Tanya Khovanova's Math Blog

I spend a lot of time working on my blog, and I used to think it would be nice to get some money out of it.

Years ago I got two emails from different ad agencies at the same time. They wanted to place ads at particular essays for $50 a year. I decided to give them a try.

My first correspondent wanted a link on my “Does Alcohol in Teens Lead to Adult Woes?” essay, connecting to a website offering help to alcoholics. I agreed. But when I read the actual text, I couldn’t stop laughing. The text they wanted to use was, “Many studies have already claimed that teenage alcoholism could lead to more problems later in life.” How ironic! This ad would follow my essay explaining that one of the studies is completely bogus. I rejected them.

The second agency wanted an ad accompanying the essay “Subtraction Problems, Russian Style.” I placed it. They wrote to me (and I reproduce it with all of their errors intact):

I really appreciate your efforts on this. As I checked the text link, I have seen that the text link has been label as “Sponsor ad”. Kindly omit or delete the word “Sponor ad:” or you may changed it to “Recommended site or Relevant Site” but I would love to prefer the text link be seen as natural meaning no labeled inserted on it.

They wanted me to pretend that I recommend their product. I was naive enough to think that I was selling space on my page, but what they really wanted was for me to lie that I like their product.

Before this experiment, I hoped to find some honest ads for my blog. After this experiment, I realized how much stupidity and falsehood are involved. Since then, I ignore all offers of ads that come my way. That’s why my blog is ad-free.

I grew up in the USSR, where I was clueless about the race issues in the US. I have now lived in the US for 30 years, and still feel that there are many things about race that I do not understand. As a result, I am afraid to speak about it. I am worried that I’ll say something wrong. Recent events have encouraged me to say something. This is my first piece about race.

I came back to mathematics 10 year ago and started working at MIT. I love it. With some exceptions.

Many mathematicians are introverts or snobs or gender-biased. They are not usually friendly. I often walk down a corridor and people who are coming towards don’t notice me. If I say hello, they might not even reply or raise their eyes. It could be they are thinking about their next great theorem and do not notice me. It could be that I am not faculty and therefore do not deserve their attention. It could be that as a women I am not worth of their hello.

Soon after I started working at MIT, I was reminded of one of the reasons I left academia. It was this unfriendliness. But this time was different. First, I had grown a thicker skin. Second, I was working within a group. People who were working with me were nice to me. It was enough and so I stayed.

With time I adopted the same style: passing people without saying `Hello.’ Mostly I got tired of people not replying to my hello.

One day I was passing this man who, as had happened many times before, purposefully didn’t look at me. I thought my usual thought: another introverted/snobbish/gender-biased mathematician. Then I suddenly stopped in my tracks. My logic was wrong. This guy was Black. The unfriendliness of mathematicians is surely way worse for him than for me. It could be that he is looking at the floor for the same reason I do it: he is afraid that people will ignore his greeting. I failed to think about race deep enough before this realization. What happened next should have happened years earlier.

I took the initiative and the next couple of times I saw him, I said hello. This was all it took—two hellos—to change the whole feeling between us. The guy has a great smile.

My friend Alice reminds me of me: she has two sons and she is never straight with her age. Or, maybe, she just isn’t very good with numbers.

Once I visited her family for dinner and asked her point blank, “How old are you?” Here is the rest of the conversation:

Alice: I am two times older than my younger son was 5 years ago.
Bob: My mom is 12 times older than my older brother.
Carl: My younger brother always multiplies every number he mentions by 24.
Bob: My older brother is 30 years older than me.
Carl: My mom is 8 times older than me.
Alice: My older son always multiplies every number he mentions by 2.

How old is everyone?

(Photo by Rebecca Frankel.)

When I was in grade school, one of the teachers called me Cave Lioness. She hated my unruly hair, which reminded her of a lion’s mane. This teacher was obviously very uninformed, for female lions do not have manes.

This name calling had the opposite to the desired effect. I became proud of my mane and didn’t ever want to cut it. When I grew older, I opted for convenience and started to cut my hair short—sometimes very short.

Last year I was too busy for barbers, and my hair grew more than I intended. As it turned into a mane, I remembered the story of this nickname.

Once I was giving a math lecture and my phone, which I’ve never quite understood, was on the desk in front of me. Suddenly it rang. I didn’t pick it up, as I proceeded with my lecture. The ringing stopped, while I was explaining a particularly interesting mathematical point. After a minute, my phone said, “I do not understand a word you are saying.”

I already wrote about my first experience crocheting hyperbolic surfaces. In my first surface I added two more stitches per current stitch. It took me hours to crochet the last row: the same hours it took me to crochet the rest.

For my next project, I reduced the ratio. The light blue thingy has ratio 3/2. I continued making my life simpler. The next project, the purple surface on the left, has ratio 4/3. The last project on the right has a ratio of 5/4 and is my favorite. Mostly because I am lazy and it was the fastest to make.

I just got this picture from my friend Victor Gutenmacher, which I never saw before. My 1975 IMO team is posing at our training grounds before the Olympiad trip to Bulgaria.

Left to right: Boris Yusin, Yuri Ionin, Zoya Moiseyeva (front), Gregory Galperin (back), me, Ilya Yunus, Valentin Skvortsov, Aleksandr Kornyushkin, Sergei Finashin, Sergei Fomin (front), Alexander Reznikov (back), Yuri Shmelev (front), Yuri Neretin (back), Victor Gutenmacher.

Our coaches are in the shot as well. Surprisingly, or not surprisingly, all of them moved to the USA. Yuri Ionin, now retired, was a professor at Central Michigan University. Gregory Galperin is a professor at Eastern Illinois University. Sergei Fomin is a professor at the University of Michigan. Victor Gutenmacher worked for BBN Technologies and Siemens PLM Software, and is now retired.

There are two more adults in the picture: Valentin Anatolievich Skvortsov, our leader and Zoya Ivanovna Moiseyeva, our deputy leader. Skvortsov was working at the math department of Moscow State University at that time. The University was angry that he didn’t block some students with Jewish heritage from the team thus allowing them to be accepted to Moscow State University without exams. I wrote a story of how Zoya persuaded Alexander Reznikov not to go to Moscow University to help Valentin. It ruined Alexander’s live, and didn’t even help Valentin. 1975 was Valentin’s last trip as the leader.

I do not like making objects with my hands. But I lived in Soviet Russia. So I knew how to crochet, knit, and sew — because in Russia at that time, we didn’t have a choice. I was always bad at it. The only thing I was good at was darning socks: I had to do it too often. By the way, I failed to find a video on how to darn socks the same way my mom taught me.

Then I came to the US. I suddenly found myself in a rich society, where it was cheaper to buy new stuff than to spend the time doing things with my hands. So I happily dropped my craftsmanship.

After not working with my hands for 28 years, one day I needed hyperbolic surfaces for my classes and I couldn’t find any to buy. Hyperbolic surfaces are famous for providing an example when the Euclid’s Fifth axiom doesn’t work. These hyperbolic surfaces look flat locally, so you can continue a line in any given direction. If you draw a line on such a surface and pick a point that is not on the line, then you can draw many lines through the point that are parallel to the given line.

My students are more important than my dislike of crochet, so I decided to just do it myself. I asked my friend Debbie, who knows how to crochet, for advice, and she gave me more than advice. She gave me a hook and a piece of yarn and reminded me how to work the hook. She started me with a small circle. After that all I had to do was add two stitches for each stitch on the perimeter of the circle. The finished product is this green ballish thing that looks like a brain, as in the photo.

Outside the starting circle, each small surface segment of this “brain” looks the same, making the “brain” a surface of constant curvature.

I chose a ratio of 2 to 1, adding two new stitches for each previous stitch. With this ratio, my flattish surface started looking like a ball very fast. The length of the perimeter doubled for every row. Thus each new row I crocheted took the same total amount of time that I had already spent on the whole thing. All the hours I worked on this “brain,” I kept thinking: darn, it is so unrewarding to do this. Annoying as it was, the thing that kept me going was my initial decision to continue to use up all the yarn Debbie had given me. In the end, with this ratio, half the time I worked was spent making the final row.Share:

A cartoon based on my script is posted on TEDEd: Can you solve the Leonardo da Vinci riddle?.Share:

My mom died in April of 2017. I didn’t even consider flying to Russia for her funeral. April-May is my most demanding work period. We were preparing for the annual PRIMES conference. Four of the projects that I personally mentor were presented at the conference. As a head mentor, I was also helping on all the other projects. During these months, I do not have time to breath.

I felt intensely guilty missing the funeral, but I blocked my emotions and worked. I didn’t shed a tear. Come June-July, I have another busy work period running Mathroots and RSI. August is often a slow month, which I usually use to finish papers that I am writing with my students. But in August, 2017, I needed to put the papers aside and give myself time to grieve. My mood was getting darker and darker. At some point I realized that I was depressed. Surprisingly, I still didn’t shed a tear.

I had been depressed before, and I do not ever want to be in that place again. I ordered myself to stop mourning, and with some positive self-talk, I was able to get myself out of the depression. In the process I didn’t work much in August, leaving me with a huge backlog of papers: I had about 20 papers that needed my immediate attention.

When the academic year began in September, my work was more stressful than ever. On one hand I had a pile of unfinished papers, and on the other hand our programs were growing bigger and more taxing. I limped along and did my best until April of this year. Because I had more stress than ever before. Because April-May is my most intense work time, I had to cancel my social life, stop watching TV, and drop my exercise regime to be able to prepare for our annual PRIMES conference. I was so busy I completely missed the first anniversary of my mom’s death. In the year since her death I had been mourning, but I was still unable to cry. When I realized that I had forgotten this date, I felt more severe guilt than ever. I called my sister in Moscow. She told me that she had ignored the death anniversary too. She had done it on purpose. It is better to celebrate life than death, she told me, and it made me feel better.

When the PRIMES conference was over, it was clear that my work was overtaking my life. I decided to go away for a day to rethink my priorities.

I googled Googled around for a place to go, and found the Innisfree garden. The website claimed that the garden is recognized as one of the world’s ten best gardens. Sounded fitting for rethinking a life.

The Innisfree Garden is different from other gardens that I have seen. With my untrained eye, I couldn’t distinguish what was man-made and what was nature. Slowly it became clear that things that look like nature are in reality a work of genius. The human touch amplified the natural beauty of the land and transformed it into something out of this world: beautiful, peaceful, and serene.

I spent hours in the garden. When I was about to leave, my floodgates were open. I started crying. Mom, I love you; please forgive me.Share: