People often remark that in the last decade the situation of women in mathematics has dramatically improved, both in Canada and in the United States. And they are right! The most immediate example is the election, as the new President of the CMS, of Katherine Heinrich, who not only is a talented mathematician and a great organizer who happens to be a woman, but is a very active militant for women's inclusion in mathematics.
This is but one sign. A few months ago, Ingrid Daubechies, a young mother of two toddlers, became the first woman full professor of mathematics at Princeton University, where, for the first time in its history, half a dozen young women at different ranks are teaching (and doing!) math.
So, some people argue, "You see, it was a matter of time, things are improving, why do you persist with your sessions on women in math?"
Well, why indeed. One reason is that what has been achieved, although considerable -- against the bleak background of a field where women were invisible only a few years ago -- is still quite modest. More importantly, what has been achieved can be reversed, and a slight change of social climate can provide a good pretext for such reversal. The current powerful drives against affirmative action both in the United States and in Canada are a case in point. Examples show that when there are no reminders about women mathematicians, colleagues tend not to "remember" us.
Just one such example: the invited participation of women in the International Congresses of Mathematicians (ICMs). Singular, yet illustrative of the general situation of women in math and how we may be ignored. In more than a century of ICMs there had been no women plenary speakers until 1932 (Emmy Noether), and not another one until 1990 (Karen Uhlenbeck). Before the 80's only a handful of women were among the hundreds of invited speakers. After a public protest at ICM 78 on the systematic omission, a few women were invited to speak at ICM 82 (which met in Warsaw in 1983). But no further reminder about women was made there, and none were initially invited to ICM 86, resulting in new protests, some late invitations, and more women at ICM 90. Finally, in 1990, the International Mathematical Union (IMU) passed a resolution "to take into account that many qualified women were available as speakers for ICM 94." This brought to the latest ICM the unprecedented number of ten women invited speakers (out of a total of a hundred and sixty five lecturers), two of them delivering plenary lectures. At every ICM which was not preceded by an explicit reminder to consider women candidates, many outstanding mathematicians were passed over.
This historical sequence points to two needs: to alert the community about women's existence and to make constant reminders.
Was the "reminder resolution" of IMU a call to overlook standards? The larger representation of women at ICM 94 in no way diluted its mathematical quality. On the contrary, the plenary addresses of Ingrid Daubechies and Marina Ratner at Zurich were indisputably among the best. No chauvinistic critic challenged, at least publicly, the excellence of women's contributions.
The discrimination against women had been generic, not specific or personal. Yet it had not disappeared, as suggested by the numbers, and there seemed to be an invisible "quota system." The eight women nonplenary speakers lectured in eight of the seventeen sessions, one in each session. It seemed as if the selection panels, although aware enough to consider women candidates, felt that they had filled their duty as soon as the first one accepted. And this is not an isolated occurrence.
A personal anecdote: Years ago, a friendly colleague told me his department was considering hiring a junior person in our field and asked me for a top candidate. After some thought I mentioned one of the best junior researchers in the field. His answer was "But we already have a woman!" and mine to him, "So, would you hire a man for the job? I assume your faculty already has at least one man!"
Do women need "special treatment" not to be overlooked? For a variety of reasons, not all of them obvious, the answer seems to be yes. And it provides the rationale for the prizes, honorary lectures and mathematical events "for women only." Is that "reverse discrimination?" I don't think so.
Both the American and the Canadian Mathematical Societies have recently instituted new honors specially designated for women. Let me analyze the example of the Ruth Satter Prize of the AMS, dedicated by the well-known mathematician Joan Birman to the memory of her sister, a chemist. Many people frowned at a prize for women mathematicians. Don't we have enough prizes in the Society? Don't they go to deserving people? Yes to both questions! But none of them have gone to women. Is it because there are no deserving women candidates? Maybe so, but when the Satter Prize went first to Dusa McDuff -- later elected FRS (Fellow of the Royal Society) -- and then to Lai-Sang Young and to Sun-Yung Alice Chang, each a leader in her field, nobody felt there had been the dreaded "lowering of standards." These are top researchers, worthy of the highest honors, that could compete for any prize. But it took the creation of the Satter Prize to highlight their achievements.
These recognitions have an educational effect on the mathematical community. Not only do some individuals get their due, but more significantly, their merits are explained and publicized. Thus our whole community learns that there are women who have made outstanding contributions, and what those contributions are. This is especially important in the case of younger people, like Lai-San Young, who had already influenced their fields, but who may not have been recognized outside them.
Recognition is important if we want to reach the people who do not want to discriminate, but who cannot remember the name of a woman mathematician when the time comes to make a nomination for an editorial board or a selection committee.
And let's be fair. How is it with each of us? I can speak from experience. It required conscientious training to "remember" women every time I had to put together a conference or a program. I knew only men! Well then, look for women, even if you do not know them personally. Chances are that you do not know them because nobody else "remembers" them, so they go to fewer places where they can meet others.
Do we need to go to extra lengths to find suitable speakers who happen to belong to underrepresented groups? Absolutely yes. The fact that the first name that comes to mind is that of somebody well known, who happens to be white and male, should make us automatically think about what other person, who happens to be non-white and/or female and not as well known, would make us proud to bring to the same event.
The problem is not so much those diehard retrogrades who hate women intellectuals on principle and talk about our less-developed brains and our innate inferiority. The problem is the honest people who insist they do not discriminate and are against quotas (those favoring women and minorities, mind you) and who may earnestly think that everything will be okay if only we ignore the issue, and just use initials before last names to conceal gender.
The problem is the good guys of both genders who are not trained to be good enough. To them we have to provide information and the opportunities to get in contact with women mathematicians whom they can admire, as well as women colleagues they have to respect. And then ask everybody to remember every day that there are people who may be different from them, yet still love to do what we love to do: mathematics.
A question often asked when discussing affirmative action measures toward women and other underrepresented groups is "Will they feel demeaned by being included through such a measure?"
Many times I had friends telling me "Certainly you'd be offended to receive an offer because of your gender and not your mathematics!" Sure I would, if the offer was not appropriate to the level of my mathematics. But I would find it much more offensive if an offer for which I was mathematically competent did not come because of my gender!
As I favor affirmative action measures, let me be explicit about my own "golden rule": to accept each opportunity that one deserves; to reject any exaggerated offer that would make one stick out as a "token" and is thus made just to fulfill some real or imaginary "quota." Of course, one needs a high level of self-confidence to follow such a rule, and self-confidence is much less abundant among young women mathematicians than among their male counterparts.
This lack of confidence does not come about by chance. Many women have faced a lifetime of suspicion about their talent, their commitment to work, their credentials. So, how would they feel about getting a job just because there is an opening in a "female slot?" Badly, unless they join a group that wants them and wants to take advantage of such a slot as a gain to the group. Thus the solution is much more up to the group than to the individual, and there is where education is needed.
Senior women can make a difference. For instance, by not frowning at special programs for women, but taking advantage of them and, thus, making them acceptable, and even desirable, for younger women.
Let me, through an example, be specific here. In 1982 the National Science Foundation started a program of Visiting Professorships for Women in Science and Technology, which yearly sponsors a score of women to visit top institutions. This program highlights the existence of women scientists in places where there are few or no women faculty. It has enabled, for instance, outstanding women engineers working outside academia to teach engineering students who had never encountered a woman engineer before. In the case of mathematics, it provided a great opportunity for financial support for women researchers to work at top institutions.
But at first it took some courage to apply! Who wanted to be singled-out as going places "as a woman?" Fortunately, "somebody" did, the opportunity was put to good use, no stigma was attached, and soon the numbers soared. Now the list of past recipients of this award looks like a "who's who" of women mathematicians in the U.S. It became prestigious, and some institutions offer it as a possibility (which is obviously to their own advantage, since someone else pays) to the mathematicians they want to invite and who happen to be women.
So, the program turned out to become a successful way to have more women at institutions where they will be well received, where they will highlight the existence of women researchers to predominantly male faculties and to graduate students of both genders, and where they themselves will have excellent research opportunities.
Affirmative action programs of this sort are useful, economical, and produce a lot of good, both to individuals and to their communities. It is up to us to see that they do not disappear in the current anti-affirmative-action hysteria sweeping the United States, and that, on the contrary, they are increased at various levels of the educational and research pipelines.
The gains of recent decades could be wiped out in one generation, just as the ICM program committees forgot to invite women as soon as the reminding pressure was relaxed.
We have achieved much. But we are striving for nothing less than the right of all people to do mathematics. For that we have to work together, women and men, so that the mathematical community is weaned from the need for constant reminders of the existence of women in its midst.
When the biggest affirmative action effort in the history of humankind -- that favoring white males -- ceases, no further affirmative action will be needed and we will all have more time to concentrate on mathematics.