Perfect Rigour Read online

  By the time I met Ryzhik, he was seventy, teaching again—at a new elite physics-and-math school—playing chess in the afternoons, and given to looking back kindly on his life, which had been lived largely in the shadow of the Soviet compromise. He had been denied entry to Leningrad University because he was Jewish. “They did not even manage to find a problem I couldn’t solve: I sat for three hours after the exam was over, I solved them all, and still they failed me. I was just a boy. I went home and cried.” He graduated from Herzen, the second-tier college, and was later cut from its faculty because there were too many Jews. He never managed to defend his doctoral dissertation, which was based on the geometry textbook he coauthored and was criticized for violating every rule of Soviet teaching methodology.71 In the hours I spent with him, the only regret he expressed concerned his failure to bring together the very strange experiment of a class in which Grisha Perelman had been his student.

  The drama of this teacher surely passed Perelman by, as did most of what surrounded him at School 239. He never attended the literary Tuesdays, which contained poetry and generally reached beyond the mandatory school reading list. He probably did not follow the story when the School 239 principal Viktor Radionov was fired amid charges of pedophilia.72 He was surely oblivious to the countless ideological inspections, which required the teachers and the more attuned students to be on their best Soviet-school behavior, which came naturally to Perelman anyway. He almost certainly never posted a question on the supposedly anonymous question-and-answer board run by the history teacher Pyotr Ostrovsky, who impressed students with his willingness to entertain even risky political questions73 and who was later exposed as a KGB informant74 who tracked down those tricky questioners and denounced them and their parents.

  While careers teetered and entire lives were ruined, and while some children thrived in the liberal math-school atmosphere and others labored anxiously to keep up, Perelman studied mathematics. A classmate recalled seeing Perelman and Golovanov stop about halfway between the underground station and the school to write formulas frantically on the sidewalk in front of what happened to be the U.S. consulate. In all likelihood, Perelman did not notice the consulate, or the popular movie theater that was housed in the church building to which the school was adjacent, or the school’s grand semicircular marble staircase and the white marble boards with the names of national olympiad prize takers, on which Perelman’s own name would eventually appear in gold. To his classmates, he appeared a sort of math angel: he sounded his voice only if a solution required his intervention; looked forward to Sundays, sighing happily and saying that he could “finally solve some problems in peace”; and if asked patiently explained any math issue to any of his classmates75 though apparently utterly unable to conceive of anyone not comprehending such a simple thing. His classmates repaid him with kindness: they recalled his civility and his mathematics, and none ever mentioned to me that he walked around with his shoelaces undone—not a particularly uncommon occurrence at the school anyway—or that by the time he was in his last year of school, his fingernails were so long they curled.76

  Other School 239 graduates thanked the school for opening their minds; for teaching them that intelligence, erudition, and civility were rewarded; and for giving them a head start in their higher education. If it ever occurred to Perelman to thank anyone for something so intangible, he should have thanked School 239 for leaving him alone. One suspects that Rukshin’s entire club-class design worked for only two people: Rukshin and Perelman. It was destructive for other kids, and it was tragic for Ryzhik, but it allowed the symbiosis of Perelman and Rukshin to continue unchallenged and Perelman’s view of the world to remain undisturbed—but also unexpanded. Like all protective bubbles, the environment of the math school served not only to shield but also to isolate its inhabitants. It ensured that Perelman’s relentlessly logical approach to life was never challenged, allowing him to concentrate on mathematics to the exclusion of—literally—almost everything else. It let him avoid confronting the fact that he lived among humans, each with his or her own ideas and thoughts, to say nothing of emotions and desires. Many gifted children realize with a start as they mature that the world of ideas and the world of people compete for their attention and their energy. Many make a difficult choice in favor of one or the other. Not only did School 239 spare Perelman the choice; it kept him from noticing that the tension between people and mathematics even existed.

  PERFECT RIGOR

  A PERFECT SCORE

  4

  A Perfect Score

  SOMETIME DURING THE FINAL year of school, Ryzhik would have difficult, delicate talks with some of his students’ parents. He would ask them to think about their child’s chances for university admission. Ryzhik, who himself had cried when he was turned away for being Jewish, endeavored to warn parents who he felt had not given the issue enough thought. There were subtleties in the admission process, of which he was acutely aware. Leningrad University’s Mathematics and Mechanics department had a quota of two Jews admitted per year, which was enforced strictly but not zealously: unlike its Moscow counterpart, the Mathmech, as it was known, did not delve into the family histories of applicants in an effort to root out hidden Jewish relatives. At the same time, Mathmech turned away non-Jewish applicants burdened with Jewish-sounding surnames.1

  “I had a student named Filipovich,” recalled Ryzhik. “It’s not a Jewish name, but it might sound Jewish, so just in case, they did not accept her. Olga Filipovich got run over by the system.” Parents had to be warned and then directed to schools with more liberal admissions policies, if need be. Ryzhik had two rules: he did not talk to the students directly about this, preferring that they learn the facts from their parents, and he talked to the parents only when he judged it absolutely necessary. He said he hated meddling, and he surely must have hated acting as the unwilling agent of an absurd and cruel system of discrimination. But when he had to, he engaged the parents in what he called “a standard conversation: that you have to be mindful of what you are doing to spot the child, and you have to have a plan for what you are going to do if it doesn’t work out. And how are you going to explain this to the child? I had been through it all myself.”

  The children in question were not that young—Soviet schools generally graduated seventeen-year-olds—but the stakes were indeed too high for many adolescents to understand and to handle. The Soviet system of college admissions was based on a set of four or five exams, generally a combination of oral and written formats, for which the applicant had to be physically present at the college. Therefore, a high-school graduate could apply to two colleges, at most, in one summer. If he was male and he failed to gain admission, he would be drafted into the military. When Perelman was graduating, the Soviet Union was in the third year of its war in Afghanistan; roughly eighty thousand conscripts were serving there at any given time,2 and conscription was what every parent feared most.

  For a Jewish adolescent who was exceptionally gifted in mathematics, there were only three available college strategies: choose a college other than Leningrad University, with less discriminatory admissions policies; bank on being one of only two Jews accepted in a given year; or become a member of the Soviet team at the International Mathematical Olympiad—members of the team, which numbered four to eight people each year, were admitted to the colleges of their choice without having to take the entrance exams. Boris Sudakov, a boy Rukshin had believed was no less naturally talented than Perelman but who had performed erratically in competitions, chose the first strategy. Alexander Levin, the reigning number two at the math club, chose the second strategy. By the time Perelman was in his last year of secondary school, he had one silver and one gold medal from the All-Soviet Math Olympiad to his name, and it seemed a certainty to him and to everyone around him that he would travel to the international competition and return triumphant, assured of a place at the Mathmech. It was a relief for Ryzhik, who was par
ticularly loath to meddle in the life of a student he respected so highly, especially since trying to prove the anti-Semitic nature of admissions policies to either Grisha or his mother might very well have been an impossible task. Lubov Perelman, it seemed, had an extraordinary gift for denying the obvious, and she had passed this gift along to her child.

  The basic questions of parenthood—what to tell your child, when, and how much—are tinged with fear in a totalitarian society, where dissidence is punished. What if the child says the wrong thing at the wrong time, exposing the family to danger? My own parents, active consumers and sometime producers of samizdat, chose to give me unfettered access to information, occasionally admonishing me to keep my mouth shut. On several occasions I spilled more than I should have, and this fortunately went unnoticed—but while I am ever grateful to my parents for treating me like an adult, the risk they took was probably unwise. Most other parents kept to a policy of never exposing their children to anything that could not be safely repeated at school. Lubov Perelman seems to have pursued an even more radical strategy: she taught her son that the world worked exactly as it should.

  “He never believed there was anti-Semitism in the Soviet Union,” Rukshin told me on a couple of occasions, repeating this observation with the kind of joyous wonder with which he had informed me that Grisha was never interested in girls, as though the denial of anti-Semitism too were evidence of Perelman’s unparalleled purity.

  When I asked Golovanov, who also happened to be Jewish, whether this was true, he was uncharacteristically stumped. No, he had never discussed the topic with Perelman, but how could anyone in his right mind believe there was no anti-Semitism in the Soviet Union? “He was not stupid,” Golovanov assured me.

  How can one not believe in something as evident as Soviet anti-Semitism? This raises two other questions: What is belief? And what is evidence? Soviet anti-Semitism was not quantifiable. Nor was it absolute: for example, the number of Jews accepted to Mathmech appeared to vary from year to year. Never was discrimination practiced so openly as to be articulated: when a Jew was turned down for a job or for university admission, a reason other than the person’s Jewishness was generally cited. When Perelman was thirteen, all the boys who took prizes at the Leningrad citywide math olympiad at his grade level3 were Rukshin students and Jewish; the surnames of prize takers and honorable-mention recipients included Alterman, Levin, Perelman, and Tsemekhman. This was worse than just four Jewish boys; this was four obviously Jewish boys. As Rukshin remembered it, the university professor who chaired the city jury that year, himself a Jew, looked at the list and sighed. “We ought to have fewer of these sorts of winners.”

  Starting in the eighth grade, those who took first and second places in the city olympiad would advance to another round of competition4 to select the city representative for the national competition. Predictably, the winners that year came from Rukshin’s club: Alexander Vasilyev and Nikolai Shubin took first place; Perelman, along with two more boys and a girl from Rukshin’s club, took second place.5 The rules dictated that the six teenagers advance to the selection round, but all six were Jewish. Still, the names of the two top-prize takers were not as obviously Jewish as Perelman was: Vasilyev was a Slavic surname, and Shubin, while Jewish, did not sound quite as offensive as Perelman did to those who were offended by the Jewishness of others. So, apparently in an attempt to avoid reprimands, the organizers suggested scrapping the selection round and simply sending either Vasilyev or Shubin to the nationals. Rukshin waged a fight to have a selection tour and to have Perelman take part in it. Rukshin’s ambitions as coach melded with his indignation on behalf of his favorite student, and he succeeded—almost: the organizers agreed to hold a selection round, but only between top scorers Shubin and Vasilyev. “I pleaded, I swore, I screamed, and I threatened,” recalled Rukshin. In the end Perelman was not allowed to compete, but the organizers said he could attend the selection round to practice solving problems if he so wished.

  Except that Perelman did not want to attend the selection round. “He kept saying, ‘But I really didn’t solve as many problems as Shubin and Vasilyev,’” said Rukshin. “I mean, if ever the Soviet regime could rear a Jewish boy who believed that man was always rewarded in accordance with his accomplishments, here he was.” Finally, Rukshin strong-armed Perelman into attending, and Perelman ended up solving seven out of seven problems—the next-best result was three out of seven—and going to the nationals. Rukshin chalked up another strategic victory in the battle against anti-Semitism even as Perelman demonstrated that the existence of anti-Semitism could not be proved. So why should he believe in it? That would be like believing an object was a sphere just because it looked round only to discover that it had a tiny hidden hole.

  My own father had cried following his first round of university admissions exams, just as Ryzhik had. My mother had walked out of her exam when she saw the word Jewess in black ink next to her name on a sheet of paper on the examiner’s desk. Both of my parents had been warned about anti-Semitic admissions policies and had decided to trust their abilities to break through. As long as I can remember, they talked of the prospect of my own college entrance exams with dread—what I now understand to be the chilling dread of trying to explain to your child that some of the world is so unfair as to make all hope futile. I know that this dread was a large part of the reason for my parents’ decision to emigrate.

  Lubov Perelman acted as though reality corresponded to the rules—and for the moment, reality accommodated her, albeit with a lot of help from Grisha Perelman’s small phalanx of supporters.

  Sometime in the fall of 1981 Alexander Abramov, the young coach of the Soviet IMO team, traveled to Leningrad to ask Rukshin who among his students would likely be joining the team. Rukshin’s reputation as a brilliant coach had already been established, so it was certain he would be offering someone. He named two people: Perelman and Levin.6 Both were graduating from high school that year, making it the last year they were eligible to compete.

  Members of the math club believed Perelman to be the undisputed and unreachable number one and Levin his distant but stable and also hardly reachable number two. City competition results bore this out, and, in the self-absorbed way of adolescents in general and members of Rukshin’s club in particular, the students believed Perelman and Levin were the top two mathematics competitors in the whole huge country. In Rukshin’s opinion, Levin’s potential indeed equaled or even exceeded Perelman’s. But in this competition, Levin had too many disadvantages. “His parents did not understand what it was to be a mathematician,” explained Golovanov. “Grisha’s mother understood it very well, while Levin’s parents thought studying mathematics might be useful if one wanted to become an engineer.” In other words, they failed to see the value of the single-minded devotion Rukshin inspired in his students. Levin’s parents apparently insisted he pay as much attention to his schoolwork as to the math club. “He was too good a student at the school, consequently he did not always attend the club, and that was his silly accident, the gate that had been left open, so Alik was done in by his conscientiousness,” said Golovanov, referring to the fortress gate that, legend has it, brought down Constantinople in the fifteenth century. “At the All-Soviet competition he solved all the problems with the exception of the one that had actually been solved at the club.” It was a freak accident: only very, very rarely and contrary to all rules and logic was a problem used in the All-Soviet competition one that had been floated elsewhere. But since every math problem had a human author and an idea behind it, no one could guarantee uniqueness. And in this particular case, in April 1982, a problem that was offered to competitors in the All-Soviet Mathematical Olympiad was one whose solution had been written down neatly by every member of Rukshin’s math club—at least, everyone who had shown up. Alexander Levin had not come to the club that particular day. He did not solve the problem in the competition,7 and he did not make the Soviet IMO tea
m. And though surely this was not intended by Levin, Rukshin, or even Perelman, it was fitting; that year only Rukshin’s favorite, brightest, singular student went to the IMO. Rukshin had worked for this for six years, shaping Grisha into the ideal competitor.

  The Leningrad city competition looks very much like any session of a Petersburg math club:8 competitors sit in classrooms solving problems, and when one considers a problem solved, he raises a hand to call attention to himself; a pair of judges then escorts the competitor out of the classroom to listen to his solution and make a judgment on the spot on its quality; the competitor then returns to the classroom to either rework his solution or go on to another problem. As Rukshin recalled, at the selection round Perelman was explaining his solution to one of the problems. He had talked his way through one of the possible outcomes when the two judges who were his audience turned to leave, saying that his solution was correct. “Wait!” he shouted,9 grabbing one of them by the tail of his suit jacket. “There are three more possible outcomes.”