by Masha Gessen
Perelman needed someone to guide him along his path to dinosaurhood—or at least someone who would not get in his way and who would shield him from others if necessary. He was strongly drawn to Viktor Zalgaller,4 a geometer then in his sixties.
I interviewed Zalgaller in early 2008 in Rehovot,5 about twenty miles south of Tel Aviv. The town was built around the Weizmann Institute, a mathematics research facility with which Zalgaller was affiliated though he did all his work at his apartment, where his wife lay nearly motionless in the final stages of Alzheimer’s disease. “The woman no longer manages the house,” Zalgaller said apologetically as he welcomed me in. It was a messy place, lived in awkwardly, with Zalgaller’s crumpled bedding on the living room couch, and a clutter of books, papers, and teacups where apparently a homey order had once reigned. Zalgaller himself was similarly unkempt: unshaven, wearing a crewneck sweater over gray pajamas, but entirely coherent and pointedly businesslike in his manner. He spoke of Perelman with awed affection, which was what he had always felt for him: “I had nothing to teach him from the beginning,” he claimed.
Zalgaller was a World War II veteran, a charismatic teacher who had almost single-handedly shaped6 the mathematical curriculum and teaching style of School 239 (in the 1960s he had taken time off from research and university teaching to do this), and he was an incomparable storyteller. All of this had made him popular around the university and at the Leningrad Mathematics Institute, but none of those qualities held any special appeal for Perelman. “He liked me, I have no doubt about it,” Zalgaller told me. “It may have had something to do with ethics. What I thought about what people must do.” When I asked him to elaborate, Zalgaller claimed, “He liked my style of communicating with students. He must have known that I would not be strict and that studying with me would be interesting.” In fact, it seemed Perelman had fairly little concern for the teaching style of his instructors. What must have drawn him to Zalgaller was a more particular aspect of the way he related to the world, exemplified by a story Zalgaller told me but forbade me to tape, apparently because it concerned him, and not Perelman—Zalgaller thought it improper to talk about himself. I wrote it down from memory as soon as I left his apartment.
Like most Soviet men of his generation, Zalgaller joined the Red Army in the early days of World War II, and like a very lucky few he spent the entire four years of the war in the service and survived with nary a scratch. He graduated Leningrad University in the late 1940s, just as Stalin’s anti-Semitic Campaign Against Cosmopolitans was getting in full swing and Jews all over the Soviet Union were finding themselves universally turned down by colleges, graduate schools, and employers. Zalgaller was one of five Jews from his graduating class who applied to stay on in graduate school. All were deserving, thought Zalgaller, but when the list of those accepted for graduate study was posted at the university, Zalgaller found his own name on it—and none of the other Jewish students. So he turned the graduate school down.
The old man saw that I now expected him to tell me that he was unwilling to play by rigged rules, that he wanted to stay on in graduate school but could not if he felt he was doing it at another student’s expense. “I was no fighter against anti-Semitism,” he said, correcting my unspoken misconception with evident irritation. “I just didn’t want to be dependent on those people.” If he was the only Jew accepted, he would be in receipt of a favor—and that was what he turned down.
Zalgaller proceeded, stubbornly and almost miraculously, to construct a career on his own terms, accepting only those favors he was certain he could repay and conducting himself in accordance with a code that was not only more confining than that of others but also—perhaps equally important to Perelman—often indecipherable to anyone but Zalgaller himself. In the early 1990s, when Soviet researchers started having to write their own funding proposals, Zalgaller devised an ingenious way to solve the perceived dilemma of making the direction of his research contingent on the preferences of funders: he applied for money for projects he had already successfully completed but had not published and then used that money to finance his next project. Surely it was this complicated but internally coherent set of ethical perceptions and behaviors that appealed to Perelman, who asked Zalgaller to be his thesis adviser.
“I had nothing to teach him,” Zalgaller repeated. “So what I did was just give him small problems that had evaded solution. Once he solved them, I saw to it that they were published. So by the time Grisha graduated from university, he already had several published papers.” In other words, he continued to feed Perelman’s brain, continuing what Rukshin had done and ever so gently helping Perelman find his way as a self-declared dinosaur.
Perhaps the single most fateful incident in Perelman’s lifetime was the appearance, in Perelman’s first year at Leningrad University, of a larger-than-life presence in the form of a small old man with a square gray beard. His name was Alexander Danilovich Alexandrov7 (his patronymic was generally used, in order to distinguish him from numerous other Alexander Alexandrovs); he was a living legend, and miraculously and almost ridiculously, he was teaching geometry to first-year Mathmech students.
Alexandrov had started out as a physicist but dropped out of graduate school8 in the 1930s because, he once explained, “I can’t promise that I’ll always do what I’m expected to do.” One of his two advisers, the physicist Vitaly Fok, reportedly said to him, “You are too decent.” The other, the mathematician Boris Delone, added, “You are too much not a careerist.” He went on to defend two dissertations by the time he was twenty-five, receive a number of prestigious prizes, and in 1952 become president of Leningrad University at age forty.
“Alexandrov had a great influence on Grisha,” claimed Golovanov, who had witnessed the beginning of their relationship firsthand: he too attended Alexandrov’s freshman geometry course that year. “He was just the type, psychologically, who could exert that kind of influence. To sum up who Alexandrov was, briefly: he was a Young Pioneer of colossal intellectual might. I know quite a lot about him, and I think he is a person who never once in his life wanted to do something bad. Naturally, with this sort of approach to things, he committed bad deeds on an industrial scale—but he never once wanted to.” Golovanov was fully aware that his description fit his friend Perelman just as well as it did their teacher. “There is a wonderful [Latin] saying,” he continued, “that people consider incorrect, for some reason: Vos vestros servate, meos mihi linquite mores, ‘I will go my own way and let others stick to theirs.’ From a moral standpoint, this position is unassailable. And I think you know at least one other person who acts in accordance with this motto—he just happens not to be a university president,” unlike Alexandrov. He happened to be Grisha Perelman.
Alexandrov owed his appointment as president of the university to his background as both a physicist and a mathematician: the two sciences had grown so important during the Soviet nuclear push that physicist-mathematicians had been chosen over Party functionaries to run the Leningrad and Moscow universities in the early 1950s. He was also a member of the Communist Party and remained one,9 in his true-believer style, until his death in 1999. He was by no means a loyalist, however. His most remarkable accomplishment as president of Leningrad University was preserving the study of genetics—a science banned under Stalin. While geneticists who had worked elsewhere were either jailed or reduced to employment at animal farms at best and menial jobs at worst, he ensured that seminars in genetics continued at his university. After Stalin’s death, he even managed to get international geneticists to speak there, long before official Soviet science began its slow reacceptance of genetics. In the 1950s, he played a key role in protecting mathematics from a similar destructive campaign that had seemed to be taking shape. He managed, almost single-handedly, to reframe it10 as a movement to protect the prestige of Soviet mathematics from imagined Western efforts to denigrate Soviet achievements.
Alexandrov also risked his c
areer—and ultimately lost his post as university president—by supporting mathematicians who came under attack for being either ideologically unreliable or Jewish. In 1951, the year before he became university president, he managed to intervene when the university’s department of mathematical analysis was in danger of dissolution because it was staffed primarily by Jews. The department’s members had exhausted all their appeals—no one felt powerful or brave enough to help. Then one of the mathematicians dared ask Alexandrov to step in,11 which was a desperate move on her part, since she had previously made an enemy of Alexandrov by mocking his sideline studies in philosophy. Alexandrov responded and devised a way to stem the attack by replacing the department chair. Almost forty years later, Alexandrov would play a key role in securing Perelman’s academic career in the face of anti-Semitic discrimination, and another ten years after that, Olga Ladyzhenskaya, the daring mathematician from that department of mathematical analysis, would become the last person who successfully shielded Perelman from the world of real-life mathematicians.
Alexandrov was a believer—a literal one. He had engineered Leningrad University’s move out of the city, and when a former student reproached him for this years later, as he was traveling to the university on one of the overcrowded commuter trains with hard bench seats, Alexandrov shouted for the entire train car to hear: “I believed in the Party program! It said in the appendices that Leningrad would be developing southward and the center would move southward! And then they started building northward.” The former student, a very prominent mathematician, commented in a later memoir12 that by the 1960s everyone knew Party documents were not to be believed. He was probably missing the point: Alexandrov, like Perelman, lacked the disbelieving gene; he had the ability to reject, resist, and even hate, but he could not disbelieve.
Alexandrov was fired as the president in 1964 and proceeded to spend the next two decades in what still amounted to exile13 of the not-entirely-self-imposed variety in Siberia, helping to create a science town there. In his seventies, he returned to his university with what turned out to be a vain hope of reclaiming a place there: he wanted to fill a vacant chair in geometry.14 In the run-up to the chair election, he taught a first-year course and charmed students in part because of his openness about the absurdity of his predicament. He was given to quoting, among other things, the numerous poems Mathmech students made up about him. Poems like this one:
Danilych labored in the math field
Danilych rose every morning
Too bad his efforts could but yield
A course the students found boring
Eventually Alexandrov’s hopes of obtaining the chair in geometry were dashed15 by academic and Party authorities, and he moved to a position at the Leningrad mathematical research institute—but not before he had chosen Grisha Perelman as his protégé. While other students might have been drawn by Alexandrov’s legendary status, his informal approach to teaching, and his intellectual expansiveness, Perelman gravitated not to Alexandrov’s style but to his essence, contradictory and rigid as it was.
Indeed, had it not been for Alexandrov’s bizarrely fearless management of the university, Perelman’s career might have taken an entirely different path. As it happened, the study of topology was barely represented at the university until the early 1960s. When Alexandrov looked for a person who might launch the field in Leningrad, he stumbled upon Vladimir Rokhlin, a student of Kolmogorov’s and Pontryagin’s who was then eking out an anchorless existence in Moscow. He had served time in the Gulag, was still under surveillance, and was generally considered unhirable.16 Alexandrov brought Rokhlin to Leningrad and managed to provide him not only with a teaching job17 at the university but also with an apartment. In Leningrad, Rokhlin would see twelve of his students’ dissertations to completion, including that of Mikhail Gromov,18 one of the world’s leading geometers today and the man who would be largely responsible for introducing Perelman to the international mathematics community.19
Perelman likely did not know much of this about Alexandrov, and if he had known, he might have disregarded what amounted to Alexandrov’s heroism as mere politicking. Nor could he have predicted the role Alexandrov would play in his career. What certainly attracted Perelman to Alexandrov were his approaches to mathematics and to life in general.
On one hand, Alexandrov came from the academic school of unbounded generosity. “He would give topics and promising ideas away to his students,”20 wrote Zalgaller, who was a student of Alexandrov’s. On the other hand, he viewed mathematics as one long problem-solving marathon. A student recalled walking into Alexandrov’s office.
“‘So have you proved it?’ Alexandrov asked.21
“‘What should I have proved?’
“‘Anything!’
“It would be difficult to overestimate the influence of such constant expectation of results,” wrote the former student. “From that point on I aimed to be prepared for this question.”
Alexandrov was the undisputed king of geometry in Leningrad and, possibly, in all of the Soviet Union. Another student recalled Alexandrov’s reaction to a request to write a history of Soviet geometry.22 “That would be immodest,” Alexandrov had said. “There was no one there but me.” Another student wrote that he had chosen to become a geometer after hearing another professor’s words23 to the effect that “Alexandrov has discovered whole new worlds in mathematics and is now inhabiting them all by his lonesome.” Perelman’s dinosaur remark referred mostly to Alexandrov.
Around the time Perelman met him, Alexandrov was said to have made the following comment24 at a geometry seminar: “Everyone is a bastard, everyone is bad, with the possible exception of Jesus Christ. Einstein is bad too, because he did not leave America after the nuclear bomb was detonated over his objections.” He once wrote, “In the end, through the general interconnectedness of events,25 a person becomes, in some way or another, to a greater or lesser extent, party to everything that happens in the world, and if he can exert any influence whatsoever on any event, then he becomes responsible for it.” This view of individual responsibility squared perfectly with Perelman’s concept of honesty, so he adopted Alexandrov’s criteria as his own and would later apply them to everyone he encountered.
When Perelman entered the university, he became, at the advanced age of sixteen, practically an official adult. A more conventional teenager might have celebrated this transition by reassessing the rules, reshuffling authority figures, or claiming more independence. Perelman made the rules stricter, and added Zalgaller and Alexandrov to his pantheon of unassailable authority figures, where they joined his mother and Rukshin. Perelman adopted more-formal signs of his new status as a grownup: he stopped shaving, and in the math-club world, he went from being a student to being a teacher.
Following the established Kolmogorovian tradition, Rukshin sought to turn his first math-club graduates into the first math-club instructors who came from within. He chose Perelman and Golovanov—Perelman being his favorite student and Golovanov showing, even at fourteen, the potential to become a great teacher in Rukshin’s mold. Rukshin took both to summer camp as instructors. Neither experiment proved fully successful. Golovanov, it turned out, was just a boy and generally acted like one; this would pass with age, and he would indeed grow into a math coach second in mastery and charisma only to Rukshin. Perelman turned out to be Perelman, which is to say, rigid, demanding, and hypercritical; these qualities would only intensify with age, ultimately making it impossible for him to be any kind of teacher or, indeed, communicator.
Early on in his career as an instructor—either during or right after his first year at the university—Perelman observed, in conversation with Golovanov, that the basic military training that was among Mathmech’s required courses had proved useful because the military bylaws he had had to memorize could be applied directly to the running of the math club. “He said this with a smile, of course, beca
use he is very smart,” recalled Golovanov. “But one could tell that the share of humor in this supposed joke was no more than ten percent.”
At camp following his first year, Perelman served as an instructor to a remarkable group of mathematicians two years younger than he. They included Fedja Nazarov,26 now a professor at University of Wisconsin; Anna Bogomolnaia,27 now a professor at Rice University; and Evgeny Abakumov,28 now a professor at the Université de Marne-la-Vallée in Paris. Every morning Perelman gave them a set of twenty problems—roughly double the club’s usual semiweekly dose. The problems were extremely difficult, and the level of difficulty was increased with little regard for the students’ actual abilities and achievements. “The general concept always was that the carrot should be hanging just barely above the level to which the rabbit could jump,” Golovanov explained to me. “But Grisha believes that the rabbit should always be jumping higher and higher.” A student who failed to solve at least half of the problems by midday was told he or she could not have lunch. “They still got lunch, of course,” recalled Golovanov. “But undeservedly.”