Archive for the ‘Women and Math’ Category.

Should There Be Separate Math Competitions for Girls?

I grew up a purist. Mathematics was about mathematics, not about gender. I personally would never have competed in a math competition exclusively for girls. I would have felt diminished somehow. Furthermore, suppose there were separate math competitions for boys, where girls were not allowed. I would have felt outraged. By symmetry, I should have been outraged by math competitions exclusively for girls.

When I first heard about math competitions for girls, I was uncomfortable. I also noticed that my Eastern European friends shared my feelings, while my other friends did not.

There was a stage in my life when I lived in Princeton for seven years and became friends with Ingrid Daubechies, who is NOT Eastern European. She didn’t share my extreme views, and we argued a lot. Every spring, there was a big conference for Women-in-Mathematics at the Institute for Advanced Study in Princeton. But I was stubborn and completely ignored it. With one exception: when Ingrid gave a lecture there, I went just to hear her talk.

In 2008, I was living in Boston, worrying about money, as I had just resigned from my industry work to return to mathematics. Out of the blue, Ingrid called to offer me a job at that very same Women-in-Mathematics conference. I admire Ingrid and got excited about working with her. More importantly, I needed the money. So I decided to put aside my prejudice and take the job.

Being part of the conference was a revelation. Although most of the two-week conference was spent on mathematics, there were some women-and-math seminars. There, women discussed bullying by advisers and colleagues, impostor syndrome, workplace bias, the two-body problem, and other issues. And guess what? I went through all of that too. I just never realized it and never talked about it.

My biggest regret was that I hadn’t attended the conference earlier. Plus, the conference didn’t feel unfair towards men: all lectures and math seminars were open to the public, and some courageous guys sat in.

What about my symmetry test? What happens if we swap genders? Should there be separate math conferences for men, open to the public? The idea makes me laugh. Women are in the minority in math, and many conferences already feel like conferences for men open to the public. My symmetry test doesn’t quite work.

But, while I saw how helpful the support was for female mathematicians and for me, something still bugs me. Where is the fine line between minority support and unfairness? Let’s look at math clubs for girls. On the surface, there are so many math clubs, so why not have the occasional math club for girls? I can imagine a girl, not me, who would prefer to attend such a club. However, girls’ clubs often have sponsors and are much cheaper to attend than regular clubs. This is unfair to boys whose parents can’t afford a regular club. It also becomes counterproductive for girls. What if some girls go to such a club, not because they need a special environment but because it is a cheaper club? They are missing out on the fun of learning math together with boys. (Trust me, I know!) So, I am not sure where that line is.

I am older and wiser now. I do not run away from events organized for women in math. I think lunches and dinners for women in math are great. They help female mathematicians find mentors, build networks, and stay in mathematics.

What about my original question: Should there be separate math competitions for girls? In a truly equal society, math competitions should be for everyone. And, though I do not actively oppose girls’ competitions anymore, I hope the need for them will die out in my lifetime.


A Mathematical Model for Gender Bias in Mathematics

I still get comments that my place is in the kitchen, and women shouldn’t do math. Luckily, occurrences of such events are getting rarer. So the world is progressing in the right direction. But gender bias still exists. Multiple studies show that among people of the same level of intelligence, men are perceived as smarter. In layman’s terms, people think women are stupider than they are. I will give my own examples at another time. But now, I want to discuss my model for gender bias.

Let’s denote the mathematical strength of a researcher by S. In real life, if the researcher is female, people perceive her strength as smaller than S. Let us assume that there exists a bias coefficient B, a number between 0 and 1 so that a female researcher of strength S is perceived on average as having strength BS. When B is 1, then there is no bias. But the world is not there yet.

In recent years, there has been a push to hire female mathematicians. Suppose a math department has a cutoff C for hiring a math professor. Being eager to hire a female professor, the department slightly reduces the cutoff by the bias reduction coefficient R, where R is a number between 0 and 1. Thus, the cutoff to hire a female professor becomes RC, which is less than C.

Now consider Alice, who has mathematical strength S, such that SCBSRC. She is perfectly qualified to be hired by the department independent of her gender. However, the department members, on average, perceive her strength as not good enough for a male hire but good enough for a female one. Alice is hired. What happens as a result?

Many male colleagues are angry. They think that because of Alice, they couldn’t hire a male candidate they believe to be stronger. They also expect Alice to be grateful for the opportunity. How will Alice react? It depends on whether Alice herself is biased. I will give two potential scenarios.

Scenario 1. Alice is biased and realizes she is only hired because she is female. Alice thinks that her strength is below the cutoff C. Alice develops impostor syndrome and doesn’t contribute to the department and mathematics as much as she could have, reinforcing everyone’s belief that she is weaker than she actually is.

Scenario 2. Alice is not biased but realizes that she was hired for her gender and not for her mathematics. She gets angry too because she knows she is perfectly qualified. She also realizes that the department expects her to be grateful, while another male hire is thanked for taking a similar position. In this scenario, everyone is angry.

In both scenarios, the intent is to fight the bias. But as a result, no one is truly happy. A supportive environment is not created. And the idea that male and female mathematicians differ in strength is reinforced.

Recently, I talked to a male colleague about gender bias. He was adamant that he isn’t biased and, as proof, described his contribution to hiring females in his department. This is not proof of being unbiased. This is proof of trying to resolve the bias, either sincerely or due to outside pressure. However, the real proof would be to change one’s attitude towards female colleagues. As a female colleague myself, I would notice this change in attitude. But while nothing changes, I can’t accept the fact of female hires as proof of no bias.

To truly resolve the bias, we need B to be equal to 1. To improve the situation, people should collectively work on increasing the bias coefficient B. This is more about changing the attitude.

I am for hiring more female mathematicians as professors. But sometimes, I feel like hiring more female mathematicians without addressing the attitude is treating the symptoms while making the disease worse.


My Gender

Thinking about genders, we used to have only two options: male and female. Now we have more. I have a lot of young acquaintances who are non-binary. So I started to rethink my gender identity.

I was a typical girl: at least, I thought I was. I hated playing with boring dolls. I preferred cars, or even better, construction sets and board games. In second grade, I wanted to be a ballerina but later fell in love with Sherlock Holmes. My dreams switched to becoming a detective or a spy. In fifth grade, I signed up for rifle-shooting training. That same year, my school forced me to compete in an orienteering event, and I won.

Orienteering became my favorite sport, and I did it for many years. I was really good with maps. I would go to a competition, leisurely walk my course and win. Other kids were running around like crazy, but I always knew where to go and was overall faster than them. With time, other kids learned to read maps better, but I myself never learned to run faster. So I stopped winning, but I enjoyed the sport anyway.

It goes without saying: I loved math. Solving math problems was the best entertainment ever.

Later, to my surprise, I discovered that most girls liked shopping and wasted a lot of time on make-up. Not many girls were even interested in math. I actually liked that. I started having crushes on boys since second grade and enjoyed being the only girl in math clubs, having all these nerds to myself.

I grew up in Soviet Russia. While growing up, I wasn’t bombarded with gender stereotypes. My first eye-opening experience was when I was 17 years old. My long-time boyfriend knew that I liked mathematics, and this was okay. But when I told him that I planned to go to college to study mathematics, he didn’t approve. I broke up with him on the spot.

My mom used to tell me that most men do not like brainy women. My reply was that there are more men who like brainy women than brainy women. I got a new boyfriend the day after my breakup.

My gender identity didn’t bother me much in Russia. What bothered me was the Russian tradition for both spouses to work, but the house chores and child-rearing duties fell only on women. I read somewhere that, on average, in Russia, women worked for 4 hours a day more than men. Life was unfair to women but not to their self-esteems.

As I said, I grew up thinking I was a typical girl until I came to the US. This happened 30 years ago, and I was 30 at the time. In the US, I got bombarded with gender stereotypes: they made me feel inadequate and doubt my femininity. Just for reference: by that time, I was in my third marriage breastfeeding my second child. Still, according to those stereotypes, I was not a real woman.

Brain Sex

For some time, I wondered what was wrong with me. Then, I was elated to find a book called Brain Sex: The Real Difference Between Men and Women by Anne Moir and David Jessel. (This was many years ago.) Among other things, this book talks about the differences between men and women with respect to the brain. According to the book, men are better on average at abstract thinking and spatial visions, aka math and maps. Women, on the other hand, are better at connecting with people and have higher social intelligence. Boys are less interested in games related to storytelling, aka dolls, preferring more concrete activities. And so on.

The book also describes situations in which girls don’t fit the paradigm. The authors attribute this variation to the mother’s hormones during pregnancy. I found myself described perfectly in the section titled “girls who have been exposed to male hormones in the womb.” I am pretty sure that my mom didn’t take any hormone supplements while pregnant with me back in Soviet Russia. On the other hand, the description in the book was spot-on.

This book classifies me as “a male brain in a female body.”

I was glad to find myself after a period of self-doubt. I was glad that I wasn’t alone and even fit into a special category with a name.

Several years later, I met Sue Katz, a writer who also has a blog Sue Katz: Consenting Adult. She made me realize how ridiculous the whole story was: I was pressured by gender stereotypes to feel bad about myself. Then I was grateful for a book based on those same stereotypes, only because it described women like me and gave me permission to exist. I liked the book because I accepted those stereotypes in the first place. If there were no stereotypes, there wouldn’t be any problems at all.

Why can’t I just be me?

Over the past few years, I have become happier than I have ever been. I do not care what society thinks about my gender. I am no longer ashamed of not feeling 100 percent female.

I like that people in the modern world embrace the idea of individuals being themselves. For example, my daughter-in-law, Robin Dahan, designed a whole line, You-Be-You, for her company, Dash of Pep.

You-Be-You Socks

Am I non-binary? I do not know and do not care. I am just me, proudly wearing my You-Be-You socks.


Among Mathematicians

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.


Reverse Bechdel Test

A movie passes the Bechdel Test if these three statements about it are true:

  • There are at least two named women in it
  • Who talk to each other
  • About something besides a man.

Surely there should be a movie where two women talk about the Bechdel test. But I digress.

The Bechdel test website rates famous movies. Currently they have rated 4,683 movies and 56% pass the test. More than half of the movies pass the test. There is hope. Right? Actually they have a separate list of the top 250 famous movies. Only 70 movies, or 28%, from this list pass the test.

My son Alexey suggested the obvious reverse Bechdel test, which is more striking than the Bechdel test. A movie doesn’t pass the test if it

  • Has at least two named men characters
  • Whenever they talk to each other
  • They only talk about women.

I can’t think of any movie like that. Can you?Share:Facebooktwitterredditpinterestlinkedinmail

Next Tanya Khovanova

Many years ago at Gelfand’s seminar in Moscow, USSR, someone pointed out a young girl and told me: “This is Natalia Grinberg. In her year in the math Olympiads, she was the best in the country. She is the next you.”

We were never introduced to each other and our paths never crossed until very recently.

Several years ago I became interested in the fate of the girls of the IMO (International Math Olympiad). So, I remembered Natalia and started looking for her. If she was the best in the USSR in her year, she would have been a gold medalist at the IMO. But I couldn’t find her in the records! The only Grinberg I found was Darij Grinberg from Germany who went to the IMO three times (2004, 2005, and 2006) and won two silver medals and one gold.

That was clearly not Natalia. I started doubting my memory and forgot about the whole story. Later I met Darij at MIT and someone told me that he was Natalia’s son.

I was really excited when I received an email from Natalia commenting on one of my blog posts. We immediately connected, and I asked her about past events.

Natalia participated in the All-Soviet Math Olympiads three times. In 1979 as an 8th grader she won a silver medal, and in 1980 and 1981 she won gold. That indeed was by far the best result in her year. So she was invited to join the IMO team.

That year the IMO was being held in the USA, which made Soviet authorities very nervous. At the very last moment four members of the team did not get permission to travel abroad. Natalia was one of them. The picture below, which Natalia sent to me, was taken during the Soviet training camp before the Olympiad. These four students were not allowed to travel to the IMO: Natalia Grinberg, Taras Malanyuk, Misha Epiktetov, and Lenya Lapshin.

1981 IMO training camp

Because of the authorities’ paranoia, the Soviet team wasn’t full-sized. The team originally contained eight people, but as they rejected four, only six traveled to the USA, including two alternates.

I have written before how at that time the only way for a Jewish student to get to study mathematics at Moscow State University was to get to the IMO. I wrote a story about my friend Sasha Reznikov who trained himself to get to the IMO, but because of some official machinations, still was not accepted at MSU.

Natalia’s story surprised me in another way. She didn’t get to the IMO, but she was accepted at MSU. It appears that she was accepted at MSU as a member of the IMO team, because that decision was made before her travel documents were rejected.

Natalia became a rare exception to the rule that the only way for a Jewish person to attend MSU was to participate in the IMO. It was a crack in the system. They had to block visas at the last moment, so that people wouldn’t have time to make a fuss and do something about it. Natalia slipped through the crack and got to study at the best university in the Soviet Union.

Unfortunately, the world lost another gold IMO girl. Three Soviet team members won gold medals that year. Natalia, being better then all of them, would have also won the gold medal.Share:Facebooktwitterredditpinterestlinkedinmail

The Best Math Problem Solver is a Girl

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.Share:Facebooktwitterredditpinterestlinkedinmail

Polite Gender Bias

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.Share:Facebooktwitterredditpinterestlinkedinmail

Math as an Aphrodisiac

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.Share:Facebooktwitterredditpinterestlinkedinmail

Why Are We Losing Female Mathematicians?

Sanya Took an IntegralThe data from annual surveys carried out by the American Mathematical Society shows the same picture year after year: the percentage of females in different categories decreases as the category level rises. For example, here is the data for 2006:

Category Percentage of Women
Graduating Math Majors 41
PhDs Granted 32
Fresh PhD hires in academic jobs 27
Full-time Faculty 27
Full-time tenured or tenure-track faculty 12

The high percentage of female math majors means that a lot of women do like mathematics. Why aren’t women becoming professors of mathematics? In the picture to the left, little Sanya fearlessly took her first integral. I hope, even as an adult, she will never be afraid of integrals.

I am one of the organizers of the Women and Mathematics Program at the Institute for Advanced Study at Princeton In 2009 we had a special seminar devoted to discussing this issue. Here is the report of our discussion based on the notes that Rajaa Al Talli took during the meeting.

Many of us felt, for the following three reasons, that the data doesn’t represent the full picture.

First, the different stages correspond to women of different ages; thus, the number of tenured faculty should be compared, not to the number of current math majors, but rather to women who majored in math many years ago. The percentage of female PhDs in mathematics has been increasing steadily for the past several years. As a result, we expect an eventual increase in the number of full-time female faculty.

Second, international women mathematicians might be having a great impact on the numbers. Let’s examine a hypothetical situation. If many female professors come to the US after completing their studies in other countries, it would be logical to assume that they would raise the numbers. But since the numbers are falling, we might be losing more females than we think. Or, it could be the opposite: international graduate students complete a PhD in mathematics in the USA and then go back to their own countries. In this case we would be losing fewer females to professorships than the numbers seem to suggest. Unfortunately, we can’t really say which case is true as we do not know the data on international students and professors.

Third, many women who major in mathematics also have second majors. For example, the women who have a second major in education probably plan to become teachers instead of pursuing an academic career. It would be interesting to find the data comparing women who never meant to have careers in science with those women who left because they were discouraged. If we are losing women from the sciences because they decide not to pursue scientific careers, then at least that is their choice.

It is also worth studying why so few women are interested in careers in mathematics in the first place. Changing our culture or applying peer pressure in a different direction might change the ambitions of a lot of people.

We discussed why the data in the table doesn’t represent the full picture. On the other hand, there are many reasons why women who can do mathematics and want to do mathematics might be discouraged from pursuing an academic career:

  • Marriage and children distract from mathematics.
  • The lack of legal protections for pregnant women, of required maternity leave and of childcare provision.
  • The cultural skepticism that women can do math on a high level.
  • An educational system that tends to tell students that math is very difficult, thus discouraging women from the early stages of their academic life.
  • Boys tend to be more competitive than girls.
  • The lack of job opportunities.
  • A career in math often requires moving.

Our group proposed many solutions to help retain women in mathematics:

  1. Find a way to get men pregnant as well.
  2. Incorporate ideas from other countries (like Portugal), where they don’t have this problem.
  3. Increase the level of social care for pregnant women and young children.
  4. Create new laws to protect the rights of pregnant women.
  5. Educate secondary, high school and college math teachers how to present math — such as through games — as an interesting subject, not as a difficult one.

At the end of our meeting, everyone accepted Ingrid Daubechies‘ proposal that we do the following:

Each woman in mathematics should take as her responsibility the improvement of the mathematical environment in which she works. If every woman helps change what’s going on in her university or the school where she teaches, that will help solve the problem on the larger scale.