Perfect Rigour

by Masha Gessen

  The schools taught children not only how to think but also that thinking was rewarded—and rewarded fairly. In other words, they reared people who were very ill-suited for life in the Soviet Union — or, one could argue, for life in the real world anywhere. The schools produced freethinking snobs. A graduate of Kolmogorov’s boarding school recalled studying with Yuli Kim, one of the Soviet Union’s best-known dissident singer-songwriters, who taught literature at the school (until his firing was forced by the KGB in 1968): “Because of him, we felt like gods:55 We lived our lives and had our accomplishments, and we had our own Orpheus to sing our praises.”

  The Soviet system, fine-tuned to all shades of difference, rejected these kids and put every possible obstacle in their way once they graduated. The year I would have graduated from math school in Moscow (had my family not emigrated to the United States), none of the graduates would be admitted to Moscow University’s Mechanics and Mathematics department—and the teachers made a point of warning us about this. Leningrad’s School 239, most of whose graduates were convinced—some say rightly—that they could easily sleep through their freshman year at any university and still ace the exams, saw so few of its students allowed into Leningrad University that it had to forge a relationship with a second-tier college56 that would take its kids, overeducated and overconfident as they were. They may have believed they were gods, but when they emerged from high school, they found themselves outside the well-organized and well-guarded mainstream of Soviet mathematics. Not all of them—perhaps not even a majority — would become mathematicians, but those who did were destined for the very strange world of the alternative mathematics subculture.

  Kolmogorov himself was no stranger to the official mathematics establishment. He was eccentric for an insider, protected in large part by his larger-than-life standing in international mathematics, earned early and maintained with apparent ease for decades. Still, he spent months and years of his life negotiating teaching hours and salary increases and apartments for assorted members of the Academy. He was, by all accounts, extremely careful in what he said and did—and he made no secret of his fear of the secret police (and indeed hinted at a cooperative relationship with them57)—but in 1957 he was fired as dean58 of Moscow University’s Mechanics and Mathematics department following dissident rumblings among his students.

  Daily exigencies of life within the establishment notwithstanding, Kolmogorov held to the ideals he passed on to his students. He parted with his ideas with famous ease:59 after doing a few weeks’ work on the foundation of a problem, he would give it to one of his students, who might spend months or a lifetime working on it. He claimed little interest in the authorship of solutions60 as long as the great problems of mathematics were indeed solved. In other words, even when he was recognized and celebrated by the establishment as the greatest Russian mathematician of his age, he espoused every ideal of the Soviet mathematical counterculture. His numerous students were that culture’s leaders, and Kolmogorov himself its guiding light.

  His vision was gospel to his students and their students and their students’ many students. Kolmogorov had envisioned a world without dishonesty or backstabbing, without women and other undue distractions, with only math and beautiful music and just rewards for all; several generations of Russian mathematical boys believed in it. Wrote Mikhail Berg: “Many of us would have wanted to take the school with us after graduation, like a turtle’s armor, because we could feel comfortable only within the confines of its precise and logically understandable rules.”

  A life within the confines of logical and understandable rules was what Rukshin offered Perelman in exchange for the heroic feat of learning English in a summer. For his part, Rukshin would get to realize his own project. Math clubs are to math schools what afterschool band practice is to the High School of Performing Arts: one is a respite from the rest of school life but might produce brilliant professionals; the other offers total immersion and a vision of the future. They are two different, if related, worlds. Now, if Rukshin had his way, the two worlds would meld. For the first time in the history of Leningrad math clubs, virtually all suitably aged members of the club would go to high school together. Ordinarily, they had to apply—and be accepted—to receive their last two years of secondary education at either of the two Leningrad math schools, and they were spread among different classes so as not to skew math instruction too much in any particular class. It was generally expected that the club mathematicians, like professional athletes among talented amateurs, would spend some of their time at the math schools being bored and waiting for others to catch up. Rukshin had a radically different idea: create a class that consisted mostly of math-club members, add some kids from a physics club, fill it out with the help of other exceptionally gifted and motivated children, and—most important, he thought—keep everyone else out. No one who was not obsessed with mathematics, or at least with the sciences, should be allowed into the class “lest the rot catches on and spreads” was how Rukshin put it to me a quarter of a century later. When he was in a more generous mood, he explained that he’d wanted his charges to be surrounded by other kids with similar interests, since “there wasn’t an Eton School for them.” Plus, there were organizational issues: “They could all come to the club together, it wouldn’t be like one was getting out of school at one and another at four. I could make arrangements with their teachers regarding what they would be studying in mathematics and physics at school and what I would cover at the club. And concerted action is always better where it comes to gifted kids. Many of them were black sheep, and this way they could have a teacher who would shield them the same way I did.” Once the coach, and his math club, became the center of these children’s lives, he was not going to budge.

  The only snag in the plan to create a bigger and better cocoon for Perelman and his ilk was the foreign-language issue. Soviet schools generally offered either English, German, or French starting in fifth grade, and transferring from school to school was contingent on a language match. School 239 offered English and, if enough students required it, German; Perelman had been studying French for four years. Rukshin claimed his own English was bad and to illustrate this offered, “My knowledge of English leaves very much to be desired,” pronounced with the queen of England’s accent. This was vintage Rukshin: either his English was excellent and he was just fishing for compliments, or his English was as poor as he claimed but he had memorized that one phrase. Whatever the case, it was Rukshin and his bizarre English-learning project that took over Perelman’s life the summer he turned fourteen.

  Perelman’s mother allowed her son to submit to this taxing regimen without protest, as she had done with all of Rukshin’s demands—even though this meant keeping the family, which now included a toddler named Lena, in the city for the summer instead of going to the dacha like all the other Leningrad families that belonged to what might have been called the Soviet middle class. Rukshin’s own mother-in-law, he said, was furious: “Not only had her daughter married a poor mathematician but now he was dragging his Young Pioneers home.” Since they were not welcome in the apartment, Rukshin and Perelman spent their days walking the numerous scenic pathways in the town’s huge historical parks, first following textbooks and then teaching themselves conversational English by conversing in it. Once again, Rukshin proved to be an outstanding coach. At the end of the summer, Perelman was fit to study at School 239. Years later, he wrote in excellent English, not only correct but idiomatic—and while that was partly a result of the couple of years he’d spent in the United States as a postdoc, it rested on the foundation he received from Rukshin during those walks in the parks.

  Now all of Rukshin’s “black sheep” could go to school together. Twenty-seven years later I spoke with a Russian Israeli psychologist61 who was married to Boris Sudakov, one of Perelman’s club mates and, later, classmates. Boris had suggested I talk to her because she had seen something off balance in Perelman when
he visited Israel in the mid-1990s. I wondered if she’d noticed something then that had been a portent of his later oddness. “Come on,” she said, apparently irritated. “I’d seen Boris’s other classmates, and they are all like that. Weird. It’s like they are made of different stuff.” The literal translation of the Russian expression she used is “made of different dough,” which is particularly appropriate for the pudgy, pale boys who grew up into pale, doughy men.

  Collecting these kids in a single classroom struck many of the teachers at School 239 as a crazy idea. “They’d speak up at the meetings, they’d say that it would just be too hard,” recalled current principal Tamara Yefimova, who had been the vice principal back in those days. “I mean, there was this boy, for example, he was so talented, and his teacher would come to me almost in tears, and I’d ask the boy what happened, and he’d say, ‘Tamara Borisovna, I left home on time, but then I just got to thinking.’ And they were just like that, so difficult to understand: they’d be sitting in the back of the class, she’d be saying her thing, and who knows what they were doing back there, maybe thinking again.” The principal, a short, stout woman with a crewcut, looked and sounded more like everyone’s favorite gym teacher than the head of an elite school that imagined itself to be a Russian Dalton or Eton. In her youth she had run a secondary school on a military base someplace she still tried not to name. She had been sent down to School 239 by the Party to keep watch over the school’s exceedingly liberal atmosphere and was apparently accepted there as a reasonable evil: She clearly possessed a genuine admiration for the intellectuals she found herself commanding. She finessed the endless Party inspections to which the school was subjected, and she succeeded in accomplishing things none of her more cultivated predecessors had pulled off—like repairing the leaky roof and restoring the school’s magnificent auditorium. But her support for a math-club class apparently struck some of the teachers62 as a misguided expression of her fondness for intellectualism; she claimed that several teachers actually left in protest. Still, in September 1980, the first club class entered School 239.

  Some people are born to be schoolteachers. I have met a few, and they are an unusual breed: supremely sensitive, thin-skinned like the children or adolescents to whose needs they are so finely attuned, yet secure in the understanding that their best students will develop into adults who are smarter and altogether better educated than they are. Valery Ryzhik63 was born, in 1937, to teach mathematics. He was twenty-five when he started teaching at School 239, where he helped create the mathematics curriculum, and he had been teaching mathematics for twenty-eight years when, over his vocal objections, he was handed the club class of Rukshin’s creation. His job was to teach them math and also to serve as the class teacher, something like a homeroom teacher at an American high school.

  Ryzhik had the idea that teaching School 239’s average students—who had been top students at other schools, but not the exceptionally gifted sort—was best accomplished by teaching the very best students in such a manner that the rest got pulled along. Students recalled that in ordinary years he picked five top students64 at the start of the school year and focused all his attention on them while the others learned by watching. “There would be inspectors criticizing me for not working with the average kids,” Ryzhik recalled in 2008, when he had been a practicing schoolteacher for nearly half a century. “And I would say, The issue is not working with the average kids; the issue is working with the gifted kids — and that’s really hard, because, for one thing, they are all different. Another is, if you teach them in a way that’s not interesting for them, they can tolerate it for a day or two and then they get bored and start wondering what they are doing at this school. And that can’t happen. You have to make their eyes light up, and I can’t explain to you how you do that.”

  Having a group of ten exceptionally gifted students thrown at him along with twenty-five other adolescents presented Ryzhik with an apparently insurmountable challenge. The club kids were all different. Alexander Golovanov, the wunderkind, sat up front “and wouldn’t let anyone get a word in,” Ryzhik remembered. “Such a little boy.” Grisha Perelman sat in the back. He never spoke up unless a solution or an explanation required a correction. “And then he would raise his hand.” Ryzhik mimicked the movement, lifting his hand off his desk only slightly. “You could hardly see it. His was the final word.” Still, Perelman never did what other exceptional students did: he never let himself grow distracted and, say, fiddle with a different problem during class. He sat and listened to discussions that were of no pragmatic use to him; rules were rules, and if one came to class, one listened.

  Ryzhik had met kids like Perelman before. “We got someone like that every year,” he told me. “What’s curious is that they were all marked by an extraordinary modesty, a schoolchild’s reserve. There is never any conceit, and I think that’s one of the necessary conditions for something extraordinary in the future. I have seen kids like Golovanov too, but I’ve never known them to do something outstanding in mathematics—they stop at the professorial level. The ones who make it beyond are a different kind of person.” With his trained teacher’s eye, Ryzhik spotted an awe-inspiring student.

  Ryzhik attempted to form a personal relationship with Perelman—partly at the request of Grisha’s mother. She came in early in the school year to ask Ryzhik to try to ensure two things: that Grisha ate something while at school and that he tied his shoelaces. A Western mother might have bought her son slip-on shoes to wear, but Soviet stores offered no such option for the absent-minded schoolchild. Ryzhik never succeeded at either task: Perelman walked around with his laces flopping about, and he would not eat. “Maybe he could not get distracted,” suggested Ryzhik. “Maybe his entire nervous system was so tuned to the learning process that he could not stray from it. Or maybe it was a blood pressure issue—he might have felt that if he ate, his thinking would not be as precise.” Another possibility was that school food was too varied for Perelman; the cafeteria had a different menu for each day of the week. In the math-club group, every boy had his own pronounced food preference. So in the afternoons, when they made the walk from the school to the Palace of Pioneers, they made quick pit stops for the refueling of each club member. Naturally, Perelman’s system was the simplest and the fastest: he would go to the bakery on Liteyniy Prospect,65 less than halfway between the school and the club, and buy a Leningrad loaf, a large piece of wheat bread with raisins on the inside and crushed peanuts on top. Perelman did not eat peanuts, so Golovanov would scrape them off and eat them. Sometimes the ebullient Golovanov would try to help himself to the raisins also, whereupon Perelman would slap his hand hard.

  Mondays Perelman would stay at school after class and play chess in Ryzhik’s chess club. They played fast chess, a game that is believed to require more intuition than calculation, but Perelman did very well, even winning twice against Ryzhik himself—probably because what chess players call intuition is in fact the ability to grasp complex systems in a single take,66 which was exactly Perelman’s strength. But in all the weekly afternoons together, the tactful and awestruck Ryzhik never tried to venture into more personal territory with Perelman, never broached a subject that reached beyond school, chess, and mathematics. Nor did he choose him as one of the students he regularly addressed in the classroom; rather, he kept him as his “command reserve,” as he put it, for particularly difficult problems.

  To the general troops, Ryzhik tried to be an all-encompassing leader. On Sundays—the only day of leisure for Soviet schoolchildren at the time—he would take his class out of the city for hikes and orientation races. Summers, he would take groups of children on weeks-long trips in difficult terrain in the Caucasian mountains or the Siberian forests. Perelman never went. Ryzhik believed this was because he was a homebody, though he apparently did submit to the requisite math-school culture hikes organized by Rukshin for his club kids; his out-of-school self belonged to Rukshin. Both Rukshin and Ry
zhik practiced the Kolmogorovian approach: while dragging the children on long and grueling walks, they tried to shape them into the human beings they wanted to see—with Rukshin focusing more on literature, music, and all-around erudition,67 and Ryzhik on chivalry, honesty, responsibility, and other universal values.68 Ryzhik had been doing this for more than twenty years, but with the club class of 1982, he felt he failed.

  “The class split into two groups,” recalled Ryzhik. “One was a group of learners, and the other had different values. And I never did manage to connect them.” The math-club boys formed the heart of the learners’ contingent. During one of the Sunday hikes in their second and final year at School 239, one of the math-club students got a nonclub classmate involved in a chemistry experiment. He handed him a substance but failed to warn him it was highly explosive if heated. When the boy approached the campfire, the stuff blew up in his hand, severing it at the wrist. “The boy survived—thank god for that,” said Ryzhik. “And then I recall I had a talk with the kids. I remember it well. I said, ‘Imagine we are on a trip. And say, we have set up camp somewhere for the night. And say there is a lake there, and I do not like the look of the lake and I judge the approach to be unsafe, so I tell you not to go there without my oversight under any circumstances. And now imagine that one of you has decided to go for a swim during the night anyway. Who will wake me up to tell me what’s happening?’ No one! And I said, ‘Do you see what’s happening? A child might die! You may not understand this, but I do. And still, based on this silly child-corporate-value system of yours, you are going to keep quiet. That means that story with the explosion taught you nothing. You still don’t get it.’”

  Rukshin’s club-class experiment upset the delicate balance that existed at School 239 and at other math schools, as well as in the adult Soviet world, where the mathematics counterculture was allowed to exist quietly so long as it did not take its ideas to the streets. In Ryzhik’s class, the usual rules of nonconfrontation between the geniuses and the rest no longer applied: the genius contingent was too large, too male, and too adolescent for that. It was war, and Ryzhik was right in thinking he had failed to convince the students it was wrong. A quarter of a century later, the student who had slipped his classmate the bomb referred to the incident occasionally in his blog,69 recalling it with a clear lack of remorse. There is no single explanation for what happened. Perhaps Rukshin’s boys perceived their classmates as representatives of the system that had humiliated them at other schools; perhaps they had already grown to perceive anyone outside their small circle as the enemy. In any case, as always happens in war, the two sides saw each other as less than human. Ryzhik discontinued the hikes following this conversation. The following year, he cut his class time down to one day a week so he could focus on finishing a geometry textbook that he had been test-driving with his students. The year after, when he tried to return to full-time teaching at School 239, Ryzhik was turned away, apparently because the principal had come under increased pressure to cut the number of Jewish teachers.70