Archive for the ‘My Career and Personal Life’ Category.


Starting position

My brother, Mikhail Khovanov, has invented a new game: Ringiana. It is now available for iPhone, and soon should be available for Android.

In the starting position you see four multi-colored quadrants of a ring. For example, the first picture shows the starting position of level 33.

You can either swipe or touch between the quadrants. A swipe expands one quadrant into two quadrants and compresses two other quadrants into one. You can swipe clockwise or counterclockwise. The second figure shows the result of the clockwise swipe of the North opening. The NW quadrant that was half-red and half-yellow has expanded into two quadrants. The red piece now occupies the entire NW quadrant and the yellow piece—the entire NE quadrant. Two East quadrants got contracted into one SE quadrant. The former blue NE quadrant became the top blue half of the SE quadrant. The former SE half-blue half-green quadrant became the bottom half of the SE quadrant. In general the quadrant where the swiping movement starts expands in the direction of the swipe and the quadrant where the swiping movements ends together with the next quadrant compresses.


After Swipe
After Touch
End Game

You can also touch an opening between quadrants. In this case the neighboring quadrants exchange places. The third figure shows the result of touching the East opening.


The goal of the game is to reach the final position: have each quadrant in one color. The next image shows the end of this particular level. As you can see the game was finished in 7 moves. In this particular case this is the smallest number of moves possible. To tell you a secret, it wasn’t me who finished the game in the smallest number of moves: it was my brother.

There is also a tutorial for this game on youtube.


Where is My Team Now?

I was at the 1976 International Mathematics Olympiad as part of the USSR team. There were eight people on the team and I decided to find out what they have achieved in the last 40 years. Here is the picture of our team. From left to right: Sergey Finashin, Yuri Burov, Nikita Netsvetaev, Boris Solomyak, Alexander Goncharov, Tanya Khovanova, Sergei Mironov, our chaperone Z.I. Moiseeva, our team leader A.P. Savin, no clue who this is (probably a translator), Piotr Grinevich.

USSR 1976 IMO Team

The list below is ordered by the number of points received at the Olympiad.

Tanya Khovanova, 39 points: a lecturer at MIT. I am interested in a wide range of topics, mostly recreational mathematics and have written 60 papers.

Sergey Finashin, 37 points: a full professor at Middle East Technical University in Turkey, who is interested in topology. He wrote 40+ papers.

Alexander Goncharov, 37 points: a full professor at Yale University. He is the highest achiever on the team. He won the EMS Prize in 1992 and was an Invited Speaker at the 1994 International Congress of Mathematicians. He is interested in geometry, representation theory, and mathematical physics. He published 75 papers in refereed journals.

Nikita Netsvetaev, 34 points: a full professor at Saint-Petersburg University in Russia. He is interested in topology and algebraic geometry and wrote 20 papers.

Boris Solomyak, 31 points: a full professor at Bar-Ilan University. He is interested in fractal geometry and dynamical systems and wrote 90 papers.

Piotr Grinevich, 26 points: a leading scientific researcher at the Landau Institute for Theoretical Physics. He also teaches at Moscow State University. He is interested in integrable systems and wrote 80 papers.

Sergei Mironov, 24 points. Sergey became very ill while he was an undergrad. He stopped doing mathematics.

Yuri Burov, 22 points. Yuri wrote two papers, but quit mathematics after graduate school. He died several years ago from multiple sclerosis.

Six out of eight people on our team became mathematicians. Or more precisely five an a half. I consider myself a mathematician and am grateful for my position at MIT, where I run innovative programs for young mathematicians. But in the research world, a lecturer is a nobody. This makes me sad. I had to take breaks from research in order to raise my two children. And then I had to work in the private sector in order to support them. I was the best on my team and now I am the only one who is not a full professor. If you are looking for an example of how gender affects a career in academia, this is it.


I do not Trust My Gut Feeling Anymore

For many years I tried to lose weight using the idea that most appealed to me: intuitive eating. By that I mean that you eat only when you are hungry. Looking back at frustrating years of trying, I wonder what took me so long to realize that this doesn’t work.

I am most hungry at the end of a meal. The only time I want to kill people is when they get between me and my future third helping of cheesecake. I never get the same ravenous feeling if I haven’t eaten for some time, or have just started eating.

I am least hungry in the morning. I can work on my computer for hours before I even remember that I need to eat.

When my stomach signals that it needs more food, it is always wrong. Recently, I discovered what is right. I am using myfitnesspal app for my phone that counts my calories. From time to time I know that I haven’t eaten enough. At these times, I don’t experience my hunger in my gut. I feel it in my head: I feel dizzy.

I decided to drop the idea of intuitive eating and outsource the decision of when and what to eat to a higher power: my smart-phone.


My Poster Boy

Sergei and Two Sigma PosterAfter graduating from MIT, my son Sergei joined Two Sigma, a hedge-fund. Last year he came to MIT representing Two Sigma at a career fair. I visited him in his booth. He was just standing there next to himself on the poster.

I should stop worrying about him. If math does not work out, he has a chance at modelling.


Plan B

I’ve been trying to lose weight for three years. I wasn’t very successful, but I always had plan B. I just didn’t like it. I started my weight-loss journey at 245 pounds. Driven by my initial enthusiasm, I lost 25 pounds, but then I slowly gained back 20 pounds. That was it. I had to do the difficult thing: plan B.

My plan B was to log all I eat, convert it to nutrition elements, study it, and adjust my eating habits accordingly. I didn’t want to do that: it seemed so complicated. I am not good at estimating weights, nor do I know how to convert food to calories and fat. Besides, it all seemed like such a bother.

When I gained back the weight and reached 240 pounds, I didn’t feel I had much choice. At that point my friend Luba showed me how to use the phone app myfitnesspal. I loved it. The app simplified the whole challenge. I bought a small kitchen scale to help me determine food weight, but more often than not, I don’t need it. The app has a database of standard foods, as well as a barcode scanner. For example, when I take my favorite cranberry walnut roll that I buy at Trader Joe’s, I just scan the barcode and the phone tells me, “Oops. 210 calories.” This means I can only eat one a day — not all six as I might have done.

I started using this app on November 16, 2015. It seems to be working. And I made a lot of interesting discoveries.

  • Those walnuts that I eat like popcorn while watching movies have a ton of calories. They might be healthy natural food, but if I munch them throughout a movie, then I can’t eat anything else that day.
  • When I know that I can only allow myself one square of chocolate, it tastes better than pigging out on the whole bar.
  • I made a rule of logging my food before I eat it. This killed my habit of snacking. Finally, my laziness works for me.

I am losing weight, but to avoid jinxing it until I achieve a certain target, I don’t want to reveal actual numbers.

To be continued…


Evil Bananas

Although I cut most carbs from my diet, I still wasn’t losing weight. I started my weight-loss journey three years ago when I was 245 pounds. My initial excitement helped me get to 220, but then I started slowly gaining it back to 235 pounds. A couple of friends of mine who lost a lot of weight explained to me that I didn’t actually cut all the carbs from my diet. I eliminated pizza, potatoes, spaghetti, sugar, cookies, soda, and so on. But there are many carbs hidden in some very natural and healthy foods. For example, a banana has 27 grams of carbs.

I love bananas; I can live on bananas alone. But my friends convinced me to cut the bananas, too. I agreed, but in that week I gained five more pounds. I think that every time I remove something from my diet, I end up becoming more relaxed with other food.

Clearly, carbs-cutting doesn’t work. I am back to 240 pounds. Time for plan B.


Ode to Menopause

As a child I felt that society expected me to grow up and be a mother. And only to be a mother. It didn’t make any sense to me, because if all that people do is reproduce, how will progress be made? So in my teens I decided that in addition to having children, I need to do something else, something to make the world a better place.

For many years I wasn’t too successful in my plan. My children were my priority. I believed that for the first three years they needed a lot of my attention, which they couldn’t necessarily get from a nanny. Later, being a single mother was so overwhelming that I didn’t have time for other missions.

As my children grew, I felt myself imposing my own ambitions onto them. It wasn’t fair to burden my children like that. I was meant to do something with my life other than bring up children. There was no substitute — I had to do it myself.

At that time, I was working at BAE Systems, but I hated my job. Its only purpose was to support my family. So as soon as my youngest son turned 16, I resigned to come back to mathematics. Though mathematics has my full attention now, my children are still my priority. I can afford to do what I love, because it is good for my children too. I am living my own ambitions, and they have the space to live theirs.

I was supposed to write about menopause. I am writing about menopause, just give me a second. I was also raised to believe that the best thing I can do for a man is to give him children. Every time I loved someone I wanted to have a child with that person, or I thought that I was supposed to want to. Now that I can’t conceive a child for any potential future husband, I feel relieved. I can’t be blamed any more for not having children. I am so happy that my current attempt at mathematics will not be interrupted any more.

I am so glad that I live in an age when women’s life expectancy is way past menopause. I might love a man again; I might marry. I am so glad that I have an excuse not to have children. I can do what I want to do. I am free.


Finding My Own Niche

I enjoy doing research in recreational mathematics. The biggest problem is that the probability that something I’ve done has already been done before is very high. This is partially because of the nature of this area of research. Trying to find new questions that are not buried deep in the abstract means someone else could have stumbled upon the same question. In addition, I like going in different directions: geometry, number theory, probability, combinatorics, and so on. That means I am not an expert in any of the areas. This too increases my probability of doing something that has already been done before.

This is quite unpleasant: to discover that I reinvented the wheel. And I keep reinvented different wheels on a regular basis. When I complain, my mathematician friends give me the same advice over and over:

Find your own niche!

I’ve been trying to understand what they mean, and finally I got it:

Do something no one else is interested in using methods no one else can understand.

Finding a topic that is not interesting almost guarantees that other people didn’t do it before. Developing new complicated methods helps limit the number of followers and prevents the niche from becoming crowded.

Now I know why I see so many boring math papers I can’t understand.

To hell with my own niche!


Who Proved Theorem 5?

Let me start with a real story that happened a long time ago when I worked with my co-author on a math project. When I told him the idea I came up with, he dismissed it. The next day he came to me very excited with his new idea. He repeated the idea I had proposed the day before.

I said, “I suggested this exact idea to you yesterday.” He didn’t believe me. Luckily for our relationship, I knew him very well. He was not a person who lied. I remembered how preoccupied he was when I had laid out the idea to him. Now I think that he didn’t pay attention to my idea at the time, but it was lodged somewhere in his subconscious and surfaced later. I am sure that he truly believed that the idea was his. (Unfortunately, he didn’t believe me. But this is another story.)

This story made me think about the nature of collaboration and how people can’t really separate ownership of the results of a joint project. Let me tell you another story, one that I do not remember happening, although it could have.

I was working on a paper with my co-author on Sharelatex. One day an idea for a lemma came to me that we hadn’t discussed before. My co-author lives in a different time zone, so instead of discussing the idea with him, I just added Lemma 3 and its proof to our paper. I was truly proud of my own contribution.

The next day I came up with Lemma 4 while driving back home. It was another completely new direction for our research. When I came home to my laptop, I discovered my Lemma 4 neatly written and proven by my co-author. Is this lemma his? It can’t be completely his. It was a natural extension of what we discussed; he just got to a computer before me.

Did you notice in the last story that the situation is symmetric, but my hypothetical feelings are not? In a true collaboration ideas are bounced off each other. Very often people come up with the same idea at the same time, but you can’t ascribe ownership to the first person who speaks. Because of many stories like this, I made a rule for myself: never discuss in public who did what in a joint paper. Just always say “we.”

Unfortunately I keep forgetting to teach my PRIMES/RSI students that. The question usually doesn’t come up until it is too late, when one of the students in a group project during a presentation says, “I proved Theorem 5.” Oops!


My Six Jobs

I promised to explain my job situation to my readers. I currently have six part-time jobs, which I describe below in the order that I started them.

The job I have had the longest is coaching math for competitions at AMSA Charter School. I started there in the spring of 2008 and I am still teaching there every week. I post my homework assignments on my webpage for other teachers and students to use.

The next longest has been as the Head Mentor at RSI, which I started in the summer of 2009. RSI is a great program where high school students from all over the world come to MIT to do research during summer vacations. It is amazing how much an ambitious student can do during a short five-week period. My first year I saw some great research done, but I was surprised that RSI papers were generally not available online. Beginning in 2012, at my recommendation, our Director Slava Gerovitch now posts the RSI papers at the math department RSI webpage.

As good a program as it is, RSI is too short for a research project. So we decided to develop our own program called PRIMES (Program for Research in Mathematics, Engineering, and Science for High School Students). I am also the Head Mentor in this program. I provide general supervision of all the projects and review conference slides and final papers. In addition to being the Head Mentor, I mentor my own students, which is great fun. I usually have three projects, but if something happens to a project or a mentor, I take it over.

Together with Pavel Etingof, PRIMES Chief Research Advisor, and Slava Gerovitch, PRIMES Director, I wrote an article Mathematical Research in High School: The PRIMES Experience that appeared in Notices.

My job #4, since the fall of 2013, is as a Teaching Assistant for the MIT linear algebra course.

This year I took on two more jobs at MIT. I am the Head Mentor at Mathroots, a summer program for high school students from underrepresented backgrounds. I am also teaching at PRIMES STEP, the program for gifted middle-school students in the Boston area. The goal of the program is to teach students mathematical thinking, have fun, and prepare them for PRIMES.

Overall, I have reached the stage in my career when I do not have time to breath and I still do not make enough money to pay my bills. The good news: my jobs bring me satisfaction. I just hope that I will not be too tired to notice that I am satisfied.