Love and Math

by Frenkel, Edward

  But back to my exam. Another hour and a half had gone by. Then one of the examiners said:

  “OK, we are done with the questions. Here is a problem we want you to solve.”

  The problem he gave me was pretty hard. The solution required the use of the so-called Sturm principle, which was not studied in school.4 However, I knew about it from my correspondence courses, so I was able to solve it. As I was working my way through the final calculations, the examiner came back.

  “Are you done yet?”

  “Almost.”

  He looked at my writings and no doubt saw that my solution was correct and that I was just finishing my calculations.

  “You know what,” he said, “let me give you another problem.”

  Curiously, the second problem was twice as hard as the first one. I was still able to solve it, but the examiner again interrupted me halfway through.

  “Not done yet?” he said, “Try this one.”

  If this were a boxing match, with one of the boxers pressed in the corner, bloodied, desperately trying to hold his own against the barrage of punches falling on him (many of them below the belt, I might add), that would be the equivalent of the final, deadly blow. The problem looked innocent enough at first glance: given a circle and two points on the plane outside the circle, construct another circle passing through those two points and touching the first circle at one point.

  But the solution is in fact quite complicated. Even a professional mathematician would not necessarily be able to solve it right away. One must either use a trick called inversion or follow an elaborate geometric construction. Neither method was studied in high school, and hence this problem should not have been allowed on this exam.

  I knew about inversion, and I realized that I could apply it here. I started to work on the problem, but a few minutes later my interrogators came back and sat down next to me. One of them said:

  “You know, I’ve just talked to the deputy chairman of the admissions committee and I told him about your case. He asked me why we are still wasting our time... Look,” he pulled out an official looking form with some notes scribbled on it – this was the first time I saw it. “On the first question on your ticket, you did not give us a complete answer, you didn’t even know the definition of a circle. So we have to put a minus. On the second question, your knowledge was also shaky, but OK, we give you minus plus. Then you couldn’t completely solve the first problem, did not solve the second problem. And on the third? You haven’t solved it either. See, we have no choice but to fail you.”

  I looked at my watch. More than four hours had passed by since the beginning of the exam. I was exhausted.

  “Can I see my written exam?”

  The other man went back to the main table and brought my exam. He put it in front of me. As I was turning the pages, I felt like I was in a surrealistic movie. All answers were correct, all solutions were correct. But there were many comments. They were all made in pencil – so that they could be easily erased, I guess – but they were all ridiculous, like someone was playing a practical joke on me. One of them still stands out in my mind: in the course of a calculation, I wrote And there was a comment next to it: “not proved.” Really? Other comments were no better. And what grade did they give me, for all five problems solved, with all correct answers? Not 5, not 4. It was a 3, the Russian equivalent of a C. They gave me a C for this?

  I knew it was over. There was no way I could fight this system. I said, “All right.”

  One of the men asked, “Aren’t you going to appeal?”

  I knew that there was an appeal board. But what would be the point? Perhaps, I could raise my grade on the written exam from 3 to 4, but appealing the result of the oral exam would be more difficult: it would be their word against mine. And even if I could raise the grade to 3, say, then what? There were still two more exams left at which they could get me.

  Here is what George Szpiro wrote in the Notices:5

  And if an applicant, against all odds, managed to pass both the written and the oral test, he or she could always be failed on the required essay on Russian literature with the set phrase “the theme has not been sufficiently elaborated.” With very rare exceptions, appeals against negative decisions had no chance of success. At best they were ignored, at worst the applicant was chastised for showing “contempt for the examiners.”

  A bigger question was: did I really want to enroll in a university that did everything in its power to prevent me from being there? I said, “No. Actually, I’d like to withdraw my application.”

  Their faces lit up. No appeal meant less hassle for them, less potential for trouble.

  “Sure,” the talkative one said, “I’ll get your stuff for you right away.”

  We walked out of the room and entered the elevator. The doors closed. It was just the two of us. The examiner was clearly in a good mood. He said, “You did great. A really impressive performance. I was wondering: did you go to a special math school?”

  I grew up in a small town; we didn’t have special math schools.

  “Really? Perhaps your parents are mathematicians?”

  No, they are engineers.

  “Interesting... It’s the first time I have seen such a strong student who did not go to a special math school.”

  I couldn’t believe what he was saying. This man had just failed me after an unfairly administered, discriminatory, grueling, nearly five-hour long exam. For all I knew, he killed my dream of becoming a mathematician. A 16-year-old student, whose only fault was that he came from a Jewish family... And now this guy was giving me compliments and expecting me to open up to him?!

  But what could I do? Yell at him, punch him in the face? I was just standing there, silent, stunned. He continued: “Let me give you advice. Go to the Moscow Institute of Oil and Gas. They have an applied mathematics program, which is quite good. They take students like you there.”

  The elevator doors opened, and a minute later he handed me my thick application folder, with a bunch of my school trophies and prizes oddly sticking out of it.

  “Good luck to you,” he said, but I was too exhausted to respond. My only wish was to get the hell out of there!

  And then I was outside, on the giant staircase of the immense MGU building. I was breathing fresh summer air again and hearing the sounds of the big city coming from a distance. It was getting dark, and there was almost no one around. I immediately spotted my parents, who were waiting anxiously for me on the steps this whole time. By the look on my face, and the big folder I was holding in my hands, they knew right away what had happened inside.

  *This was one year before Mikhail Gorbachev came to power in the Soviet Union, and another couple of years before he launched his perestroika. The totalitarian Soviet regime in 1984 was in many ways a haunting facsimile of George Orwell’s prescient book.

  Chapter 4

  Kerosinka

  That night, after the exam, my parents and I came home quite late. We were still in the state of initial shock and disbelief about what happened.

  This was a gut-wrenching experience for both of my parents. I have always been very close to them, and they always gave me unconditional love and support. They never pushed me to study harder or choose a particular profession, but they encouraged me to pursue my passion. And of course they were proud of my accomplishments. They were devastated by what had happened at my exam, both because of the sheer unfairness of it and because they were unable to do anything to protect their son.

  Thirty years earlier, in 1954, my father’s dream of becoming a theoretical physicist had been shattered just as ruthlessly, for a different reason. Like millions of innocent people, his father, my grandfather, had been a victim of Joseph Stalin’s persecution. He was arrested in 1948 on bogus charges that he wanted to blow up the big automobile plant in Gorky (now Nizhny Novgorod), where he worked as the head of supplies. The only “evidence” presented in his indictment was that he had in his possession at the time of his arr
est a box of matches. He was sent to a hard-labor camp at a coal mine in the northern part of Russia, part of the Gulag Archipelago that Alexander Solzhenitsyn and other writers described so vividly years later. He was deemed an “enemy of the people,” and my father was therefore a “son of the enemy of the people.”

  My dad was obligated to write this on his application to the physics department of Gorky University. Even though he finished high school with honors and was supposed to be accepted automatically, he was failed at the interview, whose sole purpose was to screen out the relatives of the “enemies of the people.” My dad was forced to go to an engineering school instead. (Like other prisoners, his father was rehabilitated and released by Nikita Khrushchev’s decree in 1956, but by then it was too late to undo the injustice.)

  Now, thirty years later, his son had to go through a similar experience.

  But there was no time for self-pity. We had to decide quickly what to do next, and the first question was which school I should apply to. All of them held their exams at the same time, in August, about two weeks later, and I could only apply to one.

  The next morning my dad woke up early and went back to Moscow. He took the recommendation from my examiner at MGU seriously. It sounded like the examiner was trying to help me, perhaps, as some partial compensation for the injustice he had done. So when my father arrived in Moscow, he went straight to the admissions office at the Institute of Oil and Gas.* Somehow my dad managed to find someone there willing to talk to him privately and described my situation. The fellow said that he was aware of the anti-Semitism at MGU but said the Institute of Oil and Gas had none of this. He went on to say that the level of applicants to their applied mathematics program was quite high due to a large number of students like me, who were not accepted at MGU. The entrance exam would be no cakewalk. But, he said, “if your son is as bright as you say he is, he will be admitted. There is no discrimination against Jews at the entrance exams here.”

  “I have to warn you, though,” he said at the end of the conversation, “Our post-graduate studies are handled by different people, and I think your son probably won’t be accepted to the grad school.”

  But that was something to worry about in five years, too far ahead.

  My father went to a couple of other schools in Moscow with applied math programs, but there was nothing like the attitude he found at the Institute of Oil and Gas. So when he came back home that evening and told me and my mom the news, we decided right away that I would apply to the Institute of Oil and Gas, to their applied mathematics program.

  The Institute was one of a dozen schools in Moscow preparing technicians for various industries, such as the Institute of Metallurgy and the Institute of Railway Engineers (in the Soviet Union, many colleges were called “institutes”). From the late 1960s, anti-Semitism at MGU “created a market for placements in mathematics for Jewish students,” writes Mark Saul in his article.1 The Institute of Oil and Gas “began to cater to these markets, benefiting from the anti-Semitic policies of other universities to get highly qualified students.” Mark Saul explains:

  Its nickname, Kerosinka, reflected [their] pride and cynicism. A kerosinka is a kerosene-burning space heater, a low-tech but effective response to adversity. The students and graduates of the institute quickly became known as “kerosineshchiks,” and the school became a haven for Jewish students with a passion for mathematics.

  How did fate choose Kerosinka as the repository of so much talent? This question is not easy to answer. We know that there were other institutions that benefited from the exclusion of Jews from MGU. We also know that the establishment of this exclusionary policy was a conscious act, which probably met with some resistance at first. It may have been easier for some institutions to continue accepting Jewish students than for them to institute a new policy. But once the phenomenon grew and there was a cadre of Jewish students at Kerosinka, why was it tolerated? There are dark whispers of a plot by the secret police (KGB) to keep the Jewish students under surveillance in one or two places. But some of the motivation may have been more positive: the administration of the institute may have seen a good department developing and done what it could to preserve the phenomenon.

  I believe the last sentence is more accurate. The President (or Rector, as he was called) of the Institute of Oil and Gas, Vladimir Nikolaevich Vinogradov, was a clever administrator known for recruiting professors who were engaged in innovative teaching and research and for using new technologies in the classrooms. He instituted the policy that all exams (including the entrance exams) were given in writing. Of course, there might still be some opportunity for abuse even with written tests (as was the case with my written exam at MGU), but the policy would prevent the kind of debacle that happened at my oral examination at MGU. I would not be surprised if it was Vinogradov’s personal decision not to discriminate against Jewish applicants, and if so, it must have required some good will, and perhaps even some courage, on his part.

  As predicted, there seemed to be no discrimination at the entrance exams. I was accepted after the first exam (written math), on which I got a 5, that is, an A (gold medalists were accepted outright if they got an A at the first exam). In a bizarre twist, this 5 did not come easy to me because apparently some of my solutions were entered incorrectly into the automated grading system, and as a result my grade was initially recorded as 4, or B. I had to go through the appeals process, which meant waiting in line for hours, with all kinds of bad thoughts swirling in my head. But once I got in to speak with the appeals committee, the error was found and fixed swiftly, an apology was offered, and my entrance exams saga came to a close.

  On September 1, 1984, the school year began, and I met my new classmates. Only fifty students were accepted every year to this program (in contrast, at Mekh-Mat the number was close to 500). Many of my fellow students went through the same experience as I did. These were some of the brightest, most talented math students around.

  Everybody, except for me and another student, Misha Smolyak from Kishinev who became my roommate at the dorm, were from Moscow. Those who lived outside of Moscow could apply only if they had graduated from high school with a gold medal, which fortunately I had.

  Many of my fellow students had studied at the best Moscow schools with special math programs: schools No. 57, No. 179, No. 91, and No. 2. Some of them went on to become professional mathematicians and now work as professors at some of the best universities in the world. Just in my class, we had some of the best mathematicians of our generation: Pasha Etingof, now professor at MIT; Dima Kleinbock, professor at Brandeis University; and Misha Finkelberg, professor at the Higher School of Economics in Moscow. It was a very stimulating environment.

  Mathematics was taught at Kerosinka at a high level, and basic courses, such as analysis, functional analysis, and linear algebra, were taught at the same level of rigor as at MGU. But courses in other areas of pure math, such as geometry and topology, were not available. Kerosinka only offered the applied mathematics program, so our education was geared toward concrete applications, particularly, to oil and gas exploration and production. We had to take quite a few courses of more applied orientation: optimization, numerical analysis, probability, and statistics. There was also a large computer science component.

  I was glad that I had the opportunity to be exposed to these applied math courses. This taught me that there isn’t really a sharp distinction between “pure” and “applied” math; good-quality applied math is always based on sophisticated pure math. But, however useful this experience was, I could not forget my true love. I knew I had to find a way to learn the pure math subjects that were not offered at Kerosinka.

  The solution presented itself as I became friends with the other students, including those who went to the prestigious special math schools in Moscow. We exchanged our stories. Those who were Jewish (according to the standards I described earlier) were also failed at the exams, as ruthlessly as I was, while all of their classmates who were no
t Jewish were accepted to MGU without any problems. Through these other students, they knew what was happening at the Mekh-Mat, which courses were good, and where and when the lectures were held. So my second week at Kerosinka, my classmate (I think it was Dima Kleinbock) came up to me: “Hey, we are going to Kirillov’s course at MGU. Wanna come with us?”

  Kirillov was a famous mathematician, and of course I wanted to attend his lectures. But I had no idea how this would be possible. The grand building of MGU was heavily guarded by police. One needed to have a special ID to get in.

  “No worries,” my classmate said, “we’ll scale the fence.”

  That sounded dangerous and exciting, so I said, “Sure.”

  The fence on the side of the building was quite high, easily twenty feet, but at one point the metal was bent, and it was possible to sneak in. Then what? We entered the building through a side door and after following some long corridors ended up in the kitchen. From there, through the kitchen, trying not to attract too much attention of the staff working there, to the cafeteria, and then to the main entrance hall. Elevator to the fourteenth floor, where the auditorium was.