Mathematics Standpoint

The unreachable self-sufficiency

What does the future of Russian mathematics look like through the optics of the «brain drain» of the 1990s

Machine trans­la­tion

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.