Majority of mathematicians hail from 24 scientific ‘families’ | Hacker News Reader

Majority of mathematicians hail from 24 scientific ‘families’

nature.com

171 pointsphilip120983 comments

It's also about familial/class privilege. Once you get in with a good mentor (for academics that means advisor)...it sets you up for life. Getting into a good lab (train under uber mentor X or Y), no matter if your work is crap or not (definitely not implying elite lab work is poo, simply emphasizing to make a point) will gain you citations and socialization that a lesser one would not. Want to find good work from university of Smallville USA (or equiv int'l uni)...it exists, you just wouldn't know it from the hype. It's nobodies fault really (except our own), just the way the system is setup. To break out takes extreme amounts of work, and likely can't happen. So you end up with entrenched "genealogies" like the one for mathematics. I'd suspect you could find the same in computer science (despite it being a rather young field) and computer engineering. Things like double blind conference submissions help, but even there there is trendiness to consider as a limiting factor. Going further, breaking out of this rut requires us to disseminate how to get ahead more than anything else. Who should people talk to? Where should they apply? What programs are available? What are the best conferences/journals to submit to? These are all things people in these elite circles have (even if they don't have the $$ background) which provide them a leg up over everyone else. How we even the playing field, no idea...it's a monumental task. I for one start by not caring where somebody went to school, what they look like, what their gender is, nor how they pronounce things. Can we all do that? I certainly hope so.

In France this effect is very visible as well. Many of my colleagues at the CEA (a very good research institute where many people from the French elite system work) had parents working in research as well, many of them at the same institutes, and I think if you'd look at the statistics in detail you'd probably see some strong bias for self selection within the system. That doesn't mean that the people in the system aren't very good (they usually are), just that it's very difficult for outsiders to get in. This in turn is probably due to the lack of knowledge about how the admission system works: While the centralized tests are of course fair in the sense that everyone gets the same questions, being well prepared for them takes years of preparation that already starts by selecting the right school for your children.

What makes me a bit sad here is that there is probably much more scientific talent out there that we're not tapping into by not providing good study conditions for everyone, and this is something that we must change.

I dont think it is hard for outsiders to get in. I am exactly one such outsider.

It is true that being in a good lab helps a career, but these are nepotistic organizations. Join one as an undergrad to get experience then apply to one as a grad student or a paid research specialist. Ive seen that 100 more times than family members of colleagues.

You see the same thing in the US at consulting companies. I've met many 'dynasty' families at consulting companies where the parents worked, children currently work, and their grandchildren intern at.

>It's also about familial/class privilege. Once you get in with a good mentor (for academics that means advisor)...it sets you up for life. Getting into a good lab (train under uber mentor X or Y), no matter if your work is crap or not will gain you citations and socialization that a lesser one would not.

Which is similar to the reason why blacks haven't bounced back from slavery that "ended in 1865". The started from less than zero. Not only poor (immigrants also arrived and started poor), but also seen as dangerous/inferior etc and having to face Jim Crow laws etc, segregation (up until the 70s), redlining, poorly funded school districts, etc.

That held them down far longer than most other races, e.g. asians, jews, irish etc had to face (with the posisble exception of latinos), and never allowed them to build enough "familial/class privilege" to sustain mass movement to middle class/upper middle class.

This is an interesting comment, but it's completely irrelevant in the context of the article. They are defining 'family' as PhD student-advisor relationship, not a biological one.

Yes, and that's what jcbeard meant too.

My mistake, I meant to reply to a comment further down.

This is actually not true in pure mathematics. Students usually do not publish with their advisors, there are no labs churning out publications, advisors do not apply their names to all the products of their groups, etc. In fact, the vast majority of math PhDs from almost all institutions end up leaving academia.

The small number of families seems more likely attributable to the small size of the enterprise and the difficulty of the subject matter. It's very hard to have a good idea and equally hard to publish it. I don't know of anyone in pure math who decides about the value of a piece of work based upon pedigree.

Using the Mathematics Genealogy Project[1], I was able to produce a "family tree" of my own:

http://i.imgur.com/HvCI97I.png

Graphs produced from many of my peers end up looking very similar, true to the subject of the article.

It seems that Gauss in particular trained a great many students.

[1] https://genealogy.math.ndsu.nodak.edu/

I did one too of people I'm interested in

http://i.imgur.com/JuHbnk9.png ( http://imgur.com/a/mhFn3 )

Minsky, Abelson, McCarthy, Sussman, Steele, Dijkstra, Papert, Winograd, Erdos, Cantor, Wirth, Aho, Ritchie, Kleene, Turing etc.

Most are descended from Gauss and Euler, some from both.

What software did you use for the graph? Looks nice.

http://graphviz.org

I have a Python script that generates it. I have it run every few days via cronjob, and puts a diff of the old and new graph dotfile in my dropbox if something new is added to it.

https://github.com/thearn/math-genealogy

(note: not the most idiomatic python code, I scrambled to do it quick before a math conference)

Thx. It seems the "nice design" is just removing the bubbles + making edges bold:

    digraph genealogy {
        graph [charset="utf-8"];
        node [shape=plaintext];
        edge [style=bold];
        ...

I definitely like it better than the default bubbles digraph.

That's super cool. Only a few generations back and you start running into some huge names like Gauss, Bessel, Schwarz.

I wonder if that's unavoidable; I suspect shoulders of giants are kinda hard to avoid.

Maybe we could do some more fun stuff with this, like trying to filter out the people related to Mathematics' superstars and see who remains. Could be an indication of which maths has developed outside of the "mainstream".

Wow- you have Plethon Gemistos in your (academic) ancestry! I am amazed that lineage is tracked since that time. I note the first few branches of the tree have no institution information... probably because they date from before the fall of Constantinople! O.o

I expect theses and advising a thesis must have been a very different affair at the time, than what they are now.

> I expect theses and advising a thesis must have been a very different affair at the time, than what they are now.

For sure, I assume that before the mathematical formalism of the 19th century, these relationships were really more of a less formal mentor/mentee. Though I do feel that my advisor was definitely a great and very personable mentor in addition to the more formal (somewhat administrative role) of a modern PhD advisor.

It is insane you have Plethon Gemistos in your academic tree. :)

Not to take anything away from you, but I am wondering if the information 3-4+ hundred years back is accurate. Seems to cool to be true!

Serious question, how much does your Ph.D. advisor actually matter? I would think that the fact that scientific findings are published for everyone to read would imply that a person gets more of their knowledge from the common pool than the teachers they worked with. So basically I'm asking if these 24 families are actually meaningful in some way, or just an arbitrary grouping.

Only a bit for the 'look who I published with' factor, but a lot when it comes to teaching how to get published, how to do efficient research and work ethic in general. Unfortunately it's almost impossible to know up front how your relationship with your advisor will play out.

The sad truth is that it matters quite a bit for getting your papers into a good journal. It's just human nature (may even be subconscious) that reviewers are a bit kinder on a paper with a Harvard professor as the last author than one with a professor from the University of Southern Mississippi.

Some journals have tried double-blinded peer review, but it's difficult to do well. You have to remove important bits from the paper, like "this builds on our previous study [3]" or "our software has previously been verified and validated, see [6]".

Furthermore, people in the field kind of know who is working on what. No amount of editing will allow you to anonymize that.

A recommendation from an influential professor can help you get ahead in the queue for competitive positions.

Quite meaningful. You can observe large differences of opinion in some fields that carry on from advisor to student. Take "freshwater" vs "saltwater" economics for example.

Even in a field you might think "opinion-free" (like Mathematics) I'm sure there are big differences in approach.

At least with regards to naming, reading nLab I thought the lemmas with ambiguous names for different concepts was rather unfortunate.

Mostly, your initial years as an independent researcher will be spent working on problems that you had worked on during your doctorate degree. So in most cases, the Ph. D advisor tends to have a lot of influence both in the topic and the style of your research.

There are also many people who end up not working at all in actuality with their advisors, they end up working with fellow grad students etc.

In none of the cases are they from a common pool as you suggest. I think there is a lot of "school" philosophy in mathematics. Most productive groups tend to work on the same topics : analysis, algebra, number theory, probability etc. in the case of Soviet Union, for example, but not many on combinatorics.

Most of the other replies focus on the unfortunate (and valid) political aspects: that having an important advisor helps your career via contacts and higher likelihood of being published in top journals. But I don't think this is in the spirit of the question asked, which seems to be about whether someone's advisor has an impact on the sort of work they do (in terms of 'flavor' instead of academic impact).

Definitely the advisor usually has a big role here. Even within a given subfield, the sort of problems one decides to tackle is a very subjective thing, and the sort of problems your advisor works on / presents to you has a big influence on this. Then personal taste gets mixed in, and you get a fairly unique brand which then influences your own students and so forth (in a vaguely "genetic" way). And anecdotally, I've heard so often from professors about how their advisor's take on mathematics has influenced their own, so it does seems to be a factor.

Honestly though it seems a bit dubious that these 24 "families" share anything apart from their common ancestor ~500 years ago. If I'm an descendent of Leibniz and you are a descendent of d'Alembert, I don't think there are any interesting qualities about our research that we could guess from just that information. To use the analogy implicit in the article, the "genes" have all become uniformly distributed through the population by now.

As an example of "flavor" (picked because it's a field I have a particular interest in; with people I've "followed" peripherally for many years):

Former CTO of Mozilla, Andreas Gal, who wrote TraceMonkey, had professor Michael Franz as advisor. Gal's thesis was on tracing JITs. Michael Franz had Niklaus Wirth as advisor. Franz' thesis was on JITs - he contributed a technique called Semantic Dictionary Encoding, which was added to Oberon to allow architecture independent binaries. (Franz' thesis pre-dates the public release of Java by two years). Niklaus Wirth, obviously having a long history of compilers behind him.

Presumably that's quite unavoidable - most of the dissertations of Wirth's PhD students I've seen are on compiler technology, for obvious reasons: if you wanted to study under Wirth badly enough to in many cases move to a different country in order to do so, presumably odds were good that's where your interests were. Franz even declined a Fulbright Scholarship in order to continue studying under Wirth.

He then went on to continue work on code generation in various forms at UC Irvine - presumably most people, like Gal, seeking him out for a PhD would be people interested in the same areas.

Of course you will then be influenced - after all you hopefully don't seek out an adviser to ignore their advice...

For me, there's a vague similarity of research interest going back at least five generations.

This is an excellent question. I think it can actually matter a lot, at least in some cases. (Disclosure: I am on the faculty of a research university, and of course I don't want to think I'm wasting my time or my students' time. :-) There are a couple reasons. One, as mentioned by other posters, is that the advisor can have a lot of influence on choosing good problems to work on; in my field (applied mathematics), it can be tempting for a bright student to focus excessively on interesting but narrow technical problems, or on chasing flashy things that have little depth or substance. Second, precisely because of how much material is published these days, beginners need a guide to the field. For whatever it's worth, a good advisor's job (I think) is to put new findings in context, which is increasingly hard to do on one's own. In short, one significant way in which the advisor can have tremendous influence has more to do with decision-making, and not so much fact-finding (although sometimes that is important too).

The graph reveals what happened to the academic class during the darkest part of Germanys history: It looks like most of the mathematicians fled to the US! Also, I thought Russia produced many more matematicans than shown but maybe I'm just making false assumptions

Under Peter, Russia imported a lot of great minds, who then fled when things started to get horrible. They've produced some greats, but shockingly few when you consider how large the country their working with is.

Russia is actually not that large population-wise.

More than 140 million is pretty huge, and that's modern Russia, not what it used to be with all of its empire, and later satellite states.

Less than half the population of the US, tho', and only double the UK, you have to compare like with like.

In what way does that relate to the original point? Russia doesn't have the record of producing mathematicians at a rate of a much smaller country like Germany.

You asserted that Russia should produce more mathematicians because it is large. But large mainly empty land area will not have that effect.

You're going backwards. We already did the "per capita" thing, now you're pretending that you didn't understand what "large" meant in the first place?

I see that you have some kind of problem with what's been said about the production of great mathematical minds in Russia, so why don't you offer something contrary to the assertions made so far? Rhetorical gaming is really not an effective tool to make your point.

You said:

shockingly few when you consider how large the country their working with is

I replied that the country isn't actually that large in terms of people, so your point is invalid. Now you seem to be saying that empty land should produce more mathematicians.

Also, it's "they're".

Observe that Gauss was part of the Polcastro family tree. It takes a lot of clicking to verify as much

https://genealogy.math.ndsu.nodak.edu/id.php?id=18230 Pfaff

https://genealogy.math.ndsu.nodak.edu/id.php?id=18231 Gauss

First thing this reminded me of was master-student lineages in Buddhists, and martial arts.

There is a long lineage of gurus and students (as far as I understand it, this is academic lineage, not genetic) in the Hindu Upanishad, Brihadaranyaka: Chapter II, Section VI [1], ending with Brahman as the ultimate teacher.

There may be similar things in other scriptures as well.

[1] http://www.wisdomlib.org/hinduism/book/the-brihadaranyaka-up...

this might be useful further reading for those interested: https://en.wikipedia.org/wiki/Guru%E2%80%93shishya_tradition

Btw, there is also a Neurotree for Neuroscientists. And I bet there are other trees as well. :)

http://neurotree.org/

This is pretty common.

Us geneticists have used Flytree (later academictree.org) to figure out our lineages.

http://academictree.org/

By this analysis I wonder whether Ramanujan would be in Hardy's family? In terms of strength it should be the other way around.

This seems like a sort of non-story; what it takes for there to be a new family tree is someone entering the field without an advisor in this dataset (i.e. probably an advisor from a different field) and then taking on PhD students, etc. And that seems unlikely at different points in time for a variety of different reasons.

Is there anything similar for computer science?

The trees don't go back very far. We have at most 2 or 3 generations at this point.

That seems wrong. A fresh PhD doesn't have to wait a full generation for a graduate to father.

Too funny. Why do you think Computer Science is a unique subject of its own? Its deeply connected to mathematics and the only people doing CS back in the day were mathematicians. Go read some of Dijkstra's letters from the 50s. They are publicly available online. If you want to be a code monkey, have fun. But know that you are second rate to those that know the identities of computation. Mathematics is everything.

[1] Edsger Wybe Dijkstra was a Dutch computer scientist. A theoretical physicist by training, he worked as a programmer at the Mathematisch Centrum from 1952 to 1962. Wikipedia

You've certainly reproduced Dijkstra's opinion on the matter faithfully. Given that his life's work was pretty much to jet between conferences and bad-mouth those of his colleagues who actually DID produce useful software, it stands to reason that he would elevate mathematics over engineering.

Dijkstra contributed so much to actual computer science. You are way off base. Leslie Lamport was also a magnimonious computer scientist. Guess what his PHD was in? Mathematics with a dissertation in singularities of analytic partial differential equations. CS is absolute monkey business without a real mathematics education. Face it.

https://en.m.wikipedia.org/wiki/Leslie_Lamport

It's not that mathematics does not have its uses as a tool. However, there is a big difference between pragmatists like Lamport and Knuth, who used their mathematical knowledge in the service of engineering projects, like building their own text processing system, and dogmatists like Dijkstra, who relied on underlings to type up his handwritten papers so he would not have to sully his hands by touching an actual computer.

Granted, Dijkstra did make some contributions to CS, but he also caused immense damage to CS education by promoting his vision of CS as exclusively a branch of applied mathematics, instead of an engineering discipline employing mathematics as one of several tools. That mentality has led to much preaching about constructing programs using top-to-bottom formal methods, and very few useful programs constructed that way.

Are you talking about the Dijkstra who wrote one of the earliest operating systems that introduced most of the OS concepts we use today, including mutual exclusion algorithms, deadlock detection and prevention, kernel/user mode etc or are you talking about someone else?

While the THE multiprogramming system may have had these, Multics had them roughly at the same time, and I'm pretty sure today's operating systems trace their use of these concepts back to Multics, rather than THE.

Amazing he did all these when jetting between conferences.

Can I quote you as a reference when arguing on the Internet that our OS concepts do not owe anything to Djikstra, who was only jetting between conferences? It sounds like you are pretty sure.

That's more or less why I asked the question. A lot of people in the programming field promote the notion that you can teach yourself coding and get by just fine.

This trend kind of worries me.

You can but only because most business logic and employed programming work requires shit for brains and grunt work.

Ha, I just wrote a comment along these same lines. Given that many of the slide decks I had as a grad student had extensive genealogies at the start indicating where they evolved from I suspect that this is very much the case....despite it being a very young field.

My PhD was in a CS (AI) topic and it's listed there as "Mathematics Subject Classification: 68—Computer science".

Maybe that's because I am 5th or so generation descendant of Hilbert but then again why wouldn't other CS PhDs also have a Mathematics grandfather++ when they go back long enough?

This scarcely known researcher Sigusmondo Polcastro at the top of the list seemed a bit strange. 105,277 descendents, why so many? I looked him up and clicked through his geneaology. Turns out if follow through a few generations, you find Carl Friedrich Gauss, with 74930, or about 75% of Mr. Polcastro's family, and the first name I recognized along that tree. After Gauss you find a tree of mathemeticians like Bessel, Klein, Hilbert. It seems a bit strange not to mention him.

Interesting that Switzerland had way more math PhDs than France and Austria in the early 20th. Which part of Austria Hungary was counted? Was this an effect of the wars?

Euler?

Does a famous mathematician really lead to lots of math PhDs in his home country, hundreds of years later?

in a tree structure, isn't 24 just an arbitrary number based on which level of the tree you make your claim? if all of mathematics, for example, can be traced ultimately to the first mathematician ever, then the argument can be made that 100% of mathematicians hail from one 'family', or indeed one person.

That's a mighty peer review ring :P

Note that title may suggest this is a genetic thing, but this is about the genealogy of students and teachers, not genetics.

To further clarify: The teacher is considered the "parent" of the student in their analysis.

The result is therefore quite boring. It's like saying famous actors have worked with other famous actors, and lots of actors can thereby trace their themselves through a chain of actors back to Charlie Chaplin. (Too bad it wasn't about genetics -- now that would have been interesting.)

A teacher/mentor is not the same as "worked with".

When Kevin Bacon appears in a film with X, who is the master, and who is the student?

Obviously, Kevin Bacon is the root node of the graph, or rather the producer with the necessary vitamin C.

I also felt reminded of the Five Degrees of Kevin Bacon.

The relationship between PhD student and advisor is often much more like apprentice and master than the relationship between two actors/actresses working together.

Indeed, perhaps a more apt analogy from acting would be the many famous actors who trained under Lee Strasberg (Al Pacino, Robert De Niro, Dustin Hoffman, Anne Bancroft, James Dean, Jane Fonda, Paul Newman, Ellen Burstyn and others).

Strasberg in turn was a student of the ideas of Konstantin Stanislavski[1].

And so it goes.

[1] https://en.wikipedia.org/wiki/Method_acting

In particular, one rarely has more than one advisor, perhaps two in some circumstances.

Having worked with is a 1:n relationship

Having an advisor is 1:1 (with a few exceptions like 2 PhDs or 2 advisors for one PhD)

Actually the title suggests nothing if you understand the role of the ''s.

Waiting for this to explode in some mainstream medium...

How do they define "family"? I tried to find that in the article, but didn't see it (and didn't read every word in order to discover it).

Colloquially, you might say two families are distinct if there are no marriages or blood ties between them. But if you go back far enough, are there any distinct families by that definition, especially within one country or region?

EDIT: Nevermind. I can see how, by limiting relationships to one advisor relationship for each person, there would be more distinct families (or in another language, disconnected graphs).

Advisor-Advisee relationships now. I'm a math PhD student, and I can trace my "mathematical family" back to each of Newton, Leibniz, and the physician mentioned in the article Sigismondo Polcastro. What I learn from looking at my family tree is that it's quite interconnected. The additional relationships come from students who claim more than one advisor (like almost all of Hardy and Littlewood's students, for instance) or students who got multiple PhDs and therefore have multiple advisors.

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