Tanya Khovanova's Math Blog

I am celebrating the first hundred essays I have written for my blog. My English teacher and editor Sue Katz edited most of them. Sue Katz not only corrects my English mistakes, but also helps me to choose better and more descriptive words and rearranges my text so that it doesn’t sound like a direct translation from Russian.

If you’re looking for an editor, she’s superb.

Sue is an extremely interesting person. She was one of the first women to gain a black belt in Tae Kwon Do and taught martial arts and dance on three continents. Now she concentrates on her blog and writing. In her blog Sue Katz: Consenting Adult she writes a lot about sex and also about current affairs. She reviews books and movies and expresses her interesting and unique perspective on things. Some of my favorite posts:

• Philosophical and romantic — Six-Word Memoirs: Sought revolution, got pantsuits, want more
• Down-to-earth and funny — The Drip Dominatrix rules her bladder
• Bitter and sweet — Film Review: The Diving Bell and the Butterfly

I am not only grateful to Sue for the excellent professional job, but also for encouraging me. She laughs at my jokes and is a devoted fan of my blog. Thank you, Sue!

The computational linguistics Olympiad started in Moscow in 1962. I first participated when I was in seventh grade. The Olympiad had two sets of problems: the first set was more difficult and meant for seniors, and the second set was for everyone else. Although the sets overlapped, they were significantly different. I should mention that the Soviet Union had 10 grades at that time and prizes were awarded by grade.

I achieved my best result when I was in ninth grade, just below the senior level. During the competition, I solved all the problems for non-seniors and still had a lot of time left. Luckily for me, both sets of problems were in the same booklet, so I proceeded to solve the problems for seniors.

I won two first place prizes: for my ninth grade and for the tenth grade, too.

The following year I was in tenth grade and I felt strange. I couldn’t compete on two levels as I was overqualified for non-seniors. So it was impossible to repeat my result. I could only go downhill — winning only one first place in the best case. So, I didn’t go to the competition at all.

Someone told me that I was arrogant not to go. But what they didn’t know was that I hadn’t been able to stop worrying: what if I didn’t win first place? All my friends cheered me on during my competitions, and I was afraid to let them down. To this day I can remember my fear of performing worse than the year before.

The organizers of the computational linguistics Olympiad had another reason to think I was arrogant. After my successes, they tried to persuade me to go into linguistics. I actually considered that until someone told me that all the computational linguistics majors are later employed by the KGB. The minute I heard that, I lost all interest in linguistics for many years to come. I told the organizers that all my success was due to my impeccable logic, not to my linguistics ability, so there was no point for me to go into linguistics. My arrogance was reaffirmed.

Recently my son Sergei started to compete in the computational linguistics Olympiad, which reminded me of how interesting linguistics can be. I wonder if Sergei will get a call from the CIA.

I bought Richard a year and a half ago, and I bought him for his looks. Richard is slim, black and shiny. Richard is my first laptop, an HP Pavilion dv2000.

I stopped actively dating a while ago — I am quite happy with my life. So, I named my laptop Richard and he is my everyday male companion. Besides, Richard never complains that I didn’t do the dishes; in fact, he never even visits my kitchen.

Recently, Richard died. He just stopped booting. I went to Best Buy to try to fix him, but they told me that I could get a new one for the cost of his likely medical bills.

Why had I gone for the looks? Hadn’t I learned this lesson already with my men? This time I got a hold of myself and decided that, for my next laptop, I’m going to ignore looks altogether. My two priorities were reliability and compatibility with my operating system Ubuntu. Everyone suggested Lenovo Thinkpad. I went shopping. Even though Pavilion was still the most attractive, I turned my back on it and bought the Thinkpad.

I decided to name my new laptop Bond, James Bond. Now whenever I’m working, I am actually bonding. And, of course, his looks can be changed. I dressed up James. I gave him striking wallpaper featuring Pierce Brosnan, the most charming James Bond actor. Now James’ looks are improved, plus he is very reliable: he aims his weapon at me any time I want — all I need to do is close the windows.

While I was getting acquainted with this new man in my life, I stumbled upon an article about extended warranties from credit cards. Though my HP warranty expired, my extended warranty from the Visa card I used to buy Richard, was still valid. So I went to MicroCenter for a repair estimate. To my surprise it appeared that Richard could be recalled.

I probably should have returned James, but I wasn’t absolutely sure that Richard would be resurrected. Besides, I was scheduled to give a talk in Dallas for which I needed a laptop. So I kept James.

In a couple of weeks I got my Richard back. He is alive and well and without any hint of amnesia: no file was lost.

As I sit with my two men on my lap, I think back on all my relationships. I realize that often when I meet a new man, a second one unexpectedly appears in my life. In trying to find a reason for that, I came up with two different explanations:

1. When I am dating someone I am happy and glowy and, hence, I am more attractive.
2. When I first start dating someone, I feel insecure and nervous that I might be dumped. Thus, I need a backup to relieve my anxiety about potential pain. So, I make an extra effort and bring a second man into my life.

I have had many problems in my life, especially with men, but I went through two years of psychotherapy and changed my old patterns. I really do not need two men at the same time any more. I am not sure I need one man.

So why on earth did I end up with two laptops? Is this a sign that I need to go back to therapy? Let’s hope not. I just need to reject either Richard or James. But, whom?

Richard is an old friend. James is new and more powerful. Unfortunately, both of them are not without character flaws. Richard has energy problems: something is wrong with the battery. And James has communication problems: his wireless card is not working. I have two laptops and neither of them satisfies me fully. Maybe I should go back to therapy after all.

My initial plan was to apply for academic jobs this December. I didn’t do it. Here are my reasons:

• Overall economic situation. The financial crisis significantly lowered endowments of universities and colleges. Departments are cautious, so they are not hiring new faculty. Even some positions that were announced were later cancelled. At the same time many people from the finance industries lost their jobs and are attempting to enter academia. Thus the supply of academic jobs decreased and the demand increased at the same time, lowering my overall chances drastically.
• My research progress. My curriculum vitae is not where I want it to be. My papers have just been accepted, but have not yet been published. And usually a reputation generated by a good paper comes with a time delay after its publication, especially for new people in the field. My CV has improved, but I haven’t built my name yet.
• My mathematical voice. In my previous life I didn’t trust my heart in my research. I followed the advice of my colleagues, friends and husbands in choosing the problems for my research. Now I am trying to follow my heart. What I produce now is very different from what I used to do. Previously I worked on representation theory, string theory, integrable systems, quantum groups, networks, optimizations and so on. My new results are in combinatorics, recreational mathematics, algorithms and applied probability. I need more time for my mathematical voice to reach its full potential range.
• Recommendation letters. People from whom I used to request recommendation letters know my old results and are experts in the areas in which I no longer work. So I need to find new people in my new areas who like and appreciate my results.
• My goal has become more specific. I like entertaining people with mathematics so I want this to be a part of my job. I also enjoy blogging and popularizing mathematics. I would like to reach a large group of people to teach them about the beauty and the real-life use of mathematics. What I really want is to be a professor of recreational mathematics. Unfortunately, such a position doesn’t yet exist.

That’s why my next step must be to persuade a university or a college that they need a professor of recreational mathematics. It is obvious that such positions are needed. Recreational mathematics is the only existing field of mathematics that is very popular, but not represented in math departments. After all, recreational mathematics is very important in popularizing mathematics, in bridging the gap between the advanced research and common folks. Recreational mathematics is vital in energizing American math education in general.

Hey, are you a math faculty member? If you agree with me, talk to your Head of Department about this idea, especially if you live in the Boston area. Then give me a call.

If you remember, in my previous essay My Paper Road to Academia, my big plan was to write lots of academic papers. So far I have written eight papers this year (seven of them are uploaded to the arxiv). I also have ideas and partial results for 19 more papers, but I have stopped writing them. Here is the story of My Paper Road Block.

I started sending my papers to different places, where they were rejected. Then I was invited to the Gathering for Gardner. Participants are allowed to publish their paper in the proceedings of the conference, but we have to pay for it. So this publication really felt more like adding insult to injury than a lucky break.

Finally I realized that I can put three lucky letters — M, I, and T — on my papers. I don’t remember if I told you that I am currently holding a visiting scholar position at MIT.

I continued sending my papers out without receiving any positive response. As a result of these rejections and the long waiting periods to receive an answer, my writing process slowed down until it halted.

To my delight, a month ago I received letters of acceptance for three papers, almost simultaneously. Here is the tally so far for my eight papers:

• The number gossip paper for the Gathering for Gardner, which I can’t count as a reviewed publication.
• A paper which I’m too superstitious to describe because I am still waiting for the response.
• Three papers which were accepted.
• Three papers which were rejected (one of them twice).

The funny part is that on all the accepted papers I was affiliated with MIT, and on all the rejected papers I was not.

To be fair, I have to admit that there might be another explanation. All the accepted papers were sent out later in time. Perhaps I’m getting better at choosing the right journals.

Because of inertia, I’m still not writing papers. On the positive side, I have more time to write for this blog, and it is much more rewarding. Sometimes I reject my own essays. Sometimes I send them to myself for revision. But I judge my pieces on quality, not on my affiliation.

When I came to the US, I heard about Mensa — the high IQ society. My IQ had never been tested, so I was curious. I was told that there was a special IQ test for non-English speakers and that my fresh immigrant status and lack of English knowledge was not a problem. I signed up.

There were two tests. One test had many rows of small pictures, and I had to choose the odd one out in each row. That was awful. The test was English-free, but it wasn’t culture-free. I couldn’t identify some of the pictures at all. We didn’t have such things in Russia. I remember staring at a row of tools that could as easily have been from a kitchen utensil drawer as from a garage tool box. I didn’t have a clue what they were.

But the biggest problem was that the idea of crossing the odd object out seems very strange to me in general. What is the odd object out in this list?

Cow, hen, pig, sheep.

The standard answer is supposed to be hen, as it is the only bird. But that is not the only possible correct answer. For example, pig is the only one whose meat is not kosher. And, look, sheep has five letters while the rest have three.

Thus creative people get fewer points. That means, IQ tests actually measure how standard and narrow your mind is.

The second test asked me to continue patterns. Each page had a three-by-three square of geometric objects. The bottom right corner square, however, was empty. I had to decide how to continue the pattern already established by the other eight squares by choosing from a set of objects they provided.

This test is similar to continuing a sequence. How would you continue the sequence 1,2,3,4,5,6,7,8,9? The online database of integer sequences has 1479 different sequences containing this pattern. The next number might be:

• 10, if this is the sequence of natural numbers;
• 1, if this is the sequence of the digital sums of natural numbers;
• 11, if this the sequence of palindromes;
• 0, if this is the sequence of digital products of natural numbers;
• 13, if this is the sequence of numbers such that 2 to their powers doesn’t contain 0;
• 153, if this is the sequence of numbers that are sums of fixed powers of their digits;
• 22, if this is the sequence of numbers for which the sum of digits equals the product of digits; or
• any number you want.

Usually when you are asked to continue a pattern the assumption is that you are supposed to choose the simplest way. But sometimes it is difficult to decide what the testers think the simplest way is. Can you replace the question mark with a number in the following sequence: 31, ?, 31, 30, 31, 30, 31, … You might say that the answer is 30 as the numbers alternate; or, you might say that the answer is 28 as these are the days of the month.

Towards the end of my IQ test, the patterns were becoming more and more complicated. I could have supplied several ways to continue the pattern, but my problem was that I wasn’t sure which one was considered the simplest.

When I received my results, I barely made it to Mensa. I am glad that I am a member of the society of people who value their brains. But it bugs me that I might not have been creative enough to fail their test.

One day I got a phone call from Victor Gutenmacher, one of the members of the jury for the USSR Math Olympiad. At that time I was 15 and had won two gold medals at the Soviet Math Olympics. Victor asked me about my math education. I explained to him that although I went to a special school for gifted children, I wasn’t doing anything else. In his opinion, other kids were using more advanced mathematics for their proofs than I was. He said I was coloring everything in black and white; other kids were using calculus, while I was only using elementary math. He asked me if I would like to learn more sophisticated mathematics.

I said, “Sure.” After considering several different options, Victor suggested Israel Gelfand’s seminar at Moscow State University. He told me that this seminar might suit me because it starts slowly, picking up pace only at the end. He also told me that the seminar was like a theater. Little did I know that I would become a part of this theater for many years to come. I also didn’t know that I would meet my third husband, Joseph Bernstein, at this seminar. Joseph used to sit in the front row, and I watched his back at the seminar for more years than I later spent together with him.

The next Monday evening, I went to the seminar for the first time. Afterwards, Gelfand approached me and asked me if I had an academic adviser. I said, “No.” He asked me how old I was. I said, “Fifteen.” He told me that I was too old and that I had to choose an adviser without delay. I said, “But I do not know anyone and, besides, I need some time to think about it.” He replied, “I’ll give you two minutes.”

I paced the halls of the 14th floor of the Moscow State University for a couple of minutes, pretending to think. But really, I didn’t know about any other options. He was the only math adviser I had ever met. So I came back and asked Gelfand, “Will you be my adviser?”

He agreed and remained my adviser until I got my PhD 14 years later.

My scientific adviser Israel Gelfand was one of the greatest mathematicians in Russia. His seminar was famous.

One of the unique features Gelfand invented for his seminar was a role for a seminar participant that he called a designated listener (kontrol’nyy slushatel’ in Russian). I played this role for four years.

This is how it works. The speaker starts his lecture and Gelfand interrupts him. He then turns to me and asks if I understand what the speaker just said. If I say “no,” he says that I am a fool. If I say “yes”, he invites me to the blackboard to explain. Usually, Gelfand finds some fault in my explanation and calls me a fool anyway. As a result, whatever I do, I end up as a fool.

Ironically, I admired Gelfand for the way he conducted his seminars. I went to so many seminars where it was clear that no one understood anything. He was the only professor I knew who made sure that at least one person at his seminar — himself — understood everything.

The problem was that he convinced me that I really was a fool. I dreaded Mondays and I considered quitting mathematics. The situation changed when I started dating Andrey, my future second husband. He made a strong effort to convince me that I was not a fool; rather, Gelfand was a bully. I understood what Andrey was saying, but I wasn’t able to take it to heart. Not that I trusted my supervisor more than my lover, but I was more willing to believe that something was wrong with me than with someone else.

Andrey’s hard work wasn’t in vain. One fine day Professor G. from Western Europe was invited to give a talk at Gelfand’s seminar. During his talk Gelfand interrupted him many times, told him that he wasn’t a good lecturer, and that his results were neither interesting nor meaningful. After several hours of torture Professor G. became tearful. At that moment it hit me that Andrey was right. I am thankful to Professor G. for his tears; they opened my eyes.

The next step for Andrey was to convince me to resist Gelfand. His idea was for me to tell Gelfand, the next time he asked me if I understood: “Go f**k yourself!” (I mean the Russian equivalent).

At that time, I had never pronounced the f-word, even in my own head. But I didn’t have any other ideas. So I started preparing myself to do this. Finally one day I was ready. Gelfand interrupted the speaker and turned towards me as if he were about to ask me to be the designated listener. I looked back at him. He paused, looked at me again, and turned around. He never asked me to be the designated listener again.

In this essay I would like to explain why I am not yet a professor of mathematics.

Today at 49 I am still in search of my dream job. My gender is not the main reason that I don’t have an academic position or another job I like. My biggest problem is myself. My low self-esteem and my over-emotional reactions in the past were the things that most affected my career.

I remember how I came to Israel Gelfand’s seminar in Moscow when I was 15. He told me that I was too old to start serious mathematics, but that he would give me a chance. He said that at first I might not understand a thing at his seminar, but that every good student of his comes to understand everything in a year and a half. The year and a half passed and I wasn’t even close to understanding everything. Because of this I was devastated for a long time.

I had always had problems with my self-esteem and being a student of Gelfand just added to them. My emotional reactions, while they impacted my work in mathematics, were not exclusively related to mathematics. When my second divorce started, not only did I drop my research, I quit functioning in many other capacities for two years.

I was extremely shy in my early teenage years. By working with myself, I overcame it. When I moved to the US, my shyness came back in a strange way. I was fine with Russians, but behaved like my teenage self with Americans. For two years of my NSF postdoc at MIT, I never initiated a conversation with a non-Russian.

For the second time I overcame my shyness. Now, if you met me in person, you wouldn’t believe that I was ever shy.

I became much happier in the US, than I ever was in Russia, but still my emotions were interfering with my research. Because it was so difficult to find an academic job here, I felt tremendous pressure every time I sat down with a piece of paper to work on my research. My mind would start flying around in panic at the thought that I wouldn’t find a job, instead of thinking about quantum groups.

Over all, I think that my inability to control my emotions, together with my low self-esteem, might have impacted my career much more than the fact that I am a woman, per se. Being a mathematician is not easy; being a female mathematician is even more difficult. Still, in my own life, I know I can only blame myself.

The good news is that I have changed a lot, after many years of self-repair. This is why I have made the risky decision, at the age of 49, to try to get back to academia. And this time I have a great supporter — my new self.

This story happened at a colloquium that was conducted during the Women and Math program at Princeton last year. The room was full of women waiting for the colloquium to start. A young man appeared at the door. He looked around in complete surprise. I watched the fear fade from his face when he must have decided that he had the wrong room. He disappeared, but reappeared at the door very soon. He had obviously checked the schedule and had realized that, in fact, he had come to the right room in the first place. His face started changing colors. He was terrified. A few minutes later, he left.

I sat there thinking: women have to deal with this type of situation every week. He could afford to skip just one lecture, but if a girl wants to do math she has to be courageous almost every seminar. I mentally applauded the girls around me for being that courageous.

Wait a minute! I am a woman myself. I went to seminars where I was the only girl hundreds of times. How did I feel? Actually I think my mind never registered that I was the only girl. I never cared. The first time I really thought that the gender of people in a room might be an issue was during that colloquium last year.

I started wondering why it had never bothered me. Could it be that the Soviets did a good job of teaching me not to pay attention to people’s gender? Could be. But wondering back in time, I remembered something else too.

When I was a child I wasn’t a girly girl. I was not interested in dolls; I preferred cars. I didn’t play house or doctor; I played war. To tell the whole truth, I actually did have a doll that I loved, but I never played with it. I liked having it. The doll was a gift from my father’s second wife and it was way beyond my mother’s price range. I think I had an admiration for the quality and the beauty of this toy.

So, while appreciating the courage that the other girls might have needed to do math, I was sitting there pondering my own indifference to the gender of people at seminars and my relative comfort with large groups of men. But this comfort had its own price. I felt comfortable with the group I wasn’t a part of, while I felt different from the group I was a part of. My price of being comfortable at math seminars was loneliness.