Tanya Khovanova's Math Blog

Israel Gelfand was my scientific adviser from the time I was 15. This is the story of how Gelfand helped me, when at 20 I was an undergrad at Moscow State University. At that time, I was married to Sasha (Alexander) Goncharov, who was also Gelfand’s student.

Sasha was more driven by mathematics than I. I had a lot of different interests: I wanted to hang out with friends, go to movies and read books. Sasha only wanted to do mathematics. His only other obsession was with what our colleagues (including me) were doing mathematically. So he was constantly asking me about the math problems I was thinking about.

For example, I was sitting at my side of the desk working, and he asked me to tell him about my problem. A few minutes later, I was forced to interrupt my work to go grocery shopping, because the household chores fell to me. As soon as I returned with bread and milk, Sasha excitedly told me the solution to my problem. It made me feel stupid, as if I should have solved it while I was waiting in the line for bread and milk. That feeling blocked out all the other feelings I should have been noticing, such as frustration and annoyance with Sasha.

Without his interference, I would have happily solved the problem myself. I was about to start my serious research, but I worried that I’d end up as a supplier of new problems for his papers.

You might wonder why I didn’t stop sharing my math with Sasha. But at that time, I wasn’t very in touch with my feelings and I prided myself on being a logical person. The idea that a husband and wife would discuss their work together seemed logical. Besides, even though I wasn’t particularly interested, Sasha was always ready to tell me about his math problems. It seemed important for me to be fair and to reciprocate. So I was stuck in a situation I didn’t know how to resolve.

I never confided this issue to any math colleagues. I never mentioned it to Gelfand — mostly because I was too scared of him to initiate any conversation. Besides, Gelfand delegated most of his responsibilities to others, because he was quite famous and busy. For example, all official paperwork related to his adviser role was done by Alexandre Kirillov. With me avoiding Gelfand and Gelfand being busy, we almost never spoke one-on-one.

You can understand my surprise when one day Gelfand approached Sasha and me to have a chat. He told us that we were about to start our own research, and while he permitted me to ask Sasha about what he was doing, he would not allow Sasha to interfere with my research.

Gelfand was a great judge of character. Without anyone telling him, he perceived what was going on in our marriage and gave me an excuse to stop Sasha’s prying. It was an appreciated gift.

I would like to tell you a story from my childhood and how I started on my math path.

When I was in elementary and middle school, I was very good with mathematics. Actually, I was by far the best math student in my class and my math teacher didn’t know what to do with me. Our algebra book had 2,000 problems and was intended to cover three years of study. But I worked out those problems, one after another, whenever I had a free minute in my math class. As I result, I got way ahead of everyone else.

One day a new boy named Lenya Kostyukov joined our class. He had extraordinarily long eye-lashes that covered his eyes, and all the girls envied him. He was a nice smart kid, but other than his lashes, I didn’t notice him very much. After a year or two, he announced that he was leaving our school, because he had been accepted to a math school for gifted children.

“Why is he going to a math school? I am the math star here. Why aren’t I going to a math school?” I knew about math schools, and I knew that I was good at math; I just never made the connection. I never felt that I was supposed to apply. Despite enjoying my reputation, I just passively went with the flow. Lenya figuratively kicked me in the butt. If he can, why can’t I?

So I applied to the same school on the last permissible day and was accepted. It turned out that I accidentally went to the room where they were giving the test for a grade higher than mine. I passed it with flying colors. My parents, though, were scared of a long commute and didn’t really want me to go so far away. They found a different math school closer to home, and used my extraordinary results to convince that school to accept me, even though their application date had passed.

For many years I continued to be a very passive person. Applying to a math school was the single big step I took for myself, but it was a defining step. I am grateful to Lenya for that. Or more likely to his parents, who were actively looking around trying to find the best place for their gifted son, and as a byproduct found a place for me. Once I was on the path of mathematics, I had the guidance of teachers and supervisors, for better or for worse, which allowed me to continue to be passive.

I have described my defining moment to you, but I don’t want to leave you in the dark about Lenya’s fate. Here’s what happened to him.

As I mentioned, Leonid (Lenya’s formal name) and I ended up in different math schools, so I lost track of him. Four years later I went to study math at Moscow State University and stumbled upon a guy with very long eye-lashes. We recognized each other immediately and eventually became friends.

He was doing logic and was very good at it. He was recommended for graduate school. But by that time our MSU administration noticed his lashes too. The lashes were obviously very suspicious; they hinted at the existence of non-Russian blood in his veins. As it was the period of brutal anti-semitism at MSU, they didn’t allow him to go to graduate school.

Leonid Kostyukov dropped mathematics and became a famous writer.

The PhD program in Russia was limited to exactly three years. My son Alexey was born right after I started it, and I was distracted from my research for quite some time. At that time, my mom, who lived with us, reached her retirement age of 55. Her retirement would have been supported by the government and her pension would have been almost equal to her salary. So I begged my mom to retire and help me with my son Alexey. I couldn’t understand why she wouldn’t stop working, so I kept pressing.

At the same time, I was frantically trying to find a place for Alexey in a day care center. I finally was successful, but it backfired. Alexey started getting sick all the time. Daycare was overcrowded, with 30 kids to every adult. Workers didn’t have time to attend to every kid. Day care workers were so tired that they were relieved when a few kids stayed home sick.

After Alexey was hospitalized for two weeks with severe dysentery, my mother gave up and retired. It was one year before the end of my graduate school. In that year I wrote four papers and my thesis, and I got my PhD.

Now that I am fifty, I understand that my mother really did love her job. Being older and wiser, I recognize what a sacrifice my mother made in retiring in order to look after a grandchild.

Mom, sorry for being so pushy back then and thank you so much for all that you did for us.

Decades ago there was a study in Russia that claimed that a woman worked four more hours a day than a man on average. Men and women were equal in Russia and all had the same 40-hours-a-week jobs. Women were not, by and large, housewives, for they worked full-time.

So where did the additional four hours come from? They were devoted to house chores. In Russia, women did everything at home — at a time when life in Russia was much more difficult. For example, my family didn’t have a washer, or a dryer or a dish-washing machine. Plus, everything was in deficit, so to buy milk or a sweater, women had to stand in lines, sometimes for hours.

My mother was very bitter because her husband, my father, never helped her. So I always hoped that when I got married, my husband would take on some of the house chores.

When I married Andrey, he was somewhat helpful — better than the average Russian husband. Then, when I was at grad school, we had a baby named Alexey. Andrey convinced me that I had to take over all the child care because only women could get academic maternity leave. It seemed logical and I agreed.

In a year, when the leave was over, I felt that Andrey should take over some of these duties. He refused. He insisted that since I already had published a paper when I was an undergrad, and since he still didn’t have his research results for his PhD, that he had to stay focused on his work. I wasn’t strong enough to resist.

We signed up for government child care — private care didn’t exist — but we were on the waiting list for a couple of years. Almost no one in Russia — certainly not graduate students — could afford a private babysitter. I couldn’t really work on my PhD research because between caring for the house and the baby, I never had big chunks of time. The best I could do was to start preparing for my qualifying exams.

Allow me to digress from my main story for a moment to mention my gray notebook. This notebook was our baby diary. Initially I recorded important baby data — like the first time Alexey smiled. But later, as soon as Alexey turned one year old, he became very eloquent; and this notebook became my son’s quote book.

One day Andrey and I went out and my mom babysat Alexey, who was two years old. When we returned, my mother recited the following quote from Alexey:

When will Daddy be back from the university and Mommy from the store?

I don’t really remember the long hours in stores or the cooking and cleaning. I remember the quote.

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.