## Is There Hope for a Female Fields Medalist?

Until the introduction of the Abel prize, the Fields medal was the most prestigious prize in mathematics. The medal has been awarded 48 times and all of the recipients have been men. Can we conclude that women are inferior to men when it comes to very advanced mathematics? I do not think so.

The Fields medal was designed for men; it is very female-unfriendly. It is the prize for outstanding achievement made by people under age 40. Most people start their research after graduate school, meaning that people have 10-15 years to reach this outstanding achievement. If a woman wants to have children and devote some time to them, she needs to do it before she is 40. That puts her at a big disadvantage for winning the medal.

Recently the Abel prize for mathematics was introduced. This is the math equivalent of a Nobel prize and nine people have received the prize, all of them male. The Wolf prize is another famous award: 48 people have received it so far and they too have all been male.

On the grand scale of things, women have only recently had the option of having a career in mathematics. Not so long ago it was considered quite exceptional for a woman to work in mathematics. The number of female mathematicians is increasing, but as this is a new trend, they are younger people. At the same time, Abel prizes and Wolf prizes are given to highly accomplished and not-so-young people. That means the increase in the percentage of women PhDs in mathematics might affect the percentage of females getting the prize, but with a delay of several dozen years.

There are other data covering extreme math ability. I refer to the International Math Olympiad. The ability that is needed to succeed in the IMO is very different from the ability required to succeed in math research. But still they are quite similar. The IMO data is more interesting in the sense that the girls who participate are usually not yet distracted by motherhood. So in some sense, the IMO data better represents potential in women’s math ability than medals and prizes.

Each important math medal or prize is given to one person a year on average. So the IMO champion would be the equivalent of the Fields medal or the Wolf prize winner. While no girl was the clear best in any particular year, there were several years when girls tied for the best IMO score with several other kids. For example:

• In 1995, 14 students tied for the perfect score; two of them were girls. (Maryam Mirzakhani and Chenchang Zhu)
• In 1994, 22 students tied for the perfect score; two of them were girls. (Theresia Eisenkölbl and Catriona Maclean)
• In 1991, 9 students tied for the perfect score; one of them was a girl. (Evgenia Malinnikova)
• In 1990, 4 students tied for the perfect score; one of them was a girl. (Evgenia Malinnikova)
• In 1987, 22 students tied for the perfect score; one of them was a girl. (Jun Teng)
• In 1984, 8 students tied for the perfect score; one of them was a girl. (Karin Gröger)

In one of those years, a girl might have been the best, but because the problems were too easy, she didn’t have a chance to prove it. Evgenia Malinnikova was an outstanding contender who twice had a perfect score. In 1990, she was one out of four people, and she was younger than two of them, as evidenced by the fact they they were not present in 1991. Only one other person — Vincent Lafforgue — got a perfect score in 1990 and 1991. We can safely conclude that Evgenia was one of two best people in 1990, because she was not yet a high school senior.

This might be a good place to boast about my own ranking as IMO Number Two, but frankly, older rankings are not as good as modern ones. Fewer countries were participating 30 years ago, and China, currently the best team, was not yet competing.

Girls came so close to winning the IMO that there is no doubt in my mind that very soon we will see a girl champion. The Fields medal is likely to take more time.

1. #### Meridyth:

Your post was so inspirational. As a high school math teacher and a female, I have heard many times that males are better at math and science. Well for me this was never the case and it’s nice to see someone so emotional and well versed about the issue. Some of the facts you presented were so interesting. I didn’t know most of the information you presented before I read your blog. Thanks for bringing all this wonderful information to light!

2. #### West Karana » Web log 4/20 — Special Contest Edition:

[…] mathematician Tanya Khovanova examines how the major prizes in the field of mathematics are stacked against woman. Tanya’s blog is an inspiration and often quite a lot of fun […]

3. #### Meridyth:

I’m so glad I stumbled upon it! It’s refreshing to hear such an uninfluenced voice! I look forward to future posts!

4. #### Maria Roginskaya:

While I used to be an optimist about chances of a female mathematician to do a academical career, in this particular aspect of it (i.e. prizes awarded as a sign of high recognition) I’d be more pessimistic. If we look on the generations pasts we can see a number of examples of female mathematicians which have made a big contibution to Mathematics, but had very little recognition of this type: Emmy Noether, Olga Ladyzhenskaya, Aline Bonami (probably the later is less known but she is my personal favorite, as she worked in my own field). All of them produced beautiful Mathematics and were highly esteemed by their collegues, but there were very little of prizes around them.

The trouble is that the decision about a prize is taken by a commettee, which is unavoidably is subjective. I suspect that, when a commettee try to discuss who is “the greatest mathematician”, the natural way to proceed is to take the first one who comes to the mind. But this means that a person who in some way stands out (and not only by purely mathematical achievments) has a bonus. It is my experience that most of exceptionally bright women try to hold check on their brightness in a conversation with collegues (I assume in order to avoid harting the feeling), which is rarely the case with their male counterpart (I must admit that the best of male mathematician I’ve met do not try to show off deliberatly, but they would not “hold back” either). As the result, the female mathematicians luck that little PR-factor, which make the difference for the “high prize”.

As an illustration I can provide a story which one tells about Lars Hörmander, whom nobody would occuse for a “star” behaviour (I don’t know if it was actually true, but it is belivable): After a day of a conference some participants have met in a bar, and Lars asked the fellow next at the table about the result which he was going to present. About half an hour after the result was formulated, Hörmander returned to the question and claimed that the result is a well known theorem, which Lars himself has learnt in a standard graduate course. As a confirmation Hörmander provided an elegant proof of the result. The author of the result got white in the face, as he was supposed to present the talk the next morning, and then Hörmander admitted that it was just a joke, and he have invented the proof during that half an hour they all were seating in the bar. Provided the wide range of the quality of results presented on conferences nowdays, I do know a few female collegues, who would be able (mathematically) to repeate the joke, but I can not imagine a single one of them actually doing it. (And so they would not gain the PR-status such a joke would give.)

Thank God, Mathematics is still very far from the show buisness, and one can not enchance ones’ chances to get a prize by a lot of public scandals. Nevetheless while prizes yet indicate that their recipients are very good mathematicians, the luck of the prizes does not mean in itself that one is a less good mathematician.

5. #### misha:

I am wondering why so many people are having hard time recognizing the fact of considerable differences between men and women, a lot of them of biological origin. These differences are only amplified at the margins of the statistical distributions. Men and women are complementary and some asymmetry is inevitable. Why do we have to always compete? Why not cooperate and enjoy these differences, without dominating or taking unfair advantages of each other? There is a passage in the footnote 6 on page 156 of recently published “Musicophilia” by Oliver Sacks, that reads: “Testosterone slows the development of the left hemisphere in utero, and while both male and female fetuses are exposed to this, the male fetuses are exposed to much greater amounts.” You can easily find the full quotation by Google. Would you label Oliver Sacks a male chauvinist pig?

6. #### Maria Roginskaya:

Misha: You mix two very different statements: “there is no difference between men and women” and “there is no difference between male and female abilities in Mathematics”. (It is approximately as two very different vectors can have the same projection.)

If “cooperation and enjoyment of differences” means that I’m getting less reward for the same work as my male collegues - I refuse to cooperate. If one considers a wish for a female mathematician to recieve a high prize for mathematical achievments in a fair competition to be an attempt “to dominate and to take unfair advantage” then, yes, one is a male chauvinist pig.

7. #### esme:

While I agree with the general argument (and worrying about whether you will be able to have children or planning your career around future children can impact your career long before actual children materialize), I have to take issue with the idea that there is “one best mathematician” every year.

If you make the questions sufficiently difficult to get a single first place, the ranking at the IMO will always depend on the questions (and whether you could cope with the local food). It is simply ridiculous to assume that the Fields Medal goes to the best one (even assuming a perfect committee). Mathematicians are *not* linearly ordered.

8. #### Peter Gro:

I predict my daughter S will be the first female winner of Wolf, Abel or Fields.
Check back in 20 years time…
(She is currently 23 months old, speaks 2 languages and reading already…:)

9. #### dark:

It might be interesting to note that Maryam Mirzakhani did eventually become a very well known research mathematician. Here PhD thesis is very well known(check wikipedia).

Thank you.

10. #### gwallan:

Extremely relevant…
Sex Differences in Mathematical Aptitude

11. #### G.A.:

Even though this post is a couple of years old, I will still comment on it.
I am female, and quite sick and tired of living in a male-dominated world. However, your article is quite pathetic. It is true that women were not given wide opportunities to study advanced mathematics and do research until around half a century ago. Still, all these doors have been open for the past several decades. So if women don’t have enough interest in the subject to pursue it with absolute dedication, it is their own fault. You mention motherhood… which is quite important, of course. However, do you really believe that for a mathematician worthy of a Field medal, staying at home with a baby can be more important than mathematics? It’s a modern society we live in. There are babysitters. Daycare centers. In egalitarian societies such as Sweden, working women go back to their jobs after around 1 year of maternity leave. Staying at home for 1 year does not need affect your research. It’s mathematics we are talking about, not archaeological field research. You can do it from home. If women choose to spend 2-3 years at home with their kids, instead letting their husbands provide for the family simply because that’s the “normally accepted” way, it’s their fault. Blaming ‘motherly’ feelings for the fact that advanced mathematics prizes have never been awarded to women is simply PATHETIC.

What you write about the IMO is even more pathetic. A dozen students tie for first place, ONE of them is a girl. These are very sad statistics, I would say. You, instead, jump to the conclusion that those girls might have actually taken first place, and the only reason they didn’t is because the problems were too easy. What, may I ask, are the chances that the remaining 11 male students are all less talented than this one female? This is simply stupid. You try to somehow ‘quantify’ who is better by arguing that Evgenia Malinnikova was younger than the other participants. Sorry, but simply being younger does not make you better, and being ‘better’ is what these competitions measure.

Even so, suppose your absurd way of thinking is correct, and all these female students were simply out of luck because the ‘problems were too easy’. What became of them? These dates you have posted go back 20 years. What did these women do in those 20 years? If they really were that good, and if they were dedicated to mathematics, their results would be published, and people would know about them. All of them actually had the chance to win Fields medals, given the timeframe. Mirzakhani is known for her research, because she is doing a great job. I have never heard of Malinnikova. Even googling her does not bring up any articles, and her biggest achievement seems to be this olympiad result. So how can you ’speculate’ about mathematical abilities solely based on these statistics, and make conjectures about those 5% top achieving girls ‘winning’?

(I am not sure why you did not provide more recent statistics - are there less successful female student in more recent years, or did you just want to bring an example of your compatriot Malinnikova and make your argument even more biased and murky?)

As I wrote above, I strongly believe in gender equality, and I believe that women should be given equal opportunities as men. However, I am greatly disgusted by women ‘hiding’ behind facts such as maternity and making themselves sound underrepresented, underestimated, or somehow underprivileged. If women don’t go for mathematics as passionately as men do, or are ‘distracted’ by things like maternity, or else simply don’t have as much ‘talent’, the award givers - or men, for that matter - are not to blame. Also, keep in mind that genius is not measured by numbers. Think of Marie Curie. She lived in the 19th century! Did she have ‘opportunities’ like women do today? No way - just read her biography and you’ll see. Did she have to ‘give up’ marriage and children for the sake of science? No! Is she one of the most well-known and respected physicists that ever lived? Yes!

The international math olympiad is not data covering ‘extreme math ability’. It’s a competition with very specific types of problems taken by teenagers, and in many cases it has nothing to do with the person’s ‘extreme math ability’. You placed second at some point, good for you. When I participated, my papers were never even sent to be evaluated because of the corrupt way it was organized in my country. I saw my notebook, with a bunch of others, in the trash of the teachers’ room after the competition.

12. #### Tanya Khovanova’s Math Blog » Blog Archive » The Best Math Problem Solver is a Girl:

[…] 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 […]

13. #### Dave:

G.A. seems like the only one who is not advocating making pathetic excuses. She makes some very valid argument. And why would the oppression only be there in mathematics, and not only in for example psychology where you have, more female researchers than math? is that because they all got expelled from mathematics? won’t they have to work hard while taking care of the children? won’t they be subject to harsh critical questions by male juries? seems like they have an advantage nevertheless. Is that perhaps again due to ’subjective judges’? this is quatch because, what is more subjective: mathematics or psychology? Quatch!

14. #### Dave:

* I meant more female than male researchers

15. #### Dave:

there is some leap in logic also in one of the post. it stated that there is a bias towards choosing someone that is the odd one out. If these genius maths women are so scarce, why don’t they win the fields medal?

16. #### christopher:

a simple hyptohesis: average ability in mathematics is the same for men and women. standard deviations are different. so fewer women 4 std deviations away from the mean on both sides.

17. #### Uri:

It’s true that no woman has yet won a Fields Medal, Abel Prize or Wolf Prize. But women have won other prestigious mathematical prizes: Stefanie Petermichl and Nalini Anantharaman are recent winners of the Salem Prize (which boasts 7 Fields medalists amongst its recipients) and Claire Voisin has won the Clay Research Award (which boasts 6 Fields medalists and Andrew Wiles). So perhaps a female Fields Medalist is not so very far off? (Until 2006, no woman had won the Turing Award, the most prestigious award in computer science; since then, three have.)

One thing that doesn’t help, in my opinion, is that profiles of female mathematicians often focus on the Noethers and Lovelaces of history rather than the Petermichls, Anantharamans and Voisins of today. For role models to be effective they need to appear relevant.

18. #### Uri:

PS Even more encouraging is the European Mathematical Society Prize, which is awarded to young European researchers (”not older than 35 years”), and which has preceded a Fields Medal 9 times out 60. 8 winners so far have been women: Claire Voisin, Annette Huber-Klawitter, Sylvia Serfaty, Olga Holtz, Laure Saint-Raymond, Agata Smoktunowicz, Sophie Morel and Corinna Ulcigrai. Three of these (Saint-Raymond, Morel and Ulcigrai) are young enough to be eligible for the 2014 Fields Medal.

19. #### WOB:

I have heard these same arguments made as to why women were not the top chef, top architect, top salesperson, etc, and they’re as empty and meaningless here as they are there. Stop fretting over why one sex is stronger in this or that area than the other sex and enjoy your prowess and accomplishment where you can and do excel.

20. #### RAHMANI:

Good morning

It is possible with the great mathematician MARYAM MIRZAKHANI (Iran 05/1977 - ) PLENARY SPEAKER !! ICM 08/2014 SEOUL KORA

The lobbies mathematicians from U.S.A, Great britain, france, russia,germany,china, korea,and other countries play major work to push forward their high potential candidates
to win 2014 fields medal,
other use blog to criticize past fields medalists,why ?, I cannot say about this great mathematician name,by respect, very sorry.