Tanya Khovanova's Math Blog

In the name of privacy, I have changed the names of the men I did not marry. But there is no point in changing the names of my ex-husbands, as my readers probably know their names anyway.

I received my first marriage proposal when I was 16. As a person who was unable to say “no” to anything, I accepted it. Luckily, we were not allowed to get married until I was 18, the legal marriage age in the USSR, and by that time we broke up.

To my next proposal, from Sasha, I still couldn’t say “no”, and ended up marrying him. The fact that I was hoping to divorce him before I got married at 19 shows that I should have devoted more effort in learning to say “no”. I decided to divorce him within the first year.

My next proposal came from Andrey, I said yes, with every intention of living with Andrey forever. We married when I was 22 and he divorced me when I was 29.

After I recovered from my second divorce, I had a fling with an old friend, Sam, who was visiting Moscow on his way to immigrate to Israel.

Sam proposed to me in a letter that was sent from the train he took from the USSR to Israel. At that point I realized I had a problem with saying “no”. The idea of marrying Sam seemed premature and very risky. I didn’t want to say yes. I should have said no, but Sam didn’t have a return address, so I didn’t say anything.

That same year I received a phone call from Joseph. Joseph was an old friend who lived in the US, and I hadn’t seen or heard from him for ten years. He invited me to visit him in the US and then proposed to me the day after my arrival. The idea of marrying Joseph seemed premature and very risky, but in my heart it felt absolutely right. I said yes, and I wanted to say yes.

I was very glad that I hadn’t promised anything to Sam. But I felt uncomfortable. So even before I called my mother to notify her of my marriage plans, I located Sam in Israel and called him to tell him that I had accepted a marriage proposal from Joseph. I needed to consent to marry someone else as a way of saying “no” to Sam.

After I married Joseph, I came back to Russia to do all the paperwork and pick up my son, Alexey for our move to the US. There I met Victor. I wasn’t flirting with Victor and was completely disinterested. So his proposal came as a total surprise. That was the time I realized that I had a monumental problem with saying “no”. I had to say “no” to Victor, but I couldn’t force myself to pronounce the word. Here is our dialogue as I remember it:

• Me: I can’t marry you, I am already married.
• Victor: I am sure it’s a fictitious marriage; you just want to move to the USA.
• Me: That’s not true. It’s a real marriage.
• Victor: If it were a fictitious marriage, you wouldn’t admit it. So, it’s a fictitious marriage. My proposal stands.

My sincere attempt at saying “no” didn’t work. I moved to the US to live with Joseph and I soon got pregnant. Victor was the first person on my list to notify — another rather roundabout way to reject a proposal.

The marriage lasted eight years. Sometime after I divorced Joseph, I met Evan who invited me on a couple of dates. I wasn’t sure I wanted to get involved with him. But he proposed and got my attention. I was single and available, though I had my doubts about him.

Evan mentioned that he had royal blood. So I decided to act like a princess. I gave him a puzzle:

I have two coins that together make 15 cents. One of them is not a nickel. What are my coins?

He didn’t solve it. In and of itself, that wouldn’t be a reason to reject a guy. But Evan didn’t even understand my explanation, despite the fact that he was a systems administrator. A systems administrator who doesn’t get logic is a definite turn-off.

So I said “no”! That was my first “no” and I have mathematics to thank.

Once I read a book in Russian that mentioned a study of the children of Soviet military personnel who had to move often. The conclusion was that frequent relocation is very damaging for children’s psyche. The children had to build new friendships, which they would lose the next time they had to move. After several moves they would stop making friends; later, as adults, they would be afraid of getting close to anyone.

In September 1996, my husband, my two children and I came to Princeton from Israel for my husband’s month-long visit to the Institute for Advanced Study. After the visit we were supposed to go back to Israel, but that didn’t happen. My husband returned alone and I stayed in Princeton with my children. That’s a long and sentimental story for another time.

Meanwhile, my older son Alexey started going to Princeton High School. By this time he had attended seven schools in three different countries. In light of the evidence presented in that book about the impact on children of moving, I felt very guilty. Alexey was entering 10th grade. Moving him again not only would further damage his ability to make friends, but would also screw up his college chances. He needed a stable environment leading up to college. For example, recommendation letters are better written by people who are involved with kids for several years. I was afraid to mess up his future. I promised myself not to move him again during high school, especially as Princeton High School was one of the best public schools in New Jersey.

At the same time, I got a Visiting Scholar position at Princeton University. Although it didn’t pay me any salary, through that position I received university housing, library privileges and an office. I was living on my personal savings and the monthly check my husband was sending me from Israel. My money was running out and I felt completely lost, like so many immigrants. I was new to Princeton; I didn’t have friends there; and I was struggling with English. On top of that, I had medical problems, not the least very low energy.

Ingrid Daubechies noticed me at the Princeton math department and approached me. After our conversation, she found some money for me to work on the Math Alive course she was designing. That work was a breath of fresh air. I enjoyed it tremendously, but the part-time salary was not enough. Then I received more help from Ingrid. She appreciated my work on Math Alive a lot, but realized that I needed a different solution. She sacrificed her own interests and started recommending me around. She arranged an interview for me at Telcordia, who offered me a job as a systems engineer.

The decision to accept this job was very painful, because I did not want to leave academia. However, considering that my priority was to keep Alexey in Princeton High School, I didn’t feel I had other options. I knew that I couldn’t stay much longer at Princeton University and I was aware that getting a University job often requires relocation.

Looking back, I think the reasons behind this decision were more complex than sacrificing my career for my child. If I had known more about social supports for poor families and about other possible research jobs, or if I had been more confident in my research abilities, I might not have left academics.

Alexey triumphed at Princeton High School. The school allowed him to take math courses at Princeton University. He took several, including the course in logic by John Conway and two courses in graph theory by Paul Seymour. Alexey’s multi-variable calculus professor complained to me that she couldn’t fit her grades into the required curve. If she gave Alexey 100%, the others would have to get less than 20. Luckily, it turned out that because her class was small, she didn’t need to bother about making a curve. After three years in Princeton High School, Alexey secured an impressive resume and great recommendation letters and went to MIT to pursue a double major in mathematics and computer science.

OnlineDegree.net selected the 50 Best Blogs for Math Majors, and I am pleased that Tanya Khovanova’s Math Blog is number two. Since they did not explain their criteria, I suspected that it might be according to the number of Google hits. To double check, I Googled “math blog” and once again my blog was number two.

This might be the right moment to acknowledge the others involved with my blog. First, Sue Katz, my writing teacher and editor, corrected the English in most of my posts. Now I do not “do” mistakes in English any more, I make them.

My sons, Alexey and Sergei, are a huge support. Sometimes my poor kids have to listen endlessly to my latest idea, until I am ready to write about it. And then they will even read the final piece, and continue to encourage me.

But the most important motivators are you, my readers. Your comments, your personal emails and your feedback keep me writing.

Do you know that some Russian letters are shaped exactly as some letters in the English alphabet? The shapes are the same, but the sounds of the letters are not. My Russian last name can be completely spelled using English letters: XOBAHOBA.

The adequate translation of my last name into English is Hovanova. You might ask where the first “K” came from. For many years French was considered the language of diplomacy and the USSR used French as an official language for traveling documents.

But “H” in French is silent and “Hovanova” would have been pronounced as “Ovanova.” To prevent that, Russians used “kh” for the “h” sound.

Now to my first name. I was born Tatyana, for which Tanya is a nickname. Back in Russia, Tanya is used for children and students and Tatyana for adults and teachers. As I was a student throughout my 30 years of life in Russia, I was always Tanya. When I moved to the US, I decided to keep using Tanya, which I much preferred to Tatyana.

A psychiatrist might think that I wanted to be a student forever or refused to grow up. Or I could be accused of being lazy, as Tanya is shorter. In reality, I was just trying to be considerate. Tanya is easier to write and to spell for Americans. Anyway, I already had enough problems spelling out my last name in this country.

Now that more information is getting translated from Russian into English, I keep stumbling on references to me as to Hovanova or Tatyana. For example, the IMO official website used Russian sources to come up with the names of the Russian participants. They then translated the names directly into English, instead of going through French. As a result, on their website I am Tatyana Hovanova. This is not unique to me: many Russian names on the IMO website differ from those peoples’ passport names.

By the way, if you Google my last name you will encounter other Khovanovas. Khovanova is not a particularly unusual name. Only one of the Khovanovas that came up in my search results is a close relative. Elizabeth Khovanova is my father’s second wife and a dear friend. She is also an accomplished geneticist.

Khovanova is used only for females in Russia. The male equivalent is Khovanov. Surely you have heard of my half-brother Mikhail Khovanov and his homologies.

I started my blog about two year ago. I have written about 200 entries. According to my traffic reports, these have been the top ten most popular entries:

1. The Odd One Out
2. Divisibility by 7 is a Walk on a Graph, by David Wilson
3. The Dirtiest Math Problem Ever (Rated R)
4. My IQ
5. A Miracle Equation
6. Back-to-School Funny Pictures
7. Flexible Zipcar Algorithm
8. A Very Special Ten-Digit Number
9. What Does It Take to Get Accepted by Harvard or Princeton?
10. AMC, AIME, USAMO Contradiction

My most popular category was Math Humor.

Israel Gelfand’s memorial is being held at Rutgers on December 6, 2009. I was invited as Gelfand’s student.

My relationship with Gelfand was complicated: sometimes it was very painful and sometimes it was very rewarding. I was planning to attend the memorial to help me forget the pain and to acknowledge the good parts.

I believe that my relationship with Gelfand was utterly unique. You see, I was married three times, and all three times to students of Gelfand.

Now that I know that I can’t make it to the memorial, I can’t stop wondering how many single male students of Gelfand will be there.

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.