritage.

But we need an alex jones style headline to get in on the click bait...

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!!!

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).

[1] https://epjdatascience.springeropen.com/articles/10.1140/epj...

I was hoping not to have to dig through source material but i agree i do wonder how many Ramanujan style (isolated) mathematicians are in the field.

So basically it’s an Erdös number post.

Isn't that about co-authoring rather than teacher-pupil relationships?

Yes but the two are very related, a phd student will almost always publish papers with their advisor.

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.

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.

The majority of nobel laureates hail from just two countries.

United States — 400
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

From your link:

> 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.

There are some interesting lists here: https://en.wikipedia.org/wiki/List_of_countries_by_Nobel_lau...

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.

I do agree with sibling post on the majority of prizes awarded to citizens of two countries.

I was wondering how many of them (Einstein being an obvious example) were US citizens when the got the prize but were born elsewhere?

"Give me your poor, your tired, your huddled scientific geniuses"

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)

> ran their own talent out of their country

Or outright murdered them

Einstein go his Nobel prize in 1921 while moved to the US in 1933.

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.

https://en.wikipedia.org/wiki/List_of_Nobel_laureates_by_cou...

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

There is no Nobel for mathematics.

You need something about the Fields Medal.

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.

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