Igor Shafarevich's basic algebraic geometry.

Features The Steklov Legacy

Professor of mathematics, Ulf Persson, visits the legandary Steklov Institute, the flagship of pure mathematics in the Soviet Union. Russian mathematicians have long inspired awe among their Western colleagues. A second-rate Soviet mathematician was usually considered first-rate by Western standards.

Published in the printed edition of Baltic Worlds Pages 34-38, Vol 1 2011
Published on balticworlds.com on April 8, 2011

Russian excellence in the performing arts is legendary. Russian chess players have dominated the scene for almost a century. But that Russian mathematicians have inspired awe among their Western colleagues may not be generally known. A second-rate Soviet mathematician was usually considered first-rate by Western standards.

In 2009, the Steklov Institute celebrated its 75th anniversary. That puts its founding in 1934. Russian mathematicians from all over the world came to participate. Glossy booklets to document the event were produced. The Institute was considered the flagship of pure mathematics in the Soviet Union. To Western mathematicians it was fabled and distant, as if situated on the far side of the Moon.

The Steklov Institute is situated in Moscow, close to the Academy of Sciences of which it is a part. Physically it is on the right bank of the river, within a short stroll from the Akademicheskaya metro station. Its actual physical location has changed over the years from one building to another. Its present site is next to its old one, set off a little from Vavilova Street, its former street address. Trolleys ramble along the icy street as I make my way to the Institute, which now occupies a modern building of nine floors. There is still a guard at the entrance, but he will not stop you as long as you look like you know what you are doing. In the old days, a stranger walking in from the street would have had to produce some proof of a right to enter, usually known as a “propusk”. Having entered the building, you are now free to roam around. The bleak impression which you no doubt would have had twenty years ago is gone; instead, you can easily imagine yourself at a Western institution. You feel comfortable.

I knock at the door of the deputy director, Armen Sergeev. He is a short man with long gray hair speaking in a hoarse voice. He first came to the Institute thirty years ago. At that time it was still headed by the formidable Vinogradov. While important visitors would have been seated close to Vinogradov’s desk, someone like young Sergeev would be relegated to a corner of the room to sit on the edge of a sofa. The present director is away and a secretary supplies the keys to let us into the inner sanctum. The old furniture is still here; Vinogradov in fact brought it from its original location in Leningrad, when the mathematical section split off that year, 1934, and moved to Moscow. There was solid and plush leather furniture, green in color, art deco, probably produced in the ’20s.

The Institute is small. Vinogradov wanted the number of appointments to be kept low. When some department simply threatened to become too large, it was split off. That happened to the department of computer science.

Vinogradov was a recipient of the Stalin Prize and the title Hero of Socialist Labor. He was born in 1891 in provincial Russia. His father was a priest. He studied at the University of St. Petersburg and became a professor there in 1920. He made his reputation on what is known as the circle method in analytic number theory closely related to the work of the legendary mathematicians Hardy and Littlewood at Cambridge. Physically he was short, bald, and of extraordinary physical strength. He was an Academician. He also, one may be tempted to conclude, was an apparatchik, a power monger toeing the official line. However, the situation is a bit more complicated.

He prided himself on not being a member of the Communist Party, thus implying that his power was due solely to his scientific standing. Supposedly, he was of a Conservative Orthodox religious conviction. If so, maybe as a consequence, he did not particularly care for Jews, and acquired a reputation for anti-Semitism, and for trying to keep the institute “Judenfrei”. One should keep in mind, though, that many distinguished mathematicians who happened to be Jews were members.1 Vinogradov served as its first director for almost half a century, with the exception of the war years, when it was physically removed beyond the Urals, and he was replaced by Sobolev. Sobolev, a well-known analyst, was, unlike Vinogradov, a member of the Party. After the war, Kolmogorov and Alexandrov intervened and wrote a letter to have Vinogradov reinstated. Kolmogorov, the founder of modern probability theory, may have been the most distinguished Soviet mathematician ever.

Vinogradov died at his desk in 1983. Since then the Institute has already had a succession of four directors.

Sergeev proudly shows me the treasures of the Institute, such as the cupboard of Chebyshev, who, along with the pioneer of hyperbolic geometry Lobachevskii, may have been the most distinguished Russian mathematician of the 19th century. The cupboard is tall — so tall, in fact, that it no longer fits in this modern room. At its previous location, the ceiling was higher. Now the top has been removed and placed at its feet. Chebyshev was of the gentry, and his monogram is prominently carved on the top. There are tentative plans to set up a little institute museum in this very room.

There is a lot of paraphernalia. My host unfurls the tasseled Institute standard. In Soviet times, every institute of note had to have a flag. At the moment, a new department for the promotion of mathematics resides in the office. I am made a present of various educational toys, as well as being treated to the workings of a walking machine designed by Chebyshev, and recently reconstructed using his written instructions. But the real heart of an institute is its library. The head of the library is summoned and the most precious of its treasures are sought out. There you find the first and second editions of Newton’s Principia. You are allowed to handle them. As with old books, the quality of the paper is very good, far superior to more recent ones. In fact, the entire mathematical libraries of old Russian mathematicians have been preserved in toto, and you may inspect the volumes that once graced the shelves of a Chebyshev, or a Markov, or some other Russian mathematical luminary of the past. The journals are housed in another section of the library. The Institute has a complete run of Crelles Journal, which was founded in the early 19th century as the first mathematical journal ever. It was jump-started by the contributions of the young Abel, a Norwegian genius of mathematics, whose life was cut tragically short. There are also complete runs of the Russian journals Sbornik, Uspekhi, and Izvestiya, stemming from the mid-19th century, testifying to an already vibrant mathematical culture.

On the top floor, you can enjoy a view of Moscow, except that in recent years an unsightly skyscraper has been erected next to the premises of the Institute. Here you also find the large lecture hall. Three years ago, I attended here the meeting celebrating the 70th anniversary of the eminent Russian mathematician Arnold. The sight of slightly disoriented mathematicians earnestly discussing with each other, reveals that some other conference is going on at the moment. I spot a bust of Vinogradov in a corner as well as a glazed portrait of the original founder of the Institute or rather its precursor — Steklov, who was a mathematical physicist. Along the walls, one may view photographs of distinguished members now deceased. They present a “Who’s Who” of recent Russian mathematical history. There are in particular two photos that catch my eye, namely those of Andrei Tyurin (1940—2002) and Vasilij Iskovskikh (1939—2009), two algebraic geometers, whom I have had the opportunity to meet in person. To Tyurin we will have occasion to return. Iskovskikh was a larger-than-life figure, tragically addicted to bouts of drinking, but of an inexhaustible vitality, liable to keep his hosts up all night regaling them with old Russian songs. It took the combination of a heart attack and being hit by a car on an icy December day to do him in.

But the most legendary algebraic geometer of them all is Igor Shafarevich. It was he who founded the school of Algebraic Geometry at Steklov. His photograph is not on the wall. He is still alive, if old and in frail health. My mission is to be able to meet and interview him.

What does an educated Westerner know about Russian history? In general not much, and what is known can easily be summarized.

There are the hazy beginnings involving Viking waterways, Tartar invasions, and Ivan the Terrible of the 16th century, who casts a long shadow as an archetypical barbaric Russian despot. Peter the Great brought under his dominion the Baltic States, and thereby opened up Russia to the West, bringing it out of its medieval slumber. He built a new futuristic capital to rise out of marshes that were still part of Swedish territory. And as a capital, it would, for another two hundred years, in many ways still be located outside Russia proper. He directed affairs among German states and had his progeny married to German royalty. As a consequence, many years after the death of Peter, a young German princess would move to Russia, adapt to it, not to say adopt it, becoming its ruler as Catherine II, also known as the Great. She is a lady who captures the imagination of a reading public. She has her husband murdered (sort of), takes on many a lover, and is a groupie of the Enlightenment, corresponding not only with her relatives and similar heads of states such as Frederik the Great of Prussia and her despised cousin Gustavus III of Sweden, but also with the likes of Voltaire. The Academy in St. Petersburg had been founded by Peter I with the support of Leibniz. It flourished under Catherine, and is now located in Moscow. Not only did she invite French encyclopedists such as Diderot and d’Alembert, but more significantly, great mathematicians. One thinks of the Bernouillis but above all the Swiss mathematician Euler, whom she regaled with the highest honors, and who lived a large part of his life in Russia, dying there in 1783. Euler was astonishingly productive, and is considered to be one of the greatest mathematicians ever. He can be said to be the father of Russian mathematics, if only in a formal sense. Did he ever learn to speak Russian? It did not matter; the Academy was a showcase, a brilliant illustration of the division of the Russian society. That society consisted of a very thin veneer of European culture — in which foreign nobility, especially the Baltic Germans, played a significant role — and an inarticulate mass of peasants, who in the 17th century had been turned into serfs.

Two dates stand out in Russian history: 1812 and 1917. They mark off what we could call a Russian Golden Century. Initially there was the defeat of Napoleon under Alexander I.2 By that deed, Russia became the de facto liberator of all of Europe, and would for the rest of the century play a leading part in its politics. However, she was not fated to exercise her influence to the full extent warranted by her initial achievement. Her peripheral position made it difficult, and her ambitions were further thwarted diplomatically, first by Metternich, later by Bismarck.

Fascinating as this subject may be, it is peripheral to our concern; it suffices to remind us of the theme of insecurity. The Russians may have been barbaric, and may have suffered from a certain inferiority complex, but they certainly tended to overcompensate for it. Who could speak French with more aplomb than a highly educated Russian? Who could perform classical music better than the graduates of Russian conservatories, and for that matter who were to be the true heirs of classical music, if not Russian composers? It prompted a running debate on national identity, with the two warring camps of Westerners and Slavophiles: those who wanted Russia to become modern and assimilate into the West, and, more interestingly, those who wanted to keep that special mystical Russian character and stay apart. The debate was radical and romantic. It caused the formation of the intelligentsia, with the special Russian touch of wide interlocking interests combined with deep passion. The central issue politically and morally was the freeing of the serfs, which took place in 1861 and had momentous consequences. All of this provided the soil for an unprecedented cultural flowering, especially in literature.

1917 and its aftermath was a disaster for Russia. It meant in practice an eventual retreat into medieval isolation, combining the worst features of both the Westerners and the Slavophiles. Remarkably, however, it did not spell the end of Russian culture; it was still able to flourish, if in more indirect forms. It certainly did not spell the death of mathematics, on the contrary, the 20th century turned out to be a Golden Age for Russian mathematics. Why?

Together with my gracious host Sergeev, I enter an Irish pub close to the pedestrian mall of Arbat. My host appears to be well known here and we are directed to a reserved table. He suggests some delicious starters, recommending in particular a fish native to Lake Baikal.

How was it growing up in the Soviet Union? The picture we had in the West was of an oppressive society, where everybody learned to watch their tongue, and be mistrustful of their neighbors.

“It was not at all like that. I grew up in the neighborhood of Arbat. It was very different then of course, no pedestrian mall. As to watching your tongue, it was not that different from learning rules of good behavior. You learned from your parents what was appropriate or not. That is surely the same in all societies. In fact as a child, I was convinced that I lived in the best of all possible worlds, that the Soviet Union was the best country in the world. I was happy. And as to relations with your neighbors, they were much, much livelier in my childhood than they are today. You instinctively learned whom to trust and whom not to trust. In fact, this involved a deeper personal interaction with people. Something that may be waning to some extent now.”

When did you start to doubt that the Soviet Union was the best country in the world?

 “Probably around the time of the invasion of Czechoslovakia. Something did not really jibe. In fact, the first foreigner I ever met was back in the ’80s. He was a French mathematician. He invited me to his hotel. True to my ingrained habits, I did not show up. Then of course later I met Americans. I am very favorably impressed by them. They are very outgoing, friendly, and frank.”

A vibrant culture always has a basis. The tenor of a general education system is usually the clue. It does not have to be universal; it is enough that it involves a critical mass. It has often been noted that mathematics plays a special role, even in primary education, in Russia, and doing well in mathematics carries with it high status. A good education system tends to be elitist in the sense of seeking out, identifying, and celebrating talent regardless of race, ethnicity, and class. This is of course not the primary goal of education, but an inescapable consequence of making demands on the students and expecting them to deliver.

The first modern education system was instigated in Prussia in the beginning of the 19th century. It was all-encompassing, involving everything from primary education to the visions of Wilhelm Humboldt concerning the role of the university. It certainly exerted a wide influence and there is no reason not to think that it also shaped the Russian education system, especially in light of the close political and cultural connection between Russia and Prussia during most of the 19th century. How did the Soviet ideology mesh with the education system of the old regime? In fact, an elitist system based on merit fitted well. One should not forget that in the ’30s workers were paid according to their productivity. When it comes to hard science, ideology is confronted with a reality test. The Soviet Union had to survive. To do so it had to modernize and industrialize, if for no other reason than to provide the basis for a strong military force. The somewhat paradoxical situation arose that in isolated Siberian communities of defense research, substantial internal freedom of discourse ensued. It might not be surprising that many of the dissidents came from such backgrounds, as exemplified by Sakharov.3 A growing emphasis on science and technology was already present in late Tsarist Russia, as the classics were retreating all over Europe, despite concerted efforts to stem the tide.

There was no reason why the Soviet regime would try to reverse this trend, rather than welcoming it. As expected there was pressure to have pupils of humble backgrounds come to the fore. Petrovski, a well-known Russian differential equation man, may have this to thank for becoming the rector of Moscow University. He had given well-appreciated math courses to people who later would rise and become important and influential engineers, and would remember him fondly.

I try to press Sergeev on his educational experience. Yes, it was very demanding; there was an emphasis on science and technology. Although his father was not a scientist, he himself was very much pressured into becoming one. We are contemporaries; we grew up in the aftermath of the Sputnik. My own experience with my own father was very similar.

I have commented above on the elitist character of Russian education surviving in Soviet times. It may be instructive to make a digression on a small Eastern European country — Hungary, which, during a few decades a hundred years ago, produced an amazing number of distinguished mathematicians and scientists, the most luminous being perhaps John von Neumann. It too benefitted from an elitist school system, in which mathematical competitions played an important role. The tradition of mathematical competitions was taken up in a systematic way by the Soviet Union after the war, and by the late ’50s, they culminated in what was called Mathematical Olympiads. Initially it only involved the countries of the Soviet Bloc, nowadays it has become worldwide.

Personally, I had the privilege as a high school student of watching this close up as a participant. That was in 1968 at the height of the Brezhnev years and during the deep freeze of the Cold War, giving me my first and hence most memorable encounter with
Soviet reality. I remember Moscow as a bleak and Asiatic city, with wide avenues along which trucks raced with no concern for pedestrians. (Leningrad on the other hand made a much more congenial impression on me.) We were housed in dormitories scattered haphazardly on what I imagined to be steppes surrounding the city. The food was bad, there was no toilet paper, and postcards were given as prizes. I was touched by the latter. It may have been a bit hard on spoiled Western youth, who all experienced a big relief when returned by train to Helsinki. But my deeper emotion was that of fascination. No matter what you think of it, the presence of an independent and alternate world is reassuring, it makes the world bigger.

Mathematical competitions fit very well with the idea of chess tournaments, sports, and competitions among young performing musicians or acrobats. And the Soviet Union devoted many resources to sports during the postwar years. Incidentally, the emphasis on sports is also very much prevalent in modern Western societies, and is, ironically, the only educational arena in which competition is considered politically correct. The Soviet system took this a few steps further, by also setting up special schools for gifted pupils, be it for mathematics, physics, or some other intellectual discipline. But while in sports and chess, competition is essential — without it they would not exist — in mathematics it is incidental. What this structure really provided was a forum for extracurricular mathematical education. What my colleagues, who may or may not have excelled in competition, really appreciated was the wide exposure they were given to mathematics even at a young age. It may thus not be surprising to find out that the average Russian mathematician is much more cultured than his Western counterpart, and not only in mathematics.

We continue eating in silence. I pour some tea and sip on a sweet liquor made of honey produced by bees feeding on heather.

In the old days, science and industry worked very well in the Soviet Union. There was an inner core of pure mathematics and theoretical physics. Around it, there was a bigger ring of applied science, which in turn was surrounded by industry. Nowadays, the government tries to meddle too much. I remind Sergeev that there is the same problem in the West. There is also a lot of corruption. It may have existed, to some degree, in the communist era, but it was generally strictly curtailed by the Party. Now there are no such constraints in the system. Medvedev supposedly is very concerned about it, but the question is what will he be capable of doing personally? Russia is a very rich country; the problem is that it suffers from a lack of wise investments.

But to return to mathematics.

Mathematicians, along with similar segments of the population, were hit especially hard. But mathematicians had a way out. They were in demand. And the mass diaspora of Russian mathematicians followed. Twenty years earlier there had been a select diaspora of Jewish mathematicians, many of them of world renown. The mass diaspora was different. They went everywhere, even to obscure places such as Swaziland. Rare was indeed a Western math department that did not have at least one Russian on its staff. Commonly, Russian mathematicians formed minor colonies, and sometimes ran seminars in Russian. Many of them never bothered to learn local languages. And even if the case of outright emigration was not an issue, Russian mathematicians found it not only expedient but also necessary for survival to spend a month abroad every year earning enough to see them through the rest of the year.

The solidarity of the worldwide mathematical community is very much appreciated, my host assures me. It was great for the individuals, but it spelled disaster for Russian mathematics. It was almost impossible to attract new talent. The present demography of mathematicians contains a lacuna of about twenty years. But Russians seem to have a hard time adjusting to life abroad, surprisingly much more so than people of many other ethnic communities. Maybe this means that they will eventually return home? In fact, they have been able to appoint some young members to the Institute. They can nowadays offer reasonable salaries. Something like 1000 euros a month. It is not great. Moscow is a very expensive city; to that, I can attest. But it is sufficient for survival. Sergeev informs me that in the past, he saved as much as possible when he was abroad. Not any more. What he gets, he spends. Salaries are not the big problem, but apartments are. Buying an apartment in Moscow is prohibitively expensive; unless you already have a foothold in the city, it is out of reach. They were lucky, though, to be able to arrange something for their new young appointment.

I ask him about Shafarevich. In the late ’80s he became known outside the mathematical community through his essay “Russophobia”.4 It generated accusations of anti-Semitism. The American Academy of Sciences, of which he was a member, put pressure on him to resign.5 An official invitation to Germany was aborted for fear of controversy. That was all shameful. Recently a thesis on him written by political scientist Krista Berglund was defended in Helsinki; it involved an attempt to exonerate him.6 This is a hopeless task, the notion of anti-Semitism simply being too fluid. Some of his students were deeply embarrassed by his rhetoric. Yet even those who were most adamant in damning him as an anti-Semite still hold him in high regard, pointing out that he never sought any personal advantage from his position, nor did it affect his support of his Jewish students. His greatest crime might be his close associations with people such as Vinogradov and Pontryagin, they argue. Personally, I see him writing in the old Slavophilic tradition, inevitably stepping on a lot of toes, not only Jewish ones. But Sergeev does not know much about the Shafarevich circle. Although he knew Tyurin well, he only found out at his funeral that Solzhenitsyn’s widow was in fact Tyurin’s first wife.

This I had known for thirty years.

Alexis Rudakov was a student of Shafarevich. He is a tall, handsome man, with a slight limp, and a faint resemblance to Sean Connery. We have dinner at a Japanese restaurant. I ask him whether he felt that he lived in the best of all possible worlds when he was young. No, he has always been of a very observant nature, even as a child, when he kept asking questions about adding two and two and finding that it did not always equal four. He had some secret religious education as well. To have a Bible for private use at home was not forbidden, but to show it to others was. He was grateful that his relatives trusted him to keep secrets. Yet of course he was proud of his country in the Sputnik years, and he believes that the defense industry was very strong.

He has many memories of Shafarevich he is willing to share. Shafarevich was a dissident in the circle of Solzhenitsyn. The latter had, in the late ’60s, urged academicians to take a more active interest in society. Shafarevich had heeded the call. His activities as a dissident got him into trouble. Like most members of the Steklov Institute, he had a joint appointment at the State University of Moscow. Such appointments were temporary and as a matter of course renewed from year to year. Yet what would be more convenient than not to renew it to show displeasure? As an Academician and a member of the Steklov, he was not touched.

It was in the mid-seventies. Suslin in Leningrad had proved the Serre Conjecture. This was a remarkable achievement. Everyone was excited. He came to give a talk. The seminar room was filled to the brim, it was standing room only for late comers. It was the Shafarevich seminar, but since he had been deprived of his position at the university, he was no longer allowed to head it. Instead, Tyurin acted as his deputy. A political commissar looked in. He was suspicious. So many people, what was going on here? Who is in charge? He looked at Shafarevich, who, sitting in the front, obviously seemed in command of the scene. Shafarevich shook his head, referring to Tyurin. Where is Tyurin? There he was, waving, sitting in the back in a window smiling happily. The commissar still was very suspicious. And next year Tyurin was not allowed to head the seminar.

It was not so easy to publish. To publish in an international journal was out of the question. Starting in the ’30s, with few exceptions, everything was to be published in Russian. Many Western mathematicians learned Russian as a consequence, while most relied on regularly appearing English translations of the best Russian articles. But even publishing in Russia was not trivial. Rudakov and Shafarevich wanted to have a paper published. They needed a signature from the dean. Rudakov approached him. They had a polite interchange. He presented the document to be signed. But instead of putting pen to paper immediately, there was an extended silence. Then it was explained that the matter deserved more consideration and consultation and he was asked to return later. They decided to have it published under the auspices of the Steklov Institute instead. Vinogradov saw to that.

Shafarevich was something of a prodigy. He had made a stir in the ’40s by proving a well-known conjecture. According to legend, the distinguished German mathematician Hasse came to visit. He was impressed. It was a German problem, only a German could have solved it. Did Shafarevich have any German blood? Shafarevich denied it. The story sounds a bit fishy. Yet Shafarevich knows German very well and read a lot of German literature when young. Some even believe he had a German nanny. I guess I will find out.

Soviet mathematicians were physically isolated from the West, but news of what was happening reached them in various ways. Shafarevich might be sent a preprint, and if it seemed interesting, he would assign someone to talk on it. But Soviet mathematics was self-sufficient: people could approach him with an idea for a talk, and if the idea was good, Shafarevich would accept. People would come from Kiev or Leningrad to give talks. In the long run, the list of topics would make up an exquisite selection bearing the stamp of Shafarevich’s taste. During the talks, he often made comments, occasionally proposing related conjectures. Afterwards there were informal discussions, during which he may or may not have been present.

Another student refers to his manly intellectual face and intelligent green eyes endowing him with a magnetism further enhanced by his tall stature and powerful torso. Speaking to him, you felt yourself to be in the presence of a sage — a man of a deep and original mind, highly cultured and with broad visions. Invariably polite, unlike the more ebullient Gelfand, he always would keep a respectful distance. His mathe-matical comments invariably went to the core, and not surprisingly, as a lecturer, he was unsurpassed. Even in his eighties, he dominated seminars by his quick mind and deep comments. His dissident activities during the Brezhnev years did not exactly detract from his nimbus. No wonder he attracted the best minds. In geometry and number theory, he belonged to the supreme circle, not only in the Soviet Union.7

The Shafarevich circle was a close-knit group, and they also met privately. Their excursions were legendary: hikes in the summers, cross-country ski trips in the winter. In his memoirs,8 the GDR mathematician Koch particular refers to the Sunday hikes around Moscow. There was a meeting point but no advance commitment on the part of the participants. Once only he and Shafarevich showed up. They walked a long distance at a very fast pace. Mathematics was not an exclusive topic of discussion, on the contrary — as noted, the Russian intellectual is known for his wide-ranging interests. Shafarevich was a very fit man until recently. Like many mathematicians, he had a passion for rock climbing, an interest shared by several of his students. I recall a meeting in Rome in the spring of 1996; I sat next to Tyurin at a boring lecture. He shared with me, drawing on a piece of paper, an adventure he had had in the high mountains. There had been an avalanche; they were buried in snow. They were rescued by a helicopter. As a consequence, he had to have some toes amputated.

I believe that this also had happened to Shafarevich, at this or maybe at another occasion. I will definitely ask him.

What about Tyurin’s first wife? The connection to Solzhenitsyn is intriguing. They met when they were very young and married. Soon afterwards, they got divorced. They were always on good terms. She had started out studying mathematics, but had been sidetracked, since Kolmogorov had become very interested in mathematical applications to language and run a seminar on it. She had literary interests. She had contacted the widow of Bulgakov and received from her an original uncensored manuscript of The Master and Margarita. She typed four copies of it. Four copies was just about all you could manage with carbons. Tyurin was given a copy. The whole activity was of course very dangerous. Did he, Rudakov, ever meet Solzhenitsyn? Only once, through Tyurin. He suspects that Tyurin saw him more regularly, but it was all very secretive, so there is no way he would know. He never talked to him about it afterwards. I am curious about Shafarevich and Solzhenitsyn.

How does he like life nowadays in Russia? He spent many years abroad in Norway before returning. Rudakov admits that he likes very much the travel that has now opened up to him. When he was younger, even going to the GDR seemed out of reach, and he was very lucky that he was finally given the chance in 1986 during the early Gorbachov years. His first visit to the States in 1989 was a revelation. But living in Moscow is different now. In former times, it was after all more egalitarian, now you as a mathematician may feel yourself to be on the lower rungs of society. Mathematicians lived reasonably well in Soviet society. They did not suffer from want of money, nor — perhaps almost as important — were they distracted by its surplus, since there was little opportunity to spend it in a society which was not consumer-oriented. And if you were a member of the Academy such as Shafarevich, you would be netting 900 rubles, with possibilities of adding to it, which should be compared to an average monthly income of around 200 rubles.

The year 1991 was a disaster. The value of money plummeted overnight; savings became worthless. This was known in the West as shock therapy. To add insult to injury, a system of vouchers was introduced. It only benefitted a few of the nomenklatura and great fortunes were made. The transition to a capitalist economy was more abrupt, if less bloody, than the transition to a socialist economy had been in 1917. After all, Lenin had allowed capitalism, at least temporarily, in through the back door. No such re-admittance was given to socialist economy. End of History.

Isaak Levitan was a Russian landscape painter of the second half of the 19th century, a contemporary and friend of Chekhov and his brother. A retrospective of his art is being exhibited at the New Tretyakov Gallery. With the aid of a very limited vocabulary, one is able to read all the captions of the paintings. They are very good, some of them truly exquisite. How come I have never heard of him before? After all, I pride myself on being quite educated on art. My mobile rings. It is Sergeev. He informs me that Shafarevich has been taken to the hospital. He will be there for at least a week. There is no way I can meet and talk to him. ≈

Ulf Persson