Tanya Khovanova's Math Blog

I am interested in a career in mathematics. How hard is it to be a woman mathematician?

Let us look at some numbers from the American Mathematical Society Survey Reports for the year 2005:

• There were 40% of women among graduating math majors.
• There were 30% of women among Math PhDs granted.
• There were 11% of women among full-time tenured or tenure-track positions.

You can’t just say that women do not like math — 40% of those choosing math as a major is quite a large number, after all.

On the other hand, the downward trend of these percentages is striking. If women’s opportunities and abilities are the same as men’s, these percentages should grow with every age step, since, as we know, the percentage of women in the population increases with age due to men dying earlier.

But the numbers go down and very fast. There are many potential explanations for this, but today we’re going to look at one of them:

Women have less ability for high-level mathematics.

Was Larry Summers right when in his speech that cost him his Harvard presidency he compared math ability to height and to the propensity for criminality, and suggested that the distribution, especially standard deviation, of math ability differs for men and women?

To answer this question, I wanted to find some other data that correlates gender with math abilities. I took the results of the American Mathematical Competitions (AMC 12) for the year 2008. Among 120,000 students who participated, 43% were females. Here are some results:

• Among students scoring 72 points or higher there were 40% of girls.
• Among students scoring 98 points or higher there were 30% of girls.
• Among students scoring 134.5 points or higher there were 11% of girls.

This picture is similar to that of the academic career: the closer you climb to the top, the smaller percentage of girls you see there. Of course, winning a competition is very different from getting tenure. People who win competitions are smart and competitive — smart and competitive enough to go for money, rather than academia. On the other hand, people who are interested in mathematics often are not interested in anything else. Why would they waste their time in competitions when the Riemann Hypothesis is still waiting to be solved?

But still, both achieving tenure and winning math competitions represent mathematical ability in some sense. If Larry Summers was right and the distribution of math ability is different among males and females, then by looking around you at the percentage of females at your level, you should be able to assess how close you are to the top of the math field.

I propose the following math career predictor: Take your results in AMC 12. If among kids who did better than you, the percentage of girls is more than 11%, you do not have a chance at tenure. If the percentage of girls is more than 30%, do not waste your time working on a math PhD. If the percentage of girls is more than 40% maybe math majoring is not for you.

I hate my math career predictor. I hate it not only because it has so many flaws that it might just deserve the Ig Nobel Prize, but because it doesn’t take people’s effort into account. You really have to work very hard to be a math professor, whether you were a winner or a loser in math competitions.

You might ask why I created a math career predictor that is so flawed. My mathematician friends, those who are more honest than polite, tell me that I have no chance at getting back to academia. On the other hand, I had the second best result at the 1976 IMO, which means I have the ability. My predictor may be my only hope.

I resigned from my job half a year ago. If you remember I was planning to rebuild my career in academia and to find myself along the way.

The problem with re-entering academia is that to find a job starting September 2008, I would have had to apply in December 2007. I really didn’t want to apply before finding my new direction in mathematics and publishing some papers to rebuild my name. So I decided to apply for academic jobs in December 2008, while using the intervening year for research and to try to publish.

The problem with delaying the start of my new academic job until September 2009, is that I didn’t save enough money to cover such a long period of time. Even though I cut down my expenses significantly, I still need some additional income in the meantime. However, temporary jobs consume the time I need for research in order to go back to academia. To resolve this Catch-22 situation, I decided to choose jobs of only two kinds: first, either they pay a lot, so for a limited time of work I can buy a lot of extra time for my research; or second, they’re aligned with my goals. I wasn’t yet looking very hard for work, but nonetheless several jobs came my way.

One of the jobs I accepted was a temporary job as a math competition coach at Advanced Math and Science Academy (AMSA) Charter School. This gave me a chance to check once again how I feel about teaching. I love entertaining people with mathematics. I showed magic tricks to my students, played games with them and so on. I enjoyed myself; my students liked me. But I do not know enough tricks or games to teach 24 hours a week as a regular school teacher. I decided that I really do not want to be a school math teacher. But I love being a coach, because it takes less time and I get the best kids.

I also worked on the Organizing Committee for the Women and Mathematics Program in Princeton in May 2008. The irony is that I lived in Princeton for seven years and ignored this program for most of them. Initially I was prejudiced against such a program. I felt that I should go to lectures only for their mathematical value. The gender of the lecturer doesn’t matter.

I think I was missing the whole point of the program. I should write about this program more.

The surprising result of the last half year is that I am having a blast blogging. Wouldn’t it be fabulous to find a job in mathematical journalism, if such a profession exists.

Three years after I moved to the U.S. and had my second child here, I got an NSF postdoc position at MIT. I had had a long break from my previous research in integrable systems, so I decided to start something new for me — quantum groups. Soon afterwards I invented tetramodules and published a paper about them.

Some time later a friend of mine showed me some papers where my tetromodules had been described long before me. I felt such pain, that I couldn’t work.

I was ashamed that the quality of my paper was compromised. I was very scared that someone might think that it wasn’t original work. I felt worthless for having wasted so much energy on something that was already known.

Afterwards, I discovered that tetramodules appeared in the literature under many other names: bidimodules, Hopf bimodules, two-sided two-cosided Hopf modules, 4-modules, bicovariant bimodules. That meant that many people were reinventing them at the same time. I felt slightly better knowing that I wasn’t alone, but was in fact part of a crowd. Still, my pain impeded my ability to work and do research.

I have just read an article in the New Yorker entitled “In the Air” about some famous discoveries made simultaneously by several people. It made me realize that I am still not over that tetramodules story from 15 years ago.

Being a mathematician requires one to be emotionally strong. You need high self-esteem. Do I need to overcome my emotions or is there a niche for very emotional mathematicians? Perhaps blogging about math is such a niche.

My Number Gossip page is on hold. I am out of work and can only afford to spend time on things that can bring me my next job. As a result, numbers suffer. If you would like to support the website, consider donating to Number Gossip. With your donations, I will be able to spend more time on the website. There are many things I would like to do. Here are the three most important and fun areas that I would chose to work on.

1. Do you know that 40(forty) is the only number whose constituent letters appear in alphabetical order? I have about 1,000 unique number properties like this on my number gossip website. I also have about 600 properties in my database that need to be checked before adding them to the website. Being a perfectionist I double-check and recheck all the properties. As a result, my webpage is quite rigorous and reliable. As a downside I need a lot of time to add new unique properties to the website and 600 of such properties are waiting impatiently to join their comrades in the public view.
2. Have you heard about aspiring or untouchable numbers? What about practical or perfect numbers? There 50 famous properties like that that my website currently allows you to check for your favorite number. For example, 33 is deficient, evil, lucky and odd at the same time. There are many other properties I plan to add in the future. If you would like to know whether or not your favorite number is brilliant, fortunate or primeval, consider donating to Number Gossip.
3. Currently the limit for numbers you can input is 10,000. Some of the basic properties are very difficult to check. The expansion is not trivial and will require significant tuning of my algorithms. Even so, I would like to do that.

I’ve devoted many years to this project, and now I need some financial help. If you know a person or a company who wants to sponsor numbers, please ask them to contact me at (tanyakh at yahoo).

I did it. I handed in my resignation letter to my boss. I’m resigning effective Jan 3, 2008. If you want to know why I’m waiting until next year, I can give you several reasons.

• First, Christmas-time is usually the most enjoyable work time because no one is there. It is quiet.
• Second, I’m superstitious: I believe the way I greet the New Year determines how the New Year is going to go, so I want to be employed at the strike of the midnight clock.
• Last but not least, it appears that to get my company’s annual profit-sharing bonus, I have to be employed on December 31^st.

I am happy and sad at the same time. In four and a half years I’ve made a lot of friends and accomplished a lot professionally. Now it is my time to move forward. Where is forward? It is in the direction of a cemetery, but I would rather be doing something more meaningful to me than battle management while I am slowly crawling there.

I would like to become a professor of mathematics. How can I get to academia? I was told that applicants are measured by the number of papers they write. They expect about 3 papers per year starting after the Ph.D. I got my Ph.D. 20 years ago. I published 6 papers after my Ph.D. papers. That means I urgently need to come up with 54 papers.

There are several problems with working in industry and trying to publish at the same time:

• Some results derived at work you can’t publish because they are proprietary.
• Some results derived at work are classified.
• Journals want simulations; that means you may have to depend on colleagues.
• If your project is closed before your group finishes your simulations, you have to put your paper on hold.
• Also, if your paper is not directly a part of your project, you can’t use your official work time to write your paper.

Because of these obstacles, the papers I have started at my job are on hold. It’s unlikely that I’d be allowed to finish them during work hours.

So I started writing non-job-related papers on my weekends. I started doing this seriously a year ago. It goes very slowly and I hope to publish three papers soon, but my speed needs to be much higher than that to catch up with the 54 papers I didn’t have time to write while being a single mom and providing for my family.

So, I came up with this idea: to quit my job and write papers. I do not have enough money to support this idea for very long. Certainly, not enough time for 54 papers. We probably can survive on my savings for half a year. My goal is to write as many papers as I can in half a year and see what my real speed is. This way I can at least prove to myself that I am a mathematician for real.

The only problem is that my savings were meant for a down payment on my first house. I’ve been asking myself for awhile: What is more important− a dream job or a dream house? I just realized today that I will never be happy if I am not happy at my job and I am quite happy with the apartment I am renting now. I guess this is it − I just have to take the plunge.

For 25 years my children were my priority. I made several decisions in my life that benefited my family, but “harmed” my mathematical career. I do not regret any of my choices. After all, being a single mom made me a more confident, stronger person. Maybe this will help my career in a long run.

Now that my youngest son is 16 years old, my life can’t revolve around him anymore. Now I must think about the meaning of my life, beyond bringing up children. The only thing I want to do is mathematics. I am actually doing some math on weekends, but I really want to do it full-time. My tasks at my job are getting further and further from mathematics and research. In short, I feel that my job doesn’t fit me at this stage of my life.

I really should find another job. I am somewhat scared of change though. I think that the first thing to do is to try to turn around the situation at my current job. There is a lot of interesting mathematics in battle management. The problem is to match a math problem to a charge number. That is, I would need to convince my management that the algorithms we design need a sound mathematical basis.

Here is my decision: I will try to find some tasks at my work that include mathematics and see how I can change my situation there by the end of the year. If I don’t succeed, I will have to think of something else. Let the Web be my witness. I will report the results to you soon.

Why didn’t I think of this before?

I want to share some ideas about mathematics and about my life as a mathematician. In this blog, you’ll read about such things as the properties of numbers and sequences and how mathematicians approach practical things.

I started my life as a genius girl mathematician, winning silver and gold medals at the International Math Olympiad (IMO) as a teenager. My PhD is from Moscow State University. When I got married, I wanted to have a family and mathematics at the same time, but being a woman, this affected my mathematics career. Now my kids are growing up and mathematics is becoming more and more important in my life. This is why I decided to start this blog.