After I got my exit visa and it became clear that my trip was becoming reality, I had to come clean with Yakov Isaevich and tell him about my “extracurricular activities”: my mathematical work with Feigin and the invitation from Harvard. Naturally, he was very surprised. He was sure that I was devoting all my energy to the medical projects on which I was working with him. His first reaction was quite negative.
“And who is going to work in my lab if you go to Harvard?” he asked.
At this point Yakov Isaevich’s wife, Tamara Alekseevna, who always warmly welcomed me at their home, came to my rescue:
“Yasha, you are talking nonsense,” she said. “The kid got invited to Harvard. This is great news! He should definitely go, and when he comes back he will continue working with you.”
Yakov Isaevich reluctantly agreed.
The summer months went by quickly and the date of my departure, September 15, 1989, came. I flew from Moscow to New York’s JFK airport and then to Boston. Jaffe could not meet me at the airport personally, but he sent a graduate student to pick me up. I was taken to the two-bedroom apartment that the Math Department rented for me and another Harvard Prize Fellow, Nicolai Reshetikhin, who was arriving a few days later. It was in the Botanic Gardens, an apartment complex owned by Harvard, less than a ten-minute walk from Harvard Yard. Everything looked different and exciting.
It was late at night when I got to my apartment. Jet-lagged, I immediately went to sleep. The next morning I went to a nearby farmer’s market and got some produce. Back home, I started making a salad and realized that I didn’t have salt. There was none at the apartment, so I had to eat the salad unsalted.
As soon as I finished it, the door bell rang. It was Arthur Jaffe. He proposed to give me a quick tour around the city in his car. That was really cool – a twenty-one-year-old kid being driven around the city by the chairman of the Harvard Math Department. I saw Harvard Yard, the Charles River, beautiful churches, and the skyscrapers in downtown Boston. The weather was beautiful. I was very impressed by the city.
On the way back from the two-hour journey, I told Arthur that I needed to buy salt, and he said, “No problem, I’ll take you to a nearby supermarket.”
He took me to the Star Market on Porter Square and said that he would wait for me in his car.
This was the first time that I ever was at a supermarket, and it was a startling experience. At that time there were shortages of food in Russia. In my hometown, Kolomna, one could only buy bread, milk, and basic vegetables, like potatoes. For other food one had to travel to Moscow, and even in Moscow the best one could hope for was some low-grade mortadella sausage and cheese. Every weekend, when I came home from Moscow, I brought with me some food for my parents. So seeing aisle after aisle packed with all kinds of food at the supermarket was absolutely unbelievable.
“How do you ever find anything here?” I thought. I started walking down the aisles looking for salt, but I couldn’t find any. I guess I must have been slightly dizzy from the abundance of stuff in the supermarket; at any rate, I didn’t even notice the signs at the top. I asked someone working at the supermarket: “Where is salt?” but I couldn’t understand a word of what he said. My English was good enough to give a math lecture, but I didn’t have any experience with everyday colloquial English. The heavy Bostonian accent didn’t make understanding any easier.
Half an hour passed by, and I was really getting desperate, lost in the Star Market like in a giant labyrinth. Finally, I came across a package of salt mixed with garlic. “Good enough,” I said to myself, “let’s get out of here.” I paid and came out of the store. Poor Arthur got worried – what the hell was this kid doing in there for forty-five minutes? – so he already started looking for me.
“Losing myself in the abundance of capitalism,” I thought.
My adaptation to America had begun.
The other two recipients of the Harvard Prize Fellowship arriving in the fall semester were Nicolai Reshetikhin, with whom I was sharing my apartment (he arrived a week later), and Boris Tsygan.* They were both ten years my senior, and they both had already made seminal contributions to mathematics. I knew about their work but had never met them before in person. During that first semester, we bonded and became friends for life.
Nicolai, or Kolya as he is affectionately known to many, was from St. Petersburg. He was already famous as one of the inventors of the so-called quantum groups, which are generalizations of the ordinary groups. More precisely, quantum groups are certain deformations of Lie groups – the mathematical objects we talked about earlier. These quantum groups are now as ubiquitous as Lie groups in many areas of mathematics and physics. For example, Kolya and another mathematician, Vladimir Turaev, used them to construct invariants of knots and three-dimensional manifolds.
Borya Tsygan was a longtime collaborator of Boris Feigin, my teacher. Originally from Kiev, Ukraine, Tsygan had a big idea when he was fresh out of college, which led to a breakthrough in the field of “non-commutative geometry.” Like other Jewish mathematicians, he was kept from going to graduate school after college. Because of this, after he graduated from the university, he had to work at a heavy machinery plant in Kiev, spending all day surrounded by loud machines. Nevertheless, it was in these, less-than-perfect, conditions that he made his discovery.
People tend to think that mathematicians always work in sterile conditions, sitting around and staring at the screen of a computer, or at a ceiling, in a pristine office. But in fact some of the best ideas come when you least expect them, possibly through annoying industrial noise.
Walking around Harvard Yard and taking in the old-fashioned architecture of the brick buildings, the statue of Harvard, the spires of ancient churches, I couldn’t help but feel the exclusivity of this place, with its long tradition of the pursuit of knowledge and never-ending fascination with discovery.
Harvard’s Department of Mathematics was housed in the Science Center, a modern-looking building just outside of Harvard Yard. It had the look of a giant alien space ship that just happened to land in Cambridge, Massachusetts, and decided to stay there. The Math Department occupied three floors in it. Inside, offices mixed with common areas complete with coffee machines and comfortable couches. There was also a well-designed in-house math library, and even a ping-pong table. All this created a homey atmosphere, and even in the middle of the night you could find plenty of people there, young and old – working, reading in the library, pacing nervously in the corridors, engaged in a lively conversation, and some just dozing off on the couch... You had the feeling that you would never have to leave this place (and it seemed that some people never did).
The department was quite small in comparison with other schools: the faculty consisted of no more than fifteen permanent professors and ten or so postdocs holding three-year teaching positions. When I arrived, the faculty included some of the greatest mathematicians of our time, such as Joseph Bernstein, Raoul Bott, Dick Gross, Heisuke Hironaka, David Kazhdan, Barry Mazur, John Tate, and Shing-Tung Yau. Meeting them and learning from them was the opportunity of a lifetime. I have fond memories of the charismatic Raoul Bott, a gray-haired friendly giant, then in his late sixties, pulling me aside in the corridor and asking, in his booming voice, “How are you doing, young man?”
There were also thirty or so graduate students who all had tiny cubicles on the middle floor.
The three Russians – Kolya, Borya, and I – were greeted warmly by everyone. Although we were the beginning of a tidal wave of Russian scientists who swept American universities in the ensuing years, it was still highly unusual to have visitors from the Soviet Union in those days. Still, after a week or so in Cambridge, I felt like I blended right in. Everything seemed so natural and cool. I bought myself the hippest jeans and a Sony Walkman (remember, this was 1989!), and I was walking around town wearing headphones, listening to the coolest tracks. To a stranger I would have looked like a typical twenty-one-year-old student. My conversational English st
ill left something to be desired. To improve it, every day I would buy The New York Times and read it, with a dictionary, for at least an hour (deciphering some of the most arcane English words one could find, as I later realized). I also got addicted to late-night TV.
David Letterman’s show (which was then starting at 12:35 am on NBC) was my favorite. The first time I watched it, I couldn’t understand a single word. But somehow it was clear that this was my show, that I would really enjoy it, if only I could understand what the host was saying. So this provided some extra motivation for me. I would stubbornly watch the show every night, and little by little I started to understand the jokes, the context, the background. This was my way of discovering American pop culture, and I was devouring every bit of it. Some nights, when I had to go to sleep early, I would videotape the show and watch it in the morning while having breakfast. The Letterman show became something of a religious ritual for me.
Although the other fellows and I did not have any formal obligations, we came to the department every day to work on our projects, to talk to people, and to attend seminars, of which there were plenty. The two professors I talked to the most were the two Russian expatriates: Joseph Bernstein and David Kazhdan. Both are amazing mathematicians, former students of Gelfand, and close friends of each other, but you couldn’t imagine more different temperaments.
Joseph is quiet and unassuming. If asked a question, he would listen quietly, take his time to think, and would often say that he didn’t know the answer, but would still tell you what he thought about the subject. His explanations were crystal clear and down-to-earth, and often he would actually explain the answer that he claimed he didn’t know. He always made you feel that you didn’t have to be a genius to understand all this stuff – a great feeling for an aspiring young mathematician.
David, on the other hand, is a dynamo – extremely sharp, witty, and quick. In his encyclopedic knowledge, panache, and occasional display of impatience, he recalls his teacher Gelfand. At seminars, if he thought that the speaker wasn’t explaining the material well, he would simply walk up to the blackboard, wrestle the chalk from the speaker’s hand, and just take over – that is, if he was interested in the subject. Otherwise, he could simply doze off. It was quite rare to hear him say “I don’t know” in response to a question – he really knows pretty much everything. I’ve spent long hours talking to him over the years and have learned a lot. Later on, we collaborated on a joint project, which was a rewarding experience.
In my second week at Harvard I had another fateful encounter. Besides Harvard, there is another, lesser-known, school in Cambridge, usually referred to by an abbreviation of its name... MIT. (I am kidding, of course!) There has always been a bit of a rivalry between Harvard and MIT, but in fact the two Math Departments are very closely connected. It’s not unusual, for example, for a Harvard student to have an MIT professor as an advisor and vice versa. Students from each school often attend classes offered by the other school.
Sasha Beilinson, Borya Feigin’s friend and co-author, was appointed as a professor at MIT, and I was attending the lectures he was giving there. At the first lecture, someone pointed out to me a handsome man in his mid-forties sitting a couple of rows away. “This is Victor Kac.” Wow! This was the creator of the Kac–Moody algebras and many other things, whose works I had been studying for several years.
After the lecture, we were introduced. Victor greeted me warmly and told me that he wanted to learn more about my work. I was thrilled when he invited me to speak at his weekly seminar. I ended up giving three talks at his seminar, on three consecutive Fridays. These were my first seminars in English, and I think I did a decent job: the attendance was high, people seemed to be interested, and they asked many questions.
Victor took me under his wing. We would often meet in his spacious office at MIT, talk about math, and he would often invite me over to his house for dinner. We subsequently worked together on several projects.
About a month after my arrival, Borya Feigin came to Cambridge as well. Sasha Beilinson sent him an invitation to visit MIT for two months. I was happy that Borya came to Cambridge: he was my teacher, and we were very close. We also had a number of ongoing math projects, and this was a great opportunity to work on them. I did not realize at first that his visit would also throw my life into a great turmoil.
The news that the door to the West was now open, and mathematicians could freely travel and visit universities in the United States and elsewhere, quickly spread through the Moscow mathematical community. Many people decided to seize this opportunity and move permanently to America. They started sending applications to various universities and calling their colleagues in the U.S., telling them that they were looking for jobs. Since no one knew for how long this policy of “openness” would continue (most people expected that after a few months the borders would be sealed again), this created a sort of frenzy in Moscow – all conversations led to the same question: “How best to get out?”
And how could it be otherwise? Most of these people had to deal with anti-Semitism and various other obstacles in the Soviet Union. They could not find employment in academia and had to do mathematics on the side. And, although the mathematical community in the Soviet Union was very strong, it was largely isolated from the rest of the world. There were great opportunities for professional development in the West that simply did not exist in the Soviet Union. How could one expect these people to be loyal to the country that rejected them and tried to prevent them from working in the field they loved, when the opportunities of better life abroad presented themselves?
When he came to the U.S., Borya Feigin saw right away that a great “brain drain” was coming, and nothing could stop it. In Russia, the economy was falling apart, with shortages of food everywhere, and the political situation was becoming more and more unstable. In America, there was a much higher standard of living, an abundance of everything, and the life of the academics just seemed so comfortable. The contrast was immense. How could one possibly convince anyone to go back to the Soviet Union after experiencing all of this firsthand? The exodus of the overwhelming majority of the top tier mathematicians from Russia – or anyone, really, who could find a job – seemed inevitable, and it was going to happen very quickly.
Nevertheless, Borya resolved to return to Moscow, despite the fact that he had been struggling with anti-Semitism all his life and had no illusions about the situation in the Soviet Union. He was accepted to Moscow University as an undergraduate (in 1969, when he applied, some Jewish students were still accepted), but he was not allowed to enter the Ph.D. program there. He had to enroll at the university in the provincial city of Yaroslavl to get his Ph.D. He then had a great difficulty finding a job, until he was able to get a position at the Institute for Solid State Physics. Still, Borya found this rush to the exit disturbing. He thought it was morally wrong to leave Russia en masse like this at the time of great upheaval, like rats abandoning a sinking ship.
Borya was extremely saddened that the great Moscow Mathematical School was soon to be no more. The tight-knit community of mathematicians that he was living in for so many years was about to evaporate in front of his very eyes. He knew that he would soon be practically alone in Moscow, deprived of the greatest pleasure of his life: doing mathematics together with his friends and colleagues.
Naturally, this became the main theme of my conversations with Borya. He tried to convince me that I should go back and not succumb to what he deemed to be the mass hysteria possessing those who were trying to escape to the West. He was also worried that I would not be able to become a good mathematician in the U.S. American “consumer society,” he thought, can kill one’s motivation and work ethics.
“Look, you’ve got talent,” he would say to me, “but it needs to be developed further. You have to work hard, the way you were working in Moscow. Only then can you realize your potential. Here, in America, this is impossible. There are too many distractions and temptations. Life h
ere is all about fun, enjoyment, instant gratification. How can you possibly focus on your work here?”
I wasn’t buying his argument, at least not entirely. I knew that I had a strong motivation to do mathematics. But I was only twenty-one, and Borya, fifteen years my senior, was my mentor. I owed him everything I had achieved as a mathematician. His words gave me pause – what if he was right?
The invitation to Harvard was a turning point in my life. Only five years earlier, I was failed at the MGU exam, and it looked like my dream of becoming a mathematician was irreparably shattered. Coming to Harvard was my vindication, a reward for all the hard work I did in Moscow in those five years. But I wanted to keep on moving, making new discoveries. I wanted to become the best mathematician I could be. I looked at the invitation to Harvard as just one stage in a long journey. It was an advance: Arthur Jaffe and others believed in me and gave me this opportunity. I couldn’t let them down.
In Cambridge, I was lucky to have the support of wonderful mathematicians like Victor Kac who encouraged me and helped me in every way they could. But I also sensed jealousy from some of my colleagues: Why was this guy given so much so soon? What has he done to deserve it? I felt compelled to fulfill my promise, to prove to everybody that my first mathematical works were not a fluke, that I could do better and bigger things in mathematics.
Mathematicians form a small community, and like all humans, they gossip about who is worth what. In my short time at Harvard I had already heard enough stories about prodigies who burned out early. I’d heard some unforgiving comments about them, things like, “Remember so-and-so? His first works were so good. But he hasn’t done anything nearly as important in the last three years. What a shame!”
Love and Math Page 17
