by Masha Gessen
What was the seventeen-year-old Perelman thinking about his fifteen-year-old charges? Did he suspect that despite all of their considerable accomplishments and their desire to learn, as evidenced by their presence at the math camp, they were secretly intellectually lazy? Possibly. “He certainly thought that they did not take things seriously enough,” said Golovanov. “It’s also possible that he was so noble that he could not fathom they were just not smart enough—and anyway, considering what they grew into, those kids probably were smart enough.” More likely, this was a classic theory-of-mind problem. The seventeen-year-old Perelman — university student, olympiad champion, and universal problem-solving machine—did not and could not imagine that these math-club teenagers, who had two years’ fewer problem-solving and competition experience and who simply lacked his problem-crunching skills, could not do what he could if they really, really put their minds to it.
When depriving his hapless students of lunch failed, he started banishing them from the study room. “We tried to explain to Grisha that if a child has been accepted into camp, he cannot be held outside class for days at a time, that this was not punishment but total craziness,” recalled Rukshin. “He responded that he would not let the child into class until the child solved such-and-such. It was really hard.” Those banished included Bogomolnaia, Nazarov,29 and Konstantin Kohas;30 in another dozen years, Kohas would hold the chair in mathematical analysis at Mathmech.
So why did Rukshin keep Perelman, whose lectures could be borderline incomprehensible and whose behavior was clearly abusive? Part of the answer was surely that Rukshin loved Perelman, and having him near— this seems to have been the summer when the two shared a room at the camp—filled his time, and his teaching, with additional meaning. But it also may be that Perelman’s limitations as a teacher suited Rukshin’s perceptions of how things ought to work. Here is how Rukshin described the situation to me, using terminology from Laurence Peter and Raymond Hull’s The Peter Principle:31 “Perelman was a brilliant teacher for super-competent students, a good one for competent students, and a mediocre one for those who were moderately competent. You see, a cobalt-alloy drill bit is a wonderful instrument. But you cannot use it to drill a piece of glass: the glass will crack and crumble. Whereas a bullet will leave a neat little round hole in a piece of glass but absolutely cannot be used to drill metal. A knife and an ax perform similar jobs, but one is far superior for sharpening a pencil while the other is a better tool for felling an oak tree. A teacher is a tool. For a limited group of super-strong students, where discipline is not an issue—I mean, where it came to the organizing duties of a teacher, Perelman did not do as well. But at camp, we have always had this tradition: we do not hire a separate person for making sure the kids are clean and fed and go to bed on time, and a separate teacher who teaches them things. The Holy Trinity is a single being: a teacher, a counselor, and the boss. Because these kids would never have respected some random camp counselor anyway. They had respect for the kind of teacher who took them hiking, got wet in the rain with them, sweated in the heat, did mathematics, and discussed books—especially since back then I wasn’t much older than my students.” Rukshin was nine years older than Perelman and ten to twelve years older than most of his students, and, as his diction indicates, he clearly thought he was not just a beloved teacher but God himself. His students turned teachers were therefore angels, and as such, in his mind they had the right to be not only of clearly circumscribed utility but also unreasonable, capricious, and outright childish.
The conflict came, naturally, once the students who had borne the brunt of Perelman’s military-style mathematical discipline grew old enough to encounter him as equals. It must have been just before the summer camp season of 1985 when Perelman declared he would not teach summer camp if Nazarov and Bogomolnaia were teaching there too. Twenty-plus years later, Rukshin either could not or would not recall the nature of Perelman’s objections to the two younger teachers. It seemed Perelman found Bogomolnaia generally objectionable—because she was a girl who did not wear skirts, for example, and because he had somehow discovered that she did not always tell the truth.
“Did he catch her lying to him?” I asked Rukshin.
“No, he just found out she did not tell the truth at all times,” said Rukshin. “I tried to explain to him—I mean, only idiots tell the truth at all times, but I did not tell him that. What I did say was, Grisha, what you are describing is not a part of a human being but a feature of his relationships with others. There are people I would never lie to, and there are people to whom I have no moral obligations. I would prefer not to lie to them, but I cannot exclude the possibility that I would distort the truth or not tell the truth. He would not accept this point of view.” In fact, he probably could not; the idea that a behavior—especially a behavior he found unacceptable—was not an inherent quality but a function of something as intangible as a particular human relationship was, in all likelihood, entirely incomprehensible to him. Plus, he knew at least one person who claimed always to tell the truth and to have done so his whole life, thereby giving the lie to Rukshin’s basic premise. That person was Alexander Danilovich Alexandrov, whose gravestone in St. Petersburg is inscribed with words that translate to “The truth is the only thing to be worshipped.”
Bogomolnaia couldn’t recall the incident either, but she remembered the world of math clubs, summer camps, and Rukshin as conflict-ridden. “We were young, we were all difficult to get along with, and it was hard to work alongside one another,” she explained, and she continued in a detached tone of voice but using vocabulary that conveyed residual bitterness—mostly, I gathered, toward Rukshin. “In our little snake pit, people would come into conflict with one another for reasons that seem utterly insignificant now that I’m forty.”
Generally, Bogomolnaia thought, Perelman was poorly suited for teaching: “He just didn’t quite have the temperament32—I mean, you have to do something in addition to pure mathematics when you teach.” But rather than simply drift away from teaching, he left in a rage—a rage, it seemed, that was fostered in part by Rukshin, who did anything but discourage conflict among his little stable of math angels. “I held discussions with every teacher who had agreed to teach at camp that summer,” he told me. “We discussed it and decided that we could not take Grisha with us in light of his ultimatum.”
So it was that when Perelman was nineteen, his world began its inexorable narrowing. He lost the social setting that had nurtured him since he was ten years old. At roughly the same time, in the middle of his third year at the university, he picked his specialty, which meant that his path and Golovanov’s began to diverge; after almost nine years of traveling to every class and math club together, occasionally stopping to write formulas in chalk on the sidewalk, they now had different schedules. Here began the road that would take Perelman through the next twenty years of his life and to the point where he was speaking regularly to only his mother and Rukshin, who still got to play God in his student’s life, now without the diluting and mitigating effects of the angels.
PERFECT RIGOR
GUARDIAN ANGELS
6
Guardian Angels
WHEN HE WAS GRADUATING, his mother came to see me,” recalled Zalgaller. “She said it was his dream to stay on at our institute.” She meant the Leningrad branch of the Steklov Mathematics Institute of the Russian Academy of Sciences. Apparently Zalgaller did not think there was anything particularly strange about the mother of a grown man going to his adviser to discuss her son’s graduate-study prospects. Both Zalgaller and Lubov Perelman probably had good reason to believe that intervention was required, because Grisha himself was unwilling and unable to do what it took to stay on for graduate study.
Little had changed in graduate-school admissions policies since Zalgaller found his name on the roster in the late 1940s: graduate work was still very nearly off-limits to Jews. The Steklov Institute
was particularly odious. An open letter circulated by a group of American mathematicians1 at the world mathematical congress in Helsinki in 1978 stated, “The Steklov Mathematical Institute is a prestigious institution in the field of mathematics. For the last thirty years its director has been academician I. M. Vinogradov, who is proud of the fact that under his leadership the Institute has become ‘free of Jews.’ . . . The key positions in mathematics nowadays are occupied by people who are not only unwilling to protect the interests of science and scientists in the face of the authorities, but who go even beyond official guidelines in their policies of political and racial discrimination.”
Ivan Vinogradov, the number theorist who ran the Steklov for nearly half a century, turned the Soviet policy of anti-Semitic discrimination into a personal crusade. By the time Perelman was nearing university graduation, Vinogradov had been dead four years—not long enough to make a dent in the legacy of fifty years of anti-Semitic policies, which Vinogradov’s successors continued with greater or lesser enthusiasm but always in full accordance with basic Soviet policies. Perelman’s situation was further complicated by the fact that all Steklov decisions were made in Moscow, with the leadership of the Leningrad branch exercising little influence. In addition, the new director of the Leningrad branch, Ludvig Faddeev, scion of an aristocratic and slightly eccentric (the mathematician was named for Beethoven) St. Petersburg ethnic Russian family, had never indicated whether he personally opposed the anti-Semitic policies of his institution. “I wasn’t sure what Faddeev would think of the idea,” recalled Zalgaller—“the idea” being to offer a graduate research spot to one of the most gifted and diligent students ever seen at the Mathmech. “So I consulted Burago.” Yuri Burago was a former student of Zalgaller’s who at that time ran a lab at the Leningrad branch of the Steklov.
Together Zalgaller and Burago concocted a plan.2 Perelman’s application to the Steklov would be preceded by a preventive heavy-artillery strike. Alexander Danilovich Alexandrov would write a letter to the Steklov leadership asking that Perelman be allowed to do his graduate work at the Leningrad Steklov under Alexandrov’s supervision. The incongruity of the request—a full member of the Academy of Sciences, the man at the center of all of Soviet geometry, writing a letter on behalf of a lowly university senior—was exactly what would ensure the operation’s success. Alexandrov was not a man who either accumulated or tallied favors, but this was a case where his sheer status promised a positive outcome.
“If it had been just Burago wanting to take him on as his student, they wouldn’t have let him,” Aleksei Verner,3 a student and coauthor of Alexandrov’s, told me. “But they couldn’t say no to Alexandrov.” Valery Ryzhik, who was sitting next to Verner during this conversation, readily concurred and added that Alexandrov had personally told him what the letter had said, “that this was just the kind of exceptional situation when ethnicity should be ignored.” Leaving aside the assumptions behind this recollection—particularly the idea that Alexandrov or Ryzhik or both believed that, ordinarily, ethnicity should be taken into account—what was really striking about this story was that it seemed that everyone in the Leningrad mathematics community was in on it. Everyone, that is, except Perelman.
“I was sure Grisha would have problems with admission,” recalled Golovanov. “His papers said he was Jewish; mine, as it happened, did not. So the issue was taken up at the highest level, a level that at the time seemed beyond the clouds to me. That was pretty funny in itself. I mean, yes, Grisha is Grisha, but he was still just an aspiring graduate student. And here he had members of the Academy going to do battle for him.”
Was Grisha engaged in the effort to get him into graduate school, I asked, or was he oblivious to it? “Being engaged and being oblivious are not the sole possibilities.” Golovanov leaned back in his chair and, with a satisfied grin, reiterated a phrase he used continuously throughout our conversations: “Grisha is very smart, I keep repeating this. This is a statement that has no relationship to his mathematical talent, which is recognized by everyone. Grisha is a very smart person. That means I cannot imagine he was oblivious to the process. But I have to admit that we never talked about it at the time.”
In other words, Golovanov and Perelman, who had known each other for more than ten years, who had received the bulk of their mathematical education side by side, and who were sitting together for their graduate-school admission exams (there were two: one in their chosen mathematical disciplines and one in the history of the Communist Party), diligently avoided discussing the elephant in the room. Golovanov’s motivation was clear: he was an exaggeratedly polite man, almost painfully aware of his friend’s potential sensitivities—and in 1987, he was also acutely aware of the unfair advantage he enjoyed simply because his documents did not label him Jewish. Perelman’s behavior was also entirely in character. The system of graduate admissions, byzantine and discriminatory as it was, could not possibly have fit Perelman’s view of the mathematics world as fair and meritocratic. He might have been not just unwilling but unable to talk about the uncertainty of his future in mathematics and the scheming undertaken to save it.
In effect, Perelman’s approach to the graduate-admissions problem was a mirror image of Zalgaller’s. The older man so loathed the idea of being indebted to anyone that he had removed himself from the corrupt and corrupting system, literally crossing himself off the list. Perelman, who similarly could not have entertained the idea of being indebted to someone, ignored the behind-the-scenes aspect of his graduate-admissions process, as though crossing out that part of the narrative. In the grand scheme of things as it had been imparted to him by his teachers, Perelman, of course, was right: the indignities to which the Soviet system subjected its scholars, especially the Jews among them, had no relationship to the practice of mathematics and could lay no claim to the mathematician’s mind. Traditionally, in the second half of the twentieth century, Soviet mathematicians accepted that those who wished to practice mathematics as it ought to be practiced would be relegated to the world of unofficial mathematics, where they would have the scholarship without the perks. Those who belonged to the world of official mathematics got the office space and the salaries, the apartments apportioned by the Academy of Sciences, and even the occasional trip abroad—but had to abide the ideology, the discrimination, and the corruption. Perelman’s totalizing mind could entertain no such dichotomy; he would practice mathematics the way it ought to be practiced in the place where it ought to be practiced—the Leningrad branch of the Steklov Mathematics Institute. The benevolence of colleagues who intervened on his behalf and the kindness of friends who did not push the issue in conversation allowed him to do just that: continue living in the world as he imagined it.
In the fall of 1987 Grigory Perelman became a graduate student at the Leningrad branch of the Steklov. Alexander Danilovich Alexandrov was officially listed as his dissertation adviser—making Perelman the last mathematician who would be so honored—but in fact Perelman took up residence in Burago’s lab. No one knew this then, but there had never been a better time and place for a mathematician to start his research career.
Just over a year before Perelman graduated from Leningrad State University, Communist Party general secretary Mikhail Gorbachev announced a sweeping series of reforms, which he dubbed perestroika. At the end of 1986, physicist Andrei Sakharov, Nobel Peace Prize recipient and the Soviet Union’s leading human rights activist, was allowed to return to Moscow from the city of Gorky, where he had been under house arrest. By early 1987, all Soviet political prisoners had reportedly been released. The year 1988, just after Perelman became a graduate student, saw the dawn of the era of glasnost, the Soviet intellectuals’ brief golden age, when the readership of thick intellectual journals shot into the millions and a national public conversation about the future of Russia commenced. In 1989, the year Perelman wrote his dissertation, the entire country was glued to its TV screens watching the first semidemocra
tic elections and then the first open parliamentary debates that occurred in their lifetimes. So sweeping was the excitement of the time, not even someone as disdainful of politics as Perelman could resist the spirit entirely.
It was an extraordinary stroke of luck that Perelman began his career several years before the economic reforms of the early 1990s impoverished research institutions and condemned Russian academics to either precarious research-grant-to-research-grant existences or moorless lives of shuttling back and forth between teaching gigs abroad and research positions at home. In the late 1980s, in Golovanov’s estimation, a graduate student’s stipend still placed him “ten rubles a month above the salary level at which one could exist.” At the same time, the most important change in how Soviet academic institutions worked was already under way: the Iron Curtain was lifting. Soviet scholars were starting to travel abroad, foreign researchers could come and go unimpeded, censorship of foreign academic journals was lifted (but the economic crisis had not yet caused library subscriptions to lapse), and communication through letters and phone calls became as accessible as it should have been all along. What this meant for institutions such as the Steklov was a daily sense that change and intellectual opportunity were in the air. What it meant for Perelman was that his path to membership in the international mathematical elite would be natural and straightforward—and his view of the world would not be challenged. Plus, he would meet Mikhail Gromov.
After a certain point, Mikhail Gromov’s name becomes linked to just about every important thing that Perelman did. Everyone I interviewed to trace Perelman’s trajectory past graduate school mentioned Gromov: he recommended Perelman for this or that academic position, he brought him to this conference, he coauthored a paper with him.
