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.