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

Trump’s Ban is Good for Trump’s Business

Like many people, I was appalled by Trump’s immigration ban. On the Internet I found many essays that explained that he did not include in the ban those majority-Muslim countries in which he has business interests. See for example, an article at Forbes with a nice map, and an article at NPR.

Now the countries that are excluded are motivated to continue to support Trump’s businesses, and to offer him bribes and good deals in exchange for staying out of the ban. The countries on the list are also motivated to approach Trump and offer him a sweet business deal.

So even if the courts stopped the ban, he has already succeeded in showing every country in the world that to be on his good side requires that they pay up. And China got the hint and granted Trump a trademark he’s been seeking for a decade.

Looks like Trump’s vision of a great America is a very rich Mr Trump.

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Russian and American Children

The first time I visited the US was in 1990 at the invitation of an old friend, Joseph Bernstein. After my arrival Joseph proposed and I accepted, but my essay is not about that.

Joseph reintroduced me to his daughter, Mira, who was then in her late teens. I was struck by Mira’s charm. I had never before met teenagers like her. Of course, Joseph got points for that as I was hoping to have a child with him. When I moved to the US I met some other kids who were also incredibly charming. It was too late to take points away from Joseph, but it made me realize what a huge difference there was between Soviet and American teenagers. American teenagers were happier, more relaxed, better mannered, and less cynical than Soviet ones.

My oldest son, Alexey, was born in the USSR and moved to the US when he was eight. One unremarkable day when he was in middle school (Baker public school in Brookline), the principle invited me for a chat. I came to the school very worried. The principal explained to me that there was a kid who was bugging Alexey and Alexey pushed him back with a pencil. While the principal proceeded to explain the dangers of a pencil, I tuned out. I needed all my energy to conceal my happy smile. This was one of the happiest moments of my life in the US. What a great country I live in where the biggest worry of a principal in a middle school is the waving of a pencil! I remembered Alexey’s prestigious school in Moscow. They had fights every day that resulted in bloody noses and lost teeth. When I complained to his Russian teacher, she told me that it was not her job to supervise children during big breaks. Plus the children needed to learn to be tough. No wonder American children are happier.

I was wondering if there were any advantages to a Soviet upbringing. For one thing, Soviet kids grow up earlier and are less naive. They are more prepared for harsh realities than those American kids who are privileged.

Naive children grow up into naive adults. Naive adults become naive presidents. I watched with pain as naive Bush (“I looked the man in the eye. I found him to be very straightforward and trustworthy.”) and naive Obama (Russian reset) misunderstood and underestimated Putin.

Putin is (and, according to Forbes Magazine, has been for the last four years) the most powerful person in the world. Even though the US kept its distance from Russia, he was able to manipulate us from afar. Now that Trump wants to be close to Putin, the manipulation will be even easier. Putin is better at this game. He will win and we will lose.

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Russian Honor Code

I have always wanted to be an honest person and have followed my honor code. Soviet Russia had two honor codes. One code was for dealing with people and the other for dealing with businesses and the government. I remind you that in Soviet Russia, all businesses were owned by the government. The money paid for work didn’t have any relation to the work done. The government paid standard salaries and the businesses did whatever. Generally, that meant that they were doing nothing. Meanwhile, the government got its income from selling oil.

All people were being screwed by the government, so they had no motivation to play fair. Just as American workers do, Soviet Russians might use the work copier to make personal copies. The difference was that we didn’t feel guilty at ripping off the government. We wouldn’t just make a few necessary copies; we would make copies for our friends, our family, for strangers—as many copies as possible.

I moved to the United States in 1990. Several of my friends took time to explain to me the difference between Soviet Russia and the US. One of the friends, let’s call her Sarah, was working as staff at Harvard University. She told me the story of a recent visit by a famous Russian professor. After he left, the department received a bill. It appears that the professor, in a short visit, used several months-worth of the department’s budget allocation for copying and phone calls. I was impressed, in a good way, by the professor who I assume spent a good deal of his time making a lot of copies of papers unavailable in Russia, presumably not only for himself but also for students and colleagues. On the other hand, it was clearly wrong.

My new friend Sarah told me that in the US money does not come from nowhere, and I should include Harvard University in my honor code for people. Actually, not only Harvard, but also any place of work and the government too. Sarah also told me that since that budget problem, she was asked to talk to every incoming Russian visitor and explain to them how capitalism works. Most Russian visitors were ready to accept the rules. I too was delighted with that. It is much easier to follow one honor code than two.

I was also very happy for my son, Alexey. He was eight when we moved to Boston. Before our move I had a dilemma. Should I tell him that Lenin and Stalin were bad guys and killed millions of people? If I gave him a truthful explanation, I would also have to teach him to lie. Otherwise, if he mentioned this at school or on the street, we would be at risk of going to prison. If I didn’t teach him the truth, he might become brainwashed and grow up believing in communism, which would be very, very bad.

I was so lucky that I moved to the US: I didn’t have to teach my son to lie.

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Should You Apply to PRIMES?

If you are a high-school student who wants to conduct research in mathematics, you should check out the MIT PRIMES program. If you enjoy solving the problems in our entrance test, that’s the first indication that you might want to apply. But to determine if the program is right for you, and you are right for the program, please read the following questions and answers which have been prepared for you by Tanya Khovanova, the PRIMES Head Mentor. (This only addresses applications to PRIMES Math, and only to the research track)

Question: I do not like math competitions. Should I apply?
Answer: Math competitions are completely separate from research in mathematics. If you enjoy thinking about mathematics for long periods of time and are fascinated by our test questions, you should apply.

Question: I am good at math, but I really want to be a doctor. Should I apply?
Answer: No. PRIMES requires a huge time commitment, so math should really be your most significant interest.

Question: I want to get into Harvard, and PRIMES looks good on a resume. Should I apply?
Answer: PRIMES does look good on a resume. But if you are more passionate about, say, climate change than math, what would Harvard’s admission committee see? Our experience in the program is that if math isn’t your top interest, your math student may not be sufficiently impressive to be accepted at Harvard as a math researcher. At the same time, you will not be accepted as the top climate change student as you didn’t invest your time in that. Math research is a hard way to earn points for college. See also, the essay, Thoughts on research by Simon Rubinstein-Salzedo.

Question: My parents want me to apply. Should I apply?
Answer: Your parents will not be accepted to the program. Do not apply if you do not really, really want to.

Question: Your website suggests that I should spend ten hours a week on the PRIMES project. I can only spend five. But I am a genius and faster than other people.
Answer: We already assume that you are a genius and faster than anyone else you know. Five hours a week are not enough for a successful project.

Question: I looked at the past PRIMES projects and nothing excites me as much as my current interest in Pascal’s triangle. I doubt I should apply.
Answer: When you start working on a project, you will learn a lot about it. You will understand why, for example, Cherednik algebras are cool. The excitement comes with knowledge and invested time. Not yet being excited about Cherednik algebras is not a good reason not to apply. Besides a lot of exciting mathematics is done between several different fields.

Question: I really want to do nothing else than study Pascal’s triangle.
Answer: We try to match our projects to students’ interests as much as we can. But we almost never can fulfill a specific request as above. You might get a project related to Young diagrams, which are connected to quantum Pascal’s triangle. If this connection doesn’t excite you, you shouldn’t apply.

Question: I think I will be better positioned for research if I spend five more years studying.
Answer: There is nothing wrong with this approach. For many years the standard was to start research in graduate school. Our program is innovative. At PRIMES we are trying a different model. It may sound scary, but you will learn everything you need to know in order to do your project. If the project is in representation theory, for example, you will only learn what you need—not the whole theory. Our hope is that eventually you will take a course in representation theory and expand your grasp of it and see the bigger picture behind your project. We have a reading track for people like you who reside in Boston area.

Question: I love math, but I am not sure that I want to be a mathematician. Should I apply?
Answer: Many people start loving math early in life and then discover that there are many other things that require a similar kind of brain: computer science, cryptography, finance, and so on. We do not require from our students a commitment to become mathematicians. If you want to try research in math, you should apply. If students decide that they do not want to do research in math after finishing our program, we do not consider that a negative result. One way or another, the experience of PRIMES will help you understand better what you want to do with your life.

Question: I want to get to the International Math Olympiad. I am afraid that the time the research project takes prevents me from preparing for competitions. Should I apply?
Answer: People who are good at Olympiads often have fantastic brain power that helps in research. On the other hand, research requires a different mind set and the transition might be painful. It is possible, but not trivial to succeed in both. It is up to you to decide how you want to spend your time.

Question: I like number theory, but I do not see past PRIMES projects in number theory.
Answer: Doable number theory projects are hard to come by and we have fewer number theory projects than students who want to do number theory. There are many high-school programs that teach number theory including PROMYS and Ross programs. Our applicants like number theory because they were exposed to it. During PRIMES you will be exposed to something else and might like it as much.

Question: I found a local professor to work with on a research project. Should I apply to PRIMES?
Answer: PRIMES requires that you devote 10 hours a week to research for a year. It is unrealistic to do two research projects in parallel. Choose one. Working with someone in person may be better than by Skype at PRIMES. Also, usually our mentors are not professors, but rather graduate students. On the other hand, they are MIT grad students and projects are often suggested by professors. Our program is well structured. We guarantee weekly meetings in the Spring, we give extra help with your paper, and we have a conference. It is up to you to decide.

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Late Homework

One of my jobs is giving linear algebra recitations at MIT. The most unpleasant aspect of it is dealing with late homework. Students attempt to submit their homework late for lots of different reasons: a sick parent needing help, stress, a performance at Carnegie Hall, a broken printer, flu, and so on. How do I decide which excuse is sufficient, and which is not? I do not want to be a judge! Moreover, my assumption is that people tell the truth. In the case of linear algebra homework, this assumption is unwise. As soon as students discover that I trust everyone, there’s a sharp increase in the number of sick parents and broken printers. So I have the choice of being either a naive idiot or a suspicious cynic. I do not like either role.

Our linear algebra course often adopts a brilliant approach: We announce that late homework is not allowed for any reason. To compensate for emergencies, we drop everyone’s lowest score. That is, we allow the students to skip one homework out of ten. They are free to use this option for oversleeping the 4 pm deadline. If all their printers work properly and they do not get so sick that they have to skip their homework, they can forgo the last homework. Happily, this relieves me from being a judge.

Or does it? Unfortunately, this policy doesn’t completely resolve the problem. Some students continue trying to push their late homework on me, despite the rules. In order to be fair to other students and to follow the rules, I reject all late homework. The students who badger me nonetheless waste my time and drain my emotions. This is very unpleasant.

From the point of view of those students, such behavior makes sense. They have nothing to lose and they might get some points. There is no way to punish a person who tries to hand in homework late and from time to time they stumble onto a soft instructor who accepts the homework against the official rules. Because such behavior is occasionally rewarded, they continue doing it. I believe that wrong behavior shouldn’t be rewarded. As a responsible adult, I think it is my duty to counteract the rewards of this behavior. But I do not know how.

What should I do? Maybe I should…

  1. Persuade our course leader, or MIT in general, to introduce a punishment for trying to hand in late homework. We might, for example, subtract points from their final score.
  2. Promote the value of honorably following the rules through discussions with the students.
  3. Growl at any student who submits their homework late.
  4. Explain to them what other people think about them, when they do not follow the rules.

Maybe I should just do number 4 right now and explain what I feel. A student who persists in handing in homework late feels to me that s/he is entitled and is better than everyone else, and shows that s/he doesn’t care about the rules and honor. Again, this wastes my time, puts me in a disagreeable position, and reduces my respect for that student.

Earlier I suggested that students don’t have anything to lose by such behavior, but in fact, they do pay a price, even though they may not understand that.

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Mikhail Khovanov at Kvant

MishaRussians cherish the issues of Kvant, a famous Soviet monthly magazine for high-school students devoted to math and physics. At its peak its circulation was about 300,000, which is unparalleled for a children’s science journal. I still have my old childhood issues somewhere in my basement. But one issue is very special: it has a prominent place in my office. I didn’t receive it by subscription; I received it as a gift from my brother Misha.

Strictly speaking Misha is not my brother, but rather a half-brother. His full name is Mikhail Khovanov and he is a math professor at Columbia. The signed issue he gave me contains his math problem published in the journal. He invented this problem when he was a 10th grader. Here it is:

In a convex n-gon (n > 4), no three diagonals are concurrent (intersect at the same point). What is the maximum number of the diagonals that can be drawn inside this polygon so that all the parts they divide into are triangles?

He designed other problems while he was in high school. All of them are geometrical in nature. The journal is available online, and a separate document with all the math problems is also available (in Russian). His problems are M1038, M1103, M1108 (above), M1119, M1153, M1204. I like his other problems too. M1153 (below) is the shortest problem on his list: as usual I am guided by my laziness.

What’s the greatest number of turns that a rook’s Hamiltonian cycle through every cell on an 8 by 8 chessboard can contain?

I wanted to accompany this post with a picture of my brother at the age he was when he invented these problems—about 16. Unfortunately, I don’t have a quality picture from that period. I do have a picture that is slightly off: by about ten years.

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Ringiana

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.

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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.

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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.

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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.

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