Tanya Khovanova's Math Blog

At the 2011 IMO, Lisa Sauermann received yet another gold medal. Now she tops the Hall of Fame of the IMO with four gold medals and one silver medal.

In addition, in 2011 she achieved the absolute best individual result and was the only person with a perfect score. In previous years, there were several girls who tied for first place, but she is the first girl ever to have an absolute rank of 1.

I told you so. In my 2009 essay Is There Hope for a Female Fields Medalist?, I predicted that a girl will soon become an absolute champion of the IMO.

In that essay I draw a parallel between the absolute champion of IMO and a Fields medalist. Indeed, we get one of each per year. Lisa Sauermann is the best math problem solver in her year. Will she grow up to receive a Fields medal? I am not so sure: the medal is still unfriendly to women. Lisa Sauermann is the best math problem solver ever. Will she grow up to be the best mathematician of our century? I wonder.

My e-friend and coauthor, Konstantin Knop, designed the following problem for the 2011 All-Russia Olympiad:

Some cells of a 100 by 100 board have one chip placed on them. We call a cell pretty if it has an even number of neighboring cells with chips. Neighbors are the cells that share a side. Is it possible for exactly one cell to be pretty?

The problem is not easy. Only one person at the Olympiad received full credit for it.

From time to time my female colleagues share stories with me of great unfairness or horrible sexual harassment in the world of mathematics. I can’t reciprocate — certainly not on that level.

I do not have any horror stories to tell. Generally I am treated with great respect, at least to my face. In fact, some men have told me that I am the smartest person they ever met.

The stories I want to share are not about harassment. No single incident is a big deal. But when these things happened time after time after time, I realized: this is gender bias.

First story. A guy told me, “Your proof is unbelievably amazing.”

What can I say? It is just a compliment. Though I am not sure why the word “unbelievable” was included. Is it difficult to believe that I can produce an amazing proof? I encounter surprise too often to my taste.

Second story. Another guy tells me after I explain a solution to a math problem, “I didn’t realize it was so simple.”

Actually it wasn’t simple. When I explained the solution, it may have seemed simple, but that was because I was able to explain it to him with such clarity. People tend to downgrade their opinion of the problem, rather than upgrade their opinion of my ability. It actually affects my reputation as a mathematician.

Third story. Another guy said to me (and I quote!), “I am so dumb. I tried for a week to write the program that computes these numbers and you did it in one hour. I feel so dumb. I didn’t expect myself to be so dumb. Why am I so dumb?”

After the fourth “dumb”, I started wondering what it was all about. Many guys try to compete with me. And they hate losing to a woman. It creates a strong motivation for them to discard my brilliance and to explain away my speed, even if they have to claim temporary dumbness.

Fourth story. Someone asked me, “What is the source of the solutions and math ideas in your blog? Can you refer me to the literature?”

I do invest extra effort in citing the sources of the math puzzles I discuss. Everything else — the solutions, the ideas, new definitions, new sequences — I invent myself. I have even started inventing math puzzles. This is my blog. I thought of it myself, I wrote it myself. Has anyone ever asked Terence Tao where he takes the solutions for his blog from?

Unfortunately, this attitude damages my career. When people think that my ideas come from someone else, they do not cite me.

But all these stories however minor happen all the time, not only to me but to all my female colleagues. Gender bias is real. Next time someone tells me how unbelievably amazing my proof is, I will explode.

Recently I stumbled on a cute xkcd comic with the hidden message:

Wikipedia trivia: if you take any article, click on the first link in the article text not in parentheses or italics, and then repeat, you will eventually end up at “Philosophy”.

Naturally, I started to experiment. The first thing I tried was mathematics. Here is the path: Mathematics — Quantity — Property — Modern philosophy — Philosophy.

Then I tried physics, which led me to mathematics: Physics — Natural science — Science — Knowledge — Fact — Information — Sequence — Mathematics.

Then I tried Pierre de Fermat, who for some strange reason led to physics first: Pierre de Fermat — French — France — Unitary state — Sovereign state — State — Social sciences — List of academic disciplines — Academia — Community — Living — Life — Objects — Physics.

The natural question is: what about philosophy? Yes, philosophy goes in a cycle: Philosophy — Reason — Rationality — philosophy.

The original comic talks about spark plugs. So I tried that and arrived at physics: Spark plug — Cylinder head — Internal combustion engine — Engine — Machine — Machine (mechanical) — Mechanical system — Power — Physics.

Then I tried to get far away from philosophy and attempted sex, unsuccessfully: Sex — Biology — Natural science. Then I tried dance: Dance — Art — Sense — Physiology — Science.

It is interesting to see how many steps it takes to get to philosophy. Here is the table for the words I tried:

Mathematics wins. It thoroughly beats all the other words I tried. For now. Fans of sex might be disappointed by these results, and tomorrow they might change the wiki essay about sex to start as:

Modern philosophy considers sex …

Not personally. Someone hacked into my website.

I would like to thank my readers Qiaochu Yuan, Mark Rudkin, “ano” and Paul who alerted me to the problem. Viewers who were using the Google Chrome browser and who tried to visit my website got this message: “This site contains content from howmanyoffers.com, a site known to distribute malware.”

It took me some time to figure out what was going on. It appears that on June 19 someone from 89-76-135-50.dynamic.chello.pl hacked into my hosting account and added a script to all my html files and to my blog header. It seems that the script was dormant and wasn’t yet doing bad things.

As soon as I grasped what was going on, I replaced all the affected files.

I have had my website for many years without changing my hosting password. Unfortunately, passwords, not dissimilar to humans, have this annoying tendency to become weaker with age. I wasn’t paying attention to the declining strength of my password and so I was punished.

Now I have fixed the website and my new password is: qwP35q2054uWiedfj052!@#$%.

Just kidding.

by Gregory Marton

I recently had the following chat with a particular calculator:

• e^(e^(e^(e^e))) = 10^(10^(10^6.219196780089781))
• e^(e^(e^(e^(e^e)))) = 10^(10^(10^(10^6.219196780089781)))
• e^(e^(e^(e^(e^(e^(e^(e^(e^e))))))) = 10^(10^(10^(10^(10^(10^(10^(10^6.219196780089781)))))))

It seems odd to me that putting a few more e’s down the bottom should result in it thinking there were the same number of extra 10s at the bottom. In fact, I’ve never seen a calculator answer in this form at all. I’m especially intrigued that the final power of ten seems to be the same in all three cases, so it can’t even just be estimating. Do you have any thoughts on what screwy counting could be behind these particular answers?

May the Mass times the Acceleration be with you!

John Conway taught me how to tell time at night. But first I need to explain the notions of the “time in the sky” and the “time in the year.”

The clock in the sky. Look at Polaris and treat it as the center of a clock. The up direction corresponds to 12:00. Now we need to find a hand. If you find Polaris the way I do, first you locate the Big Dipper. Then you draw a line through the two stars that are furthest away from the Big Dipper’s handle. The line passes through Polaris and is your “hour” hand. Now you can read the time in the sky.

The hand of the clock in the sky makes a full rotation in approximately 24 hours. So if you stare at the sky for a long time, you can calculate the time you spent staring. Keep in mind that the hand in the sky clock is twice as slow as the hour hand, and it turns counter-clockwise. So to figure out how long you’re looking into the sky, take the sky-time when you start staring, subtract the sky-time when you stop staring and multiply the result by 2.

To calculate the absolute time, we need to adjust for the day in the year.

The clock in the year. A year has twelve months and a clock has twelve hours. How convenient. You can treat each month as one hour. In addition as a month has about 30 days and an hour has exactly 60 minutes, we should count a day as two minutes. Thus, January 25 is 1:50.

Fact: on March 7^th at midnight the clock in the sky shows 12:00. March 7^th corresponds to 3:15. So to calculate the solar time you need to add up the time in the sky and the time in the year and multiply it by 2. Then subtracting the result from 6:30, which is twice 3:15, you get the solar time.

You are almost ready. You might need to adjust for daylight savings time or for peculiarities of your time zone.

This time formula is not very precise. But if you are looking into the sky and you do not have your watch or cell phone with you, you probably do not need to know the time precisely.

In my life as a female mathematician I have quite often encountered a mathematician’s wife who, despite not knowing me, already hated me. It was clear that it had nothing to do with me personally, so being clueless and naive, I assumed that most men were cheaters and that their wives were extremely insecure and jealous.

Then one day one of the wives decided to be frank about her feelings. It wasn’t about cheating, she told me. It was that she felt distant from her husband. He lived in a world of mathematics from which she was excluded. I on the other hand shared this world with him.

It was very sad. It meant that I incurred their jealousy, not because of my sins, but because I am a female mathematician.

Let me tell you another story that helped me realize how all-encompassing this world of mathematics can be for some people. Once I had a very close friend who we will call Jack. I do not want to name him as he is a famous mathematician. Jack told me that the strongest emotions he feels are related to mathematics. He can only feel close to someone if he can share a mathematical discussion with them.

Now I understand the wives better. Husbands like Jack invest so much more in their math world and their colleagues than they do in their home life, that it is not surprising the wives are jealous. Because women mathematicians are scarce, when I appear in their husbands’ world, it adds another layer of worry.

Another thing that Jack told me is that he gets such a euphoric feeling when he discovers a new math idea that it is better than any orgasm. Of course, this statement made me question the quality of Jack’s orgasms, but in any case, for some mathematicians math is an aphrodisiac.

If math is an aphrodisiac, then tattooing a formula on the lover’s body may well enhance the orgasm. I just remembered the movie by Ed Frenkel. But I digress.

If math is an aphrodisiac, then I understand jealous wives even better. Without sex I can give their husbands pleasure they can’t.

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I am taking my dog to tweet. He’ll check other dog’s posts at every pole and will leave his comments.

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Not many people know that 1000 chameleons is a chabillion.

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The Internet paradox: it connects people who are far apart, and disconnects those who are close.

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We bought a cell phone for our TV set. We attached it to the remote control, so that we can call our TV when the remote is lost.

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Mary’s mom failed arithmetic. Actually, that is why Mary was born.

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Your call is very important to us. Please, hold. And in the meantime, to protect your health, our customer care team encourages you to drink a glass of water at least every two hours.

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Who is your favorite computer game character?
The stick from Tetris.

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Our new boss invited everyone to bring their keyboards to his office. He kept the employees who had worn letters and laid off the ones with worn arrows.

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My son will be a hacker. He started his career before he was born: he found a flaw in the condom.