Posted by: Alexandre Borovik | December 26, 2008

Women and Mathematics

[First published in the old blog on Monday, August 21, 2006]

It is a sad statistical fact that the number of women doing mathematical research is disappointingly small. I am confident that this cannot be explained by the psychophysiological gender differences – even if neurophysiologists find subtle variance in language and visual processing in male and female brains.

The problem, I believe, is sociopsychological rather than psychophysiological. I’ll try to outline, briefly, my vision of it.

A rarely discussed side effect of doing mathematics is that mathematics is a weapon of personal empowerment. To be successful in mathematics, you have to be bold, you have to be absolutely independent in your thinking. When you prove something new, you are in the unique position of being the only person on the Earth who knows the Truth – and is prepared to defend it. On the other hand, the principles of mathematical rigor give you the right to question whatever other mathematicians say. If this still does not sound to you as a recipe for trouble, you can also take into consideration that research mathematics is fiercely competitive. An explosive brew.

Mathematicians who grew up in this chivalrous environment tend to forget (or ignore) how psychologically tense and charged is the mathematical discourse. This becomes apparent only in comparison with other walks of life.

The example I want to give is probably extreme. Once I stayed with my American colleague over a long and lazy Labor Day weekend. My hosts and I were invited to their neighbor’s garden party, where I found myself in a company of twelve professional astrologists, exquisitely groomed ladies with loads of heavy silver jewelry, mostly Zodiac signs. Besides usual party talk, the astrologists actively discussed, between them, matters of their professional interest. It was fun to watch; their chat, saturated by astrological jargon, sound, to a lay observer like me, almost like a chat between mathematicians, but with a surreal feel in it. With some effort, I finally realized what made it surreal to me: the astrologists immediately believed, and accepted everything that their colleagues were saying to them; on their faces, there were no usual for mathematicians expression of a tightly focused mistrust. I realized why my daughter told me that she was scared to be present during my professional conversations with mathematician friends: in her words, we were looking as if we were ready to fight each other.

Mathematics is highly psychologically charged and competitive, but fights remain invisible for the onlooker and are strictly ritualized by a very strong research ethics and the principles of mathematical rigor. Arguments are rarely linked to money and, therefore, do not lead to serious bloodletting. Mathematicians usually look in disgust at the morals in many other, more practical disciplines, where high cost of research (and the scarcity of funding) and lack of clear criteria of rigor naturally instill a dog-eats-dog mentality. (A mathematician friend who recently accepted a position in one of the leading engineering departments, complained to me that his new department has no regular research seminars and that his colleagues do not talk to each other about their research: everyone is bound by gagging clauses in his research contracts with the industry.) But when money gets involved, everything becomes depersonalized: what matters is not who you are but what is your place in the pecking order. We are all accustomed to seeing fools in high places, and although the spectacle is rarely pleasant, it does not get deep under the skin. A male chauvinist can tolerate a woman in a position of superiority by treating her as yet another case of undeserved promotion.

The crucial difference of mathematics from many other walks of life is that its power games are deeply personal in the purest possible sense. To recognize someone as a fellow mathematician means to accept that she is intellectually equal (or even superior) to you and that she has the right to wear, like knight’s armor, her aura of intellectual confidence and independence. Too many men will still feel uncomfortable with that.

Unfortunately, even gender studies researchers are sometimes uncomfortable with the principle of intellectual independence when the mathematics is concerned. I was surprised to read, for example, that

The classroom structure, designed to foster independent non-collaborative thinking, is most supportive of white male, middle-class socialization models, and it continues throughuniversity (Pearson & West, 1991). It encourages sex-role stereotyped forms of communication – independence, dominance, assumption of leadership – in which males have been trained to excel. Women, conversely, feel uncomfortable and excluded in situations requiring such behavior; yet, their participation – as questioners as well as newly-minted authorities – may be critical to knowledge acquisition and school success. The importance that women place on mutual support, building collaborative knowledge, and applying it practically is devalued in comparison with the importance of individual expertise to males and their inclination to debate abstract concepts. (Wendy Schwartz and Katherine Hanson, Equal mathematics education for female students, ERIC/CUE Digest, No.~78, Feb 1992.)

Yes, mathematics is about “independent non-collaborative thinking”. But why should we assume that women are less capable of independent thinking? Why should women surrender the game without a fight?

Women remain a disadvantaged group of our society; but when you look at even more disadvantaged and vulnerable group, children, you find something even more striking. I was shocked to hear from several leading British experts on mathematical education, that, in British schools, many (if not most) teachers of mathematics routinely suppress mathematically able students because the students’ intellectual superiority makes the teachers feel insecure. I bet this almost never happens in most other school subject; but mathematics sets up the scene where it could be obvious for both the teacher and the student that the student is superior; British teachers are not trained to handle such conflicts with dignity and respect to the child.

Unfortunately, we still live in the culture where women are allowed to play, on equal footing with men, the conformity games in the office or even in politics, but are disapproved and penalized if they show real intellectual independence. The British reader, is, of course, familiar with the term “Blair’s babes”, and, for a contrast, may wish to recall the sad fate of Mo Mowlam.

I do not know the easy way to change the position of women in mathematics. I would suggest, tentatively, that when promoting mathematics, we should put more stress on its personal empowerment aspect; we should encourage competitiveness and independent thinking; we should openly talk to our students about the power games of mathematics. It does not easily fit into the existing policy of mathematical education, but it is worth trying.


Responses

  1. It’s both sad and funny to watch all those people theorizing about “why there are so few women in mathematics”, “why are there so few people in physics”, … computer science, … engineering and so on, every idea weirder than the last – and they all fail to see the simpler, more generic explanation of it all. To be successful in those fields – you have to dedicate an enormous amounts of time, starting from early childhood, and you must not be distracted while you’re at it. And that comes a lot easier for men than for women – because from puberty upwards they are a subject to sexual attention, and most of them at some point realize “Why bother, I can have everything I want without this?”. They become a lot more social, because it’s enforced upon them by the society (men in particular), sucking from their math/physics/CS time, and as a result they learn how to solve problems and achieve goals with social skills, because at a personal level it’s much more “cost effective” – with a little effort you can achieve much more for yourself, than learning all that science stuff. And it’s as simple as that, women don’t become mathematicians, physicists, whatever, because they don’t have to.

  2. Ivan, your hypothesis would seem to indicate that more ugly girls would go into math and physics than attractive girls, which the evidence most certainly doesn’t bear out.

  3. There is also a biological reason for the differences and it is called hormones. The effects of testosterone and adrenaline cannot be underestimated. It is a large part of the underlying reason for the male competitive drive and for enjoying being a “lone wolf”. This does not mean more social, collaborative, non-confrontational methods of mathematical research cannot be (extremely) successful.

    In North American culture, for whatever reason, it is presently not popular (trendy) for girls to go into maths. Most teenage girls in my neighborhood are ashamed to be labeled “geeks” or “nerds”, whereas many boys (myself included) are perfectly fine with the label. If that changes, if society starts to truly encourage girls to go into maths & sciences because it is “cool”, then you could see a tidal wave of change. Collaborative research in maths could become the norm instead of the exception.

  4. In the US girls have a different relationship with math than what I had back in Russia. I am working as a math coach at a math academy. I work with kids who are recommended by teachers. Usually boys are trying to join my program even if they are not recommended, and girls leave my program even if they are recommended and are actually very good.
    I started writing about women and math in my math blog: http://blog.tanyakhovanova.com/

  5. I think the difference stands more with the educational systems rather than anything else. In eastern Europe 12k education is free and there are many opportunities to stimulate an interested child at higher levels of math if he/she wants to pursue the challenge.

    There are no obvious financial implications of studies in any discipline and as a result the field is level. The only criteria for selection at top schools are grades and a standardized exam in math and literature which makes math skills an important factor. To top it off, math is a mandatory subject of study throughout all 12 grades. In those situations the % of girls in competitive schools is much higher than boys.

    As a female who grew up in Bulgaria, I enjoyed competing in Math and physics Olympiads every year and the benefits of the additional training I got, not because of money, but because of my own interest have stayed with me into my career in web engineering . If children are offered free extracurricular math education, required to study math throughout all of their educational years and offered the taste of challenges in the field they will be much more likely to pursue careers in math.

  6. (I apologize for my english). I m a women. I was very good at maths in the school. I was the best. I loved studing maths and i asked my older sisters to teach me what they were learning. I enjoyed very much.

    But you know i was not pushed to study mathematics and i felt a n strange girl, and because of my mathematics love i became a little bit complexed.

    I thank you for your post!

  7. According this talk by Helen Fisher, a couple of the key gender differences include…

    (a) Women generally surpass men in verbal ability, as such women are increasingly dominant in industries like journalism, public relations and communication, and writing.

    As a writer, I can attest to the strong need for independent thinking, competitiveness and confidence in order to produce good work and be recognised for it. These aspects of mathematics would not deter me.

    And (b) Women are “web-thinkers”, usually better able to take in multiple pieces of information, consider varying factors and map out more complex potential solutions etc… Whereas, men are better geared toward logical, linear thinking, that may increase their capacity for maths.

    My best friend’s little brother has Aspergers, a type of autism that makes verbalising his thoughts and feelings (something females are supposed to be very good at) almost impossible. He gets extremely frustrated and aggressive when things aren’t ordered enough for him not to have to ask for help. He’s also mildly genius, majoring in actuarial studies at university. What seems to appeal to him about maths is the linear, logical way of being able to explain and understand new ideas. He can look at a problem a hundred different ways, utilise the analytical skills he does have and come up with solutions. It’s his way of communicating.

  8. [...] Women and Mathematics [First published in the old blog on Monday, August 21, 2006] It is a sad statistical fact that the number of women [...] [...]

  9. So, the post reached no. 48 in top 100 of WordPress — not bad for a post on mathematics. Many thanks to everyone who commented on, or linked to the post. And Happy New Year to Everyone!

  10. As one of the few female mathematicians in Alexendre’s field I think he is correct.

    You probably have to be a research mathematician to understand what he is saying about being bold, needing intellectual independence, the psychologically charged and tense discourse and everyone looking and acting as if they are going to get into a fist fight any moment.

    This is typically not how women behave and when a woman does act like this (learned or natural) she gets all sorts of criticism for not being the sweet docile soft person she looks like. And all too often the criticism is from other woman, not just from men.

    Also it is possible for a student to be smarter than the teacher as is frequently the case in middle and high school and then it takes a great teacher to mentor such a student. Too many times the teachers’ ego gets in the way.

  11. I studied mathematical physics when it was ‘not done’ by girls (in the early 70′s) and was part of a very small group to continue into the post-doc stage in this field. It required a great deal of strength of purpose as, except for a few individuals including one woman teacher and my male supervisor, I was not encouraged, often discouraged and it was definitely against the cultural norm. In retrospect sadly, and boringly typically, I ‘dropped out’ of the field during my child bearing years. My daughter went on to study mathematics and I was curious to see how/whether the climate had changed. It is undoubtedly better – she has never been discouraged, indeed generally encouraged, and the best part? – that both as an undergraduate and as a postgraduate, she had/has a woman supervisor. Not that I am advocating some sort of gender apartheid – merely noting that the example provided by having some tenured women in a department (we had none) must provide a more positive environment for young women just entering the field. Unfortunately, this boot-strapping process is necessarily slow.

  12. Being a heterosexual male mathematician, I certainly do find it “sad” that the number of our female colleagues is small – very “disappointingly” indeed! These quite practical emotions are also supported by good abstract reasons: diversity is great for everybody; the natural delay in the change of the historic misrepresentation (see Anna’s comment just above) is both unethical and a missed opportunity for the development of the field. With this in mind, a reasonable amount of Affirmative Action would seem to be a relatively reasonable solution.

    Alexandre suggests to go beyond that and “put more stress” (in “promoting mathematics”!) on 4 notions, of which 2 are derivatives of “power” and one more is a derivative of “competition”. To me,
    the notions of “power” and “competition” themselves are already totally alien to the heart of mathematics. Let me not elaborate on the derivatives; instead, may I ask why on Earth would a pure mathematician care to promote his profession at all? In other words, why would one want to make it look more attractive than it actually is? (Obviously there is a need for popular expositions of the {\it subject} of math, such as Gardner’s books, but this is not what Alexandre is talking about.) Will a 10-year study of pure math earn more money to a smart person who actually does want to earn money? Will papers of a smart person who cares more about something else (e.g. power and competition) advance the field in a substantial way? Or could they only mislead others into thinking about problems they would otherwise never consider? By any chance, hasn’t this been happening increasingly ever since the nuclear arms race made physics and math fashionable and financially rewarding in the 60s?

    Here are links relevant to Peter’s
    and taramokhtari’s comments:

    http://www.viewzone.com/fingers.html

    http://www.autismresearchcenter.com/docs/papers/2001_BCetal_AQ.pdf

  13. [...] also: Women and Mathematics: Mathematics is too fiercely [...]

  14. why should we assume that women are less capable of independent thinking? Why should women surrender the game without a fight?

    Schwartz and Hanson do refer to what “men are trained to excel at” and “socialization models” rather than innate differences, at least in the quotation you provided.

    As for collaboration vs individual achievement: the average number of coauthors is 3, not 0! http://www.siam.org/pdf/news/485.pdf

    • It appears that the number 2.94 given in http://www.siam.org/pdf/news/485.pdf is the mean number of collaborators per author, not per paper. Out of curiosity I tried to count my collaborators on my more serious papers: about 20. When I say that mathematics is about “independent non-collaborative thinking” I mean that my collaborators are strong and independent non-collaborative thinkers– for otherwise what is the point of collaboration with them?

      • I see. But still, imagine an alien planet where things are different. Couldn’t it be plausible in some world that mathematicians ask each other questions, help each other, pick up the other’s slack, and so on? I mean, how could one prove that mathematics is necessarily independent and that this isn’t just an outgrowth of the idiosyncrasies the present situation?


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