Math people moving around

In the June 2014 issue of the Newsletter of the European Mathematical Society,there is
an article (by Martin Andler, from Versailles) on the invited speakers at this year’s ICM, and, in particular, on geographical shifts in their career.

Besides offering some tables, the article briefly enumerates a few perspectives on the movement of mathematicians between countries, without really endeavouring to resolve the tensions between them. My aim here will be to give a summary of the situation and what I see as a second step in the analysis of these issues, in part with the hope that readers of this blog will discuss them further.


In case you have not looked at the tables yet: the three countries in which the most speakers were born are France (30 speakers), the Soviet Union (27) and the United States (26); the next countries in the list, far behind, are Germany and the UK (12 each). This should be completely unsurprising to anybody within the mathematical community. Then we have Italy and China, each at 9, and Hungary at 8. (South America – indeed all of Latin America – has a grand total of 7, including 3 from Argentina and 2 from Brazil.)

The birth-to-PhD and PhD-to-work charts show that the US acts as a very strong attractor for prospective doctoral students (58.5 speakers born elsewhere got their doctoral degrees in the US, and no speakers born in the US got their PhDs elsewhere; here, fractional numbers indicate shared positions/studentships and the like), but not as a workplace (28.5 speakers left after getting their PhD in the States, and 21.5 moved to the States after getting their PhD elsewhere). France works almost as a closed system at the educational level (only 3 speakers born in France got their PhDs elsewhere, and 3.5 did the inverse move) and as a very mild attractor as far as jobs are concerned (8.5 foreign PhDs moved to France, including 4 from the US, and 4 French PhDs moved out of France). As for the Soviet Union – 23.5 out of 27 speakers born there live outside the successor states (13 of them in the US), 10 moved out already to get their PhDs (6 of them in the US), and nobody not born in the Soviet Union currently works in the successor states. Only 3 of the 16 speakers born in Eastern-Europe-minus-USSR got their PhD there, and only one of them works in Eastern Europe now (a Hungarian in Hungary). Again, the overall picture agrees roughly with what conventional wisdom would have expected.

As for Latin America – 7 speakers were born there, and 3.5 left for the US to their PhDs, with the others staying in their home countries (Brazil and Argentina); 2 work in the US, four work in their home countries (again, Brazil and Argentina) and one works in France (myself). Two speakers born outside South America now live there; both are former Soviet citizens working in Brazil. Of course, the numbers are so low that one should take care not to see patterns that are not really there. (The same goes for Africa – there are two speakers from there, one working in Africa and one in the States.)


The article states that there are four different ways to view geographical shifts. In its words, these are (a) individual freedom, (b) the progress of science, (c) competition (as a way to advance science), (d) brain drain.

These are not really fully parallel to each other. For instance, “individual freedom” is not really a way to evaluate what goes on, or even a way to decide policy goals; rather, it would seem to be a principle that limits what policy tools we are willing to consider. At the same time, Andler states under this heading that “there are other compelling reasons to want to leave one’s country, e.g., miserable economic conditions or completely inadequate working conditions”. This belongs under its own (central) heading – namely, the conditions that make an individual able to work as a mathematician.

The second perspective (“the progress of science”) is said to be the one that what matters is the advancement of mathematics – and that it is our collective duty to ensure that mathematicians can develop themselves and work, and our individual duty to devote our lives to advance mathematics. This I would say to be uncontroversial, as far at least as mathematicians are concerned; not only is it something many could subscribe as a guiding philosophy – it is also an entirely reasonable way to frame the entire discussion. Other parties may have other goals in mind (national prestige, say, or, in the case of funding agencies, some more or less arbitrarily set formal goal), but most of the motives we would actually consider, including completely altruistic ones, fit nicely within this framework.

(Note that the article quotes Weil on dharma here. This is an example of something unfortunate: the clearest statement of a position is made by one of its more extreme proponents, and that, of course, has the effect of making the position seem a little less tenable.)

The third perspective – namely, “competition” – states that only by competing for the best faculty and students will universities have an incentive to keep or increase their level and give to faculty and students the working conditions they need to do mathematics. All of this is true, though one thing is not addressed – namely, that it is doubtful that, at the top of the pay scale in a few countries (US, say), further increases in salaries are really improving the ability of mathematicians to do mathematics, as opposed to simply serving as a tool for universities to compete (and a factor by which a few universities have a large, in-built advantage). It is also the case that salaries and especially working conditions can be set more by tradition than by anything else: for example, in the French system, salaries are essentially uniform regardless of location (thereby making faculty at some top institutions less well paid, in real terms, than in the provinces) – whereas, in the US system, which arguably has the largest financial basis of any, positions with truly light teaching loads are very rare, and positions with no teaching loads are essentially non-existent (in comparison, France’s CNRS opens up every year several positions with no teaching for life). Of course, part of the issue here is how to convince the body hosting the researcher that having the best students, or the best researchers, is really the priority; this is evident for us, but the financial source may have other goals in mind.

Lastly, we come to the “brain drain” heading. This is stated in the following terms: countries from where people emigrate lose the investment they made in their education, and they also lose the potential for further development; wealthier countries benefit – and also neglect making necessary investments in their own primary and secondary education; “it is much cheaper to import partially or fully trained young people”.

We have to look at this issue in the light of the data above.

(a) There is one very clear case of massive migration of people with PhDs from one place, namely, the former Soviet Union; this has to do with the implosion of an entire country. (We also see that many speakers left the rest of Eastern Europe already before the PhD stage.) Other than that, what we see is that large numbers of future speakers from outside the US did their PhDs there, but that the net flow to the US after the PhD stage was actually negative.

(b) As far as Latin America (say) is concerned, the issue is not a large net outflow (there turns out to be barely any) as low overall numbers. The same is true of other developing areas. It is striking that there are no speakers from India, given its mathematical tradition. (As for East Asia, it is difficult to reach meaningful conclusions, given that the Congress is in that geographical area this time around.)

Let us make our focus a little more precise. The article mentions some arguments for and against migration; as it states, they sometimes do not apply well to mathematics, whether they are under the ‘for’ heading (it is hard to see how (to use a paraphrase) “migrants sending money back home” is relevant here – though there is an analogue, namely, those cases where somebody from X manages to obtain substantial political power in the academic community in country Y, and uses it to procure funds to develop mathematics in X) or the ‘against’ heading (is having top mathematicians work full-time in a country really something that will improve significantly the teaching of students who do not intend to become research mathematicians? – the article seems to assert this).

As for costs saved by the USA (say) on education – figures per capita can be misleading here. Figures such as “$142,000 total average expenditure per student in primary/secondary education” are obtained much like similar figures on how much a prisoner costs: the total cost of a system – much of it consisting of fixed costs – is divided by the number of students or prisoners, as the case may be. What would be relevant here is not so much the marginal cost of educating an additional student, but the cost of having a better primary and secondary education system (or the cost of programs to supplement basic education). As far as the investment that the country from which the emigrate can be said to lose – obviously, what the state invests per student is often much less in developing countries, and not all students are supported by a public education system; rather, we could speak of what a country loses (to proceed with the same sort of logic) by not investing on a working postgraduate education system.

Still, these figures can be conducive to the right picture – namely, the academic system in the United States rests to a large extent on people who got their basic and undergraduate education elsewhere. The tables in the article should be enough make that clear. An awareness of this reality could, and should, contribute to create a common sense of responsibility. (On the French side, say, it should also contribute to create a sense of possibilities.)


Let us then restate the main issue within a clearly defined framework. There are young people with a great deal of talent and interest in mathematics in every part of the world. How do we ensure that they can develop their talent fully, and put it in practice to the best of their ability?

“We” here means anybody in the world who has an interest in the development of mathematics, or who considers wasted talent a pity and a waste. The way that we are phrasing the question sets certain perspectives deliberately outside its focus – namely, those based on national prestige, or “return on investment”. At the same time, lest the focus be thought of as narrow, let us emphasize that the question should not be thought of as concerning only an individual in the short run.

Consider, within this perspective, a system whereby talent is nurtured effectively in all countries, developed further in a few, and then put to work wherever it might be the case. Such a system would be a fair solution if the chances given to all students, regardless of origin, were equal or nearly equal; it would be a feasible solution if, and only if, it were sustainable. It may not be the best solution, let alone the only conceivable solution. However, it would be, for us, within the set of admissible solutions, provided that these two crucial “if”s are satisfied.


A few brief notes to supplement the above. We are talking about research mathematicians here, and not, say, about physicians and secondary school teachers, whose retention is a different issue altogether. (This is not, of course, to say that the issues raised by Andler on “adequate working conditions” and “miserable economic conditions” would not apply there.) We may even specify “leading research mathematicians”; this is, after all, what the database on ICM speakers is about.

Second – while the focus above may not be exactly the same as that of, say, government agencies that fund or could fund mathematics, this does not mean that the goals are all that different. Even from the viewpoint of “national prestige”, almost all would now agree that it is better for a country to produce very good football players (say) that work abroad, rather than not to produce them at all. It is also the case (for mathematicians or football players) that a country’s education system may be credited to the extent that it actually contributed to a professional’s formation; people do notice this – and thus it may make little sense, from the viewpoint of prestige, to see an exit from a country’s system at the bachelor’s or doctoral level as a greater loss than an exit that happens earlier.

Lastly, since the discussion may centre on mathematics in developing countries, let us give some examples from middle-income and high-income countries to clarify the framework of the discussion. An exodus of the proportions of the one that happened around the collapse of the Soviet Union is clearly something that gives rise to a non-sustainable situation. (Many would call it an effect of a non-sustainable situation as well, particularly given academic salaries in Russia in the early 90s.) The level of the country’s system for producing young mathematicians must clearly suffer as a result of such a shock ( – and as a result of the same drastic shortfalls that gave rise to it, some would add).

A somewhat different example is that given by the case of Germany. Here, again, the tables confirm what we already thought we knew: in net terms, Germany loses people after they get their doctorates. This is so in spite of senior academic salaries that compare favorably with those in large parts of Europe. The conventional guess – which is probably correct – is that this is due to a structural problem: Germany has nothing like tenure-track or associate professorships, or postes de maître de conférences; there are temporary “collaborators” and then there are full professorships. This is a problem that will not concern us here, at least as in so far as PhDs from Germany seem to be able to find jobs elsewhere. At the same time, it is a kind of problem that would legitimately concern some people in Germany, in that the system would be able to retain more people, and attract some, if it were structured differently. The same goes for any other country in a similar situation.


At this point – with a definition of the problem and its scope – we are at the beginning of a meaningful discussion. I thought briefly about the possibility of sketching the situation in a South American country (say). I may still do so soon. However, if you have read so far (congratulations!), you probably agree that this is a good point at which to declare the discussion open, and to hear what people have to say about (a) the situation in their own home countries, or in countries they are acquainted with; (b) how we could become better at recognizing and developing mathematical talent, at a global level; (c) the same, on placing mathematicians; or rather, how, given current trends in geographical shifts after or before the PhD level, we can still find viable ways to go much further on (b), even when this is far from completely apparent, and even when this goes against an overly simplistic take on “brain drain”.

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About valuevar

I am a number theorist with side interests in combinatorics and group theory.
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5 Responses to Math people moving around

  1. This is an important discussion. First, a couple of minor comments regarding Brazil and the ICM data. One of the Brazilian speakers this year will be taking up a position at Princeton in the Fall. All speakers from Brazil at this and all previous ICMs work(ed) at IMPA. The Brazilian University system is similar to the French insofar as being fairly egalitarian, with salaries and perks in a narrow band. While there are a number of very good mathematicians in Brazilian Universities, they cannot attract the kind of people who get invited to speak at the ICM.

    Brazil has had over the years a very generous policy of overseas (and domestic) graduate fellowships. Unfortunately, I don’t think as a whole the research conditions for the returning students was very good and a different allocation of resources and more support for researchers after their PhD would have been better.

  2. valuevar says:

    Thanks, Felipe, for contributing to the discussion.

    On your first point – as I said, two of the ICM speakers are non-Brazilian-born mathematicians working in Brazil; namely, they were born in the Soviet Union. Latin America could probably have attracted more mathematicians from that area at the critical time, given Brazilian salaries (which are still a dream in most countries in the continent) and Brazilian research conditions (ditto), if only some active effort had been put in that direction.

    On your second point – I hope all readers in this blog will become aware of the fact that, if graduate work in South America has been possible (in some areas) within the last generation, it is largely thanks to the possibility of studying in top Brazilian institutions (often with Brazilian scholarships). For that matter, the summer school at IMPA has been very helpful (pity about the weather!). Some of the best students stayed in Brazil and had succesful careers there. In the longer run, we will need more than one research pole in South America, with more than one thematic focus.

    (As I also said, the ICM list of speakers shows that there is still an Argentinian school. However, it has been undermined for a variety of obvious non-mathematical reasons (varying over time) since before I was born. Chile has been developing as of late; it may still too early for this to show at the ICM level. It would be good to discuss what is going on elsewhere.)

    • Comparing Brazil on one hand with the US and Europe and on the other with the rest of Latin America will give two very different pictures, neither of which is fair. Brazil is both a source and sink for brain drain. I have a lot of opinions on this topic which I find difficult to express fully in a comment on a blog post. Brazil is just one aspect of this big discussion. It’s great that you have pointed out this article and expanded on it.

  3. Jeffrey says:

    I would be very interested to read your sketch on the situation in Latin America, especially Peru.

    With regard to (b), one promising sign is that in the last decade or so, some of Peru’s schools (namely Colegio Saco Oliveros, Colegio Prolog, and Colegio Bertolt Brecht) have gotten serious about recruiting and training its talent for the International Math Olympiad, and it shows in their drastically improved results. Peru now frequently performs at or above the level Brazil’s IMO team, which is all the more impressive when one considers Peru’s much smaller population, younger students, and limited resources:

    http://www.imo-official.org/country_team_r.aspx?code=PER

    http://www.imo-official.org/country_team_r.aspx?code=BRA

    Yes, I’m aware of the caveats made about the IMO: that Olympiad math is different from research, that many top mathematicians never participated in the IMO, that not everyone who does well at the IMO becomes a great mathematician and vice-versa (Pierre-Louis Lions won nothing!), etc. This is all true. Nevertheless, it has built up a very good batting average when it comes to identifying high level talent, as Artur Ávila, Maryam Mirzakhani, and Subhash Khot further demonstrated this year:

    http://en.wikipedia.org/wiki/List_of_International_Mathematical_Olympiad_participants

    Furthermore, because winning an IMO medal requires both high ability and a solid work ethic, elite universities can trust IMO medalists when it comes to admissions, scholarships, etc. One downside is that only six students can attend the IMO each year, and many who missed the cut could have lots of potential as well.

    It’s a shame that Raúl Chávez Sarmiento’s accomplishments didn’t get more press, as I think it would’ve done a lot to establish Peru as a country to watch. (I heard you met with him and other members of Peru’s IMO team while giving a speech there last year?) Peru’s spate of young talent has likewise extended to the chess world with names like Jorge and Deysi Cori, Emilio Cordova, and Cristhian Cruz.

    Back on topic. At the risk of sounding elitist, I think the best *short-term* strategy for Latin America and other developing countries (First World countries have entirely different problems and are beyond the scope of this comment) is to locate as much top talent as early as possible through competitions like the IMO and exams like the CONAMAT and Math Kangaroo, remove them from the rotten public education system, and cultivate their ability by connecting them with private mentors and networks, etc.

    The sad fact is that the intellectual world is very prestige-driven, and I don’t think that can be rectified all that much. It’s in the nature of the beast. However, if a country that previously wasn’t on the radar suddenly produces lots of heavyweights, people will be forced to take notice. That’s why I think Peru and the rest of Latin America should focus on cultivating their talented minority, so that they prove to the world that they can compete with the best.

    Hopefully Avila’s Fields Medal will boost the cachet of the IMPA. As you said, the region needs to expand its bases. If enough interest is stirred and certain areas become known as hubs of intellectual activity like the IMPA, the outside world will begin to invest more in the region, and thus increase opportunities for *everyone*. Hence the important of finding enough talented people to create this buzz.

    Of course, the *long-term* solution — and I think you’d agree — is complete overhaul of the education and political system, but there are so many opposing interests that I don’t see it happening in the near future.

    Would be glad to know your thoughts.

    • valuevar says:

      Hi –

      Let me reply without going into too many details. (The schools you mention are probably unknown to most readers (they are unknown to me!), and while the young people you also mention deserve all credit, they presumably want to get to be known later, because of their “actual work”.)

      I do not think there is anything wrong in focusing on the “top of the crop”, as long as it really is the “tops of several different crops”, so to speak. Most mathematicians are not top olympiad scorers, and most top olympiad scorers, unfortunately, do not become top mathematicians. Yes, there is a strong correlation between (at least) semi-successful participation in olympiads and being a reasonably good mathematician later – and yes, the olympiads should be taken as one of the entry points into the mathematical world, so to speak.

      The preparation for olympiads at several levels is probably what works best in Peru nowadays as far as mathematics is concerned. It would be silly not to build on it. At the same time, the goal should be to make it more widely known, so as to be able to select students from an even broader basis than now. (Note to people not from Peru: the situation in this respect is, fortunately, not particularly bad in this respect. Few of the top students being selected through the olympiad process come from the most expensive schools, and even fewer, if any, come from the narrow top strata of local society. Still, matters are Lima-centered, and we have to wonder whether students in most provinces ever get any idea of the existence of mathematics olympiads, or of what it takes to participate in them.) I should also emphasize that by “building on it” I mean exactly that: using the process as a means to find and educate a small- to medium-sized group of students early on.

      (Personally, I (or rather the larval form of myself) participated in olympiads only for a very short while, between the ages of 13 and 14. Preparation was very informal and haphazard at that point – but the very fact that it wasn’t too efficiently focused on olympiad-type problems was a good thing in the long run. For the most part, we just had lectures by one or two rather enthusiastic university students about mathematics they found accesible and interesting.)

      On the general situation – here is a brief rundown, which, again, will not be news to people in the country. The public system of education has been grossly underfunded for more than a generation by now. (There may be other problems with it, but it is difficult to see how it could possibly not be in deep trouble, simply given the crude, basic variable of funding.) In part as a result of that and in part because of complicated complexes that would take too long to explain, the public system has been deserted by the middle and even lower-middle classes, which prefer private schools that are often rather bad themselves. (There may be a few exceptions here and there.) More expensive schools sometimes have shiny infrastructure, but are severely hampered by the fact that their main function is to cater to academically challenged children of financially gifted parents, as the phrase goes; since they cover a small (and not particularly clever) part of the population, we can forget about them.

      In general, the better students try to finish high school as quickly as possible, and head to university at 16 or 17. There are three traditional institutions (two of them belonging to the state), a small mathematics institute, and a large number of entities that are now called universities but for the most part aren’t. The three traditional institutions are not particularly good at sharing resources with each other, to put it very politely.

      The solution is left to the reader.

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