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”.
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.
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.
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:
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:
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.
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 work in actual mathematics.)
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. Still, we should not forget that it should be only one out of several possible entry points.
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 actually 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 mostly 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. In Lima, 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. Sometimes, the three traditional institutions do not seem particularly good at sharing resources with each other, to put it politely. (This may be a more serious attitude problem in some places than in others.) There is also a great deal of disorganization and the habit of moonlighting, left over from the time (not completely over yet…) when an associate or full professorship at a state university did not pay a living wage.
Solution: left to the reader. Use no more than 500 words.
Obviously I agree with you that we should cast as wide a net as possible. E.g., the list of Math Canguro winners contains far more names than could possibly participate at the IMO, though Peru’s IMO team is often drawn from this talent pool:
Click to access ganadorescanguro2012.pdf
I’ve no doubt that almost all of those kids have potential. Based on that list above, it does seem quite Lima-centered. As I suspected, students from Colegios Saco Oliveros, Bertolt Brecht, and Prolog are vastly overrepresented. I notice lots of Quechua surnames as well, which is a good sign of upward mobility for them.
It’s my impression that many university professors in Peru still do not have PhDs, which makes it difficult for any top-quality research to get done. I’ve learned that French Polytech has recently collaborated with Peruvian universities in holding the Laurent Schwartz Olympiad for college students. Some of the winners have ended up pursuing their graduate studies at French Polytech. This is an auspicious development, and further ties and talent exchanges with French research institutions should be sought. Perhaps you could act as a mediator in this regard?
If French authorities need convincing that it’s worth the investment, you could point to Peru’s IMO performance as relatively objective proof of Peru’s nascent talent. I agree with all the qualifications you make about Olympiad performance, but administrators and admissions committees often want standardized tests and other measures through which they can quickly assess a student’s potential. The IMO offers a sort of international standard on that account, since exams and diplomas from developed vs. developing countries are not comparable. Yes, there are many flaws with an exam-driven and credentialist culture, but for the moment I don’t see any way around it.
(For Peruvians who wish to study abroad, I would recommend France, the UK (or Europe in general), and Brazil over the US, but it’s a long story as to why.)
I´m also interested in the topics of this post and comments.
The results of the Peruvian IMO team are very surprising since it is not a result one would expect using IQ statistics (I know it is a controversial topic but it has predictability). One would think that the large population of Lima ( 9 million and 1/3 of the country total population) contributes very much to this since it the pool of talent is close geographically. But there also is a “testing culture” that is caused by the entrance exams of prestigious national universities. So low and middle-low income people incentive the pursue of mathematical scholarship since it can be a possible mean to acquire better economic returns. Knowing this, It is possible to say that the “searching system” of talent is working very good in Peru right now? Have we reached a pinnacle at least at the high school level?
On the other hand I know that many Peruvian ex-olympians do not follow math in university. Why is this? The obvious answer is for economic reasons but that is not the fundamental answer. I´m partially surprised that there does not exist a career like mathematical engineering in any university, it seems like a good balance between safety and passion. Not all people are crazy enough to try to be a mathematician, even the ones with talent, when you live in a place like Peru. Also, at top universities of Lima the level of science teaching is very low and focused on “engineering” topics. This must be changed at least to favor the possible talented minority. I´m thinking in something like the ecole normale supérieure or la Scuola Normale di Pisa where even a prospective biologist needs to know real analysis. Maybe the host could pull some strings, now that the CONCYTEC is trying to invest in science development.haha
I’d rather not comment on whether IQ statistics (which one?) mean anything here (or elsewhere). Let me just confirm the impression that there is a large contingent of very good students coming from the lower-middle and rising lower class. I do not know whether the searching system is good – in fact, there is not much of a very active search that I know of, at any level; it may just be that there is, numerically, such a large pool of talent that some of it has to survive, given some chance. I’d also agree that there may be a bit of a “perverse good” effect of bad academic salaries – everybody knows that professors aren’t well paid (it used to be worse), but it is a stable job – and they are not poorly paid with respect to the (truly poor) majority of the population.
The “IQ statistics” he has in mind are those of the corrupt Richard Lynn. It’s rehashed nineteenth century racialism and Social Darwinism. Hardly an original idea to be found. If you want an idea of the kind of “scholarship” Lynn produces, see here:
He actually lifted fake numbers from a hoax website, submitted them to an academic journal, and somehow got published. His IQ studies are littered with similar problems: unrepresentative samples (N values as small as 9!), distortion of his sources, misreporting of his sources, unsystematic use of his sources, even citing sources that don’t exist! Not to mention other unsound methodology, such as using PISA scores as proxies for IQ.
But from a racialist perspective, the PISA scores don’t make sense. Countries like Argentina and Uruguay do just as bad or worse than countries like Mexico and Colombia. The most parsimonious explanation is that there are many things terribly wrong with Latin America’s education (and political) system which drag down their PISA scores. You’ve already listed some of the obvious negative factors affecting Peru’s education system. IQ is also affected by years spent in school, the quality of education, the amount of time one spends reading at a young age, etc. None of this is surprising to anyone who’s not a racialist ideologue.
But this is one reason I favor the kind of “elitist” approach above. Racialism is frequently a justification for the status quo and a simplistic explanation for the contrast in the economic/scientific/technological development between certain regions of the world. However, if that gap is narrowed, even if only by a highly accomplished elite (e.g. a wave of science Nobels or Fields Medalists), then the racialist worldview is undermined.
Of course, the long-term goal should be to match the First World, but there are many impediments to that happening soon. Finding and cultivating an intellectual elite is something that can be done right now. There’s no reason Peru and other Latin American countries can’t have at least one institution on the level of IMPA in Brazil or Sharif University in Iran, both of which now count a Fields Medalist among their alumni.
To reiterate why discussing the “IQs” of developing nations is silly, Chile’s IQ increased 25 points over the last 30 years:
What Jeffrey said about IQs. Also, we should not speak as if there were anything wrong with focusing on the most able, or the best performing students. (As has already been noted, large and by they do *not* come from the top of the socioeconomic ladder, even though access to contests, preparation, etc., is in all likelihood unfairly concentrated in the capital.) Raising the general level is obviously also a worthwhile goal, but there are other people who are at least as qualified as we are to work on that.
On the Ecole Polytechnique: actually, I *did* act as a mediator at one point. You see, when an official from Ecole Polytechnique first went to Peru to see whether to set up arrangements for students to be able to take the exam there, I was conscripted from the hallway in San Marcos (where I was teaching a summer course) in order to serve as an impromptu translator!
The system is now in place and seems to be working well, in that a steady stream of students has been coming. I should look into the details at this stage, but this really does fill a gap: it allows students towards the middle or the end of their undergraduate studies (that is, the point up to which one can study mathematics in Peru without necessarily falling behind…) to apply for a (full) scholarship (meaning truly full, as in, housing and stipend included) to study abroad.
(It would be pretty hard to get into a top doctoral program in the US without, say, a master’s from IMPA first. As for scholarships for undergraduate students in the US – in most places, they are rare, as opposed to the situation in my time, when they were extremely rare, outside a few good but non-top institutions.)
I agree that there is no reason why there should be only one world-class institute in South America. It is also the time to diversify – there is a very heavy slant towards dynamical systems. Of course, it is much better to be good at one thing than at none, but surely now there could be more in the way of support and development in other areas. In the short run – neighbouring countries should share resources – my impression is that this is already happening at an unofficial level. Let us also hope that IMPA will also play a role in the drive towards geographical and thematic diversification, which will most likely benefit all parties involved in the long run.
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