What does the future of Russian mathematics look like through the optics of the «brain drain» of the 1990s
What won’t allow to build in isolation a mathematics comparable in power and diversity with the Soviet one? The intellectual generation gap, giving rise to gerontocracy, marginalization, and the spread of pseudoscientific schools, suggests Corresponding Member of the Russian Academy of Sciences Ilya Shkredov.
The last thing I want to do is prophesy. In my predictions I rely on existing trends and some historical analogies. A simple enumeration of what we already know and the innocent hypothesis that the ongoing processes in Russia will continue and only accelerate will easily show us what awaits Russian mathematics.
The current outflow of qualified personnel from Russia is certainly not the first. What can we learn from our previous experience?
The departure of many scientists in the 1990s, caused by the usual attitude to man in our country, dealt a strong blow to mathematics and science in general.
The first obvious consequence of this departure was that a number of mathematical fields in Russia disappeared. No, they have not disappeared completely; this is probably impossible, but they have moved on, so to speak, to a lower energy level. Work in these fields continues, but it is quite impossible to compare them with research during the heyday of the Soviet mathematical school. Many of these fields were discovered by Soviet geniuses, such as Andrey Kolmogorov. At that time, these fields of science were still small and could develop normally within one country. But they grew, they became known in other countries, and new researchers and new schools joined them. The departure of most Soviet scientists left such fields with only fragments, which can no longer be assembled into something whole, even if one imagines that all those who left came back. Time has simply passed, the child has left its cradle and no longer fits into it.
On the other hand, of course, there were fuller rivers in the USSR and Russia, such as function theory, which has a rich history. Here the departure did not affect it as critically, but the general rule remained — and these sciences moved to a lower energy level. Here whole segments of modern research have been missed, and perhaps forever.
The second consequence is the generation gap that emerged after the departure of the 90s. Most of the people who left were mature, mature scientists. There is a situation where grandfathers teach their grandchildren. In such a situation, the young researcher finds himself trapped in an initial choice. He will either have to develop by himself at great cost, or be confined to a narrow range of questions, not being able to enter the open sea of modern mathematics. This may be a common problem for all young researchers throughout the scientific world, and not everyone is able to solve it. But the lack of a middle generation makes such an exit especially difficult. Peers or somewhat older fellows are unlikely to help here. Alas, the result is often an almost Freudian fixation on the juvenile plot.
All of this applies not only to candidates, but also to doctors of science working on some narrow topic. There are quite a few of them now, and there will be even more. This leads to a situation where Russian science is drifting farther and farther away from the relevant issues of modern mathematics, and is becoming more and more isolated and provincial.
Here we need to make two reservations, which, nevertheless, are important for the completeness of the picture.
First, a dialogue between the younger and older generations, even in the absence of a middle generation, has been taking place over the last 20 years. It is very good that young people, albeit with great difficulty, have been able to engage with really difficult things and productions. Even though these tasks are not quite modern, some are still relevant. For young people, because of their naturally limited horizons, this was useful. But it did not help at all to develop a taste for modern mathematics, to understand which problems are of interest to the entire mathematical world, and which are local.
Secondly, in some mathematical disciplines Russian science competed quite successfully. I am talking about the so-called young sciences or, more broadly, about young topics. In mathematics, the «age» scale is peculiar. Even disciplines that have been developing for a century are considered infants. But here I am talking about very «embryos» that are only a few decades old. (An example of such an embryo would be combinatorics, of which E. Szemerédi said that it is now on the same level as number theory in the time of P. Fermat). Young people do not need to learn much to get to the very front of such a discipline. Here one mathematician or one mathematical school can control the whole field. In a sense, the Soviet pattern I have already mentioned has been repeated in the new times. Of course, even under these conditions, success could and has been achieved, since our young people are no worse than anyone else. I think that in such «embryonic» directions it will be possible to work successfully in the times when this unhappiness is over. But it is clear that the more ramified sciences with a higher threshold of entry, requiring much study and the participation of different mathematical schools — these sciences will be forever inaccessible to Russian researchers.
It is clear from this construction of mine that there can be no exhaustiveness and self-sufficiency of Russian science under the new conditions (and hence no phantasmagorical return to the Soviet period is also possible). It only remains to add that mathematical Russia is now a rather small country which will become even smaller in the future, and only lazy person has not spoken about the almost universal lag in current research in it.
Another consequence of the gap discussed is the supremacy of the large older generation. These mathematicians are no longer able to think fast enough; they cannot keep up with the accelerating times. This is a natural process, and it has a natural solution: the gradual transfer of power to a strong middle generation, and then to the young. But in reality, no one in Russia takes young scientists seriously, and the middle generation is virtually non-existent. What will happen under the new conditions? The older generation will not get younger. The serious scientists who still remain in their ranks will leave us. The departure of scientists from both the middle and younger generations will widen the gap even further. In this sense, the resulting chasm will be tragically unique for science in Russia.
I would also like to note another sad trend, which is probably not directly related to the 1990s, but which will progress in the future. I am talking about something that is not at all new to Russian science: pseudoscientific schools. Putting aside the direct bad faith that does not require discussion, this phenomenon can be seen as the next degree of marginalization. In these kinds of «schools,» however local, but honest scientific work loses all cultural meaning. And this is where Russia is not unique. In many countries this sort of thing takes place. The saddest thing is the fate of young people involved in the work of such pseudoscientific schools. After all, young scientists could reach modern mathematics, but under these conditions they do not have a chance. I don’t even think they have the motivation to get out of the quite authoritative cargo cult that surrounds them, since this is the only form of science they know of. This is even worse than nothing. Based on my experience of monitoring Russian science, I believe that such trends will only develop in the future.
There will be science in Russia; it is not going anywhere. In mathematics, which does not depend on equipment supplies, you can always sit and think about something useful. But I am talking about the quality of science. A real scientist (and I suppose real science, too) is a person who is constantly evolving. Missing a couple of years is already critical. And ten years of some kind of administrative activity and/or survival does not allow one to call a mathematician a serious modern scientist.
Actually, the scientific level is not a constant or some intimate knowledge. It is a variable. It is a view that must change. Actually, a constantly evolving experience with science determines the level of a scientist!
Even before the tragedy took place, we had many mathematicians who talked in all seriousness about the excellent state of (at least part of) science in Russia. In the local coordinates of such mathematicians, this was not even a direct lie. They simply did not see much, they had no one to compare themselves with, they did not know how things were in the world (I remember Paul with his «they measuring themselves by themselves, and comparing themselves among themselves, are not wise» 2 Cor 10:12). This is another consequence of isolation and provincialism.
Even before the unfortunate events in Russia, the scientific path of a mathematician striving to solve global problems was difficult and traveled by only a few. Today I simply do not see how such a path is possible in principle. Yes, you can evolve, you can try to understand what humanity has done on one particular subject, you can even make relative progress on this subject. But to realize on your own what deep enough science has done, and to get to the very forefront of a developed field, even if only in a specific point, is simply not enough for one mathematical life.
Look at the Fields prizes (that’s another proxy). Yes, there are exceptions, like Grigori Perelman (although if you look at his life more closely, he is not such an exception). But if we talk about the normal way, the Fields Prize is always a team effort. Not even in the sense that it requires the work of a strong team. The laureate must be nurtured and, one might say, «accelerated» by communication with a range of strong scientists and schools. Only by quickly assimilating the experience of previous mathematical generations and achieving real-world productions can he or she, thanks to his or her talent, fly off into outer space. Stanislav Smirnov was a genius both in Russia and abroad, but he would not have been able to reveal himself fully in Russia, I believe: the barrier would have been too high to overcome.
It is likely that in the near future either embryos will survive in Russia, they have the best chance, or relatively young trends created in the Soviet period. How long will they last? I don’t think we need to guess here either, but just look at how soon a provincial school left behind by its founder usually dies. (There are many examples of this kind in Russia. It is easier for me to reason about number theory: it has now died almost everywhere except in Moscow, in Khabarovsk soon after the RAS reform, in St. Petersburg some time after Yuri Linnik or Anatoli Andrianov). The timing will be comparable, although much depends on the accumulated «subcutaneous fat». Again, it is possible to be quite self-sufficient in a narrow topic, working in a small group, and get world-class results. But the general trend will be toward marginalization. Incidentally, another consequence of provincialism, and some indirect indicator of it, is the almost complete absence in Russia of universal mathematicians (like Terence Tao and Peter Sarnak).
Finally, it is possible to ask when this wound will heal. This I do not know, but, for some reason, German science comes to mind, which, despite Gerd Faltings and Peter Scholze, has never fully recovered. I don’t want to embellish or exaggerate, but I do want this simple reasoning to be spelled out and brought into the rational field.
Text: ILYA SHKREDOV
Ilya Shkredov 20.03.2023