A portrait of the mathematician as a young woman, Part II

Description

This is my translation of a talk by the mathematician Michèle Vergne. In it, Vergne reflects on her youth and how she became a mathematician in a sexist world. There are no stories of violence or male brutality to be had here. Vergne writes instead of the winsome face of patriarchy—a face that is, in fact, only too familiar to anyone who has lived in a state of society. This is the second part of my translation of the talk.

Born in 1943, Vergne studied and worked in France and the United States, becoming a professor at MIT, at the École normale supérieure de jeunes filles, and a director of research at CNRS (the French National Centre for Scientific Research). Her field of mathematical research is representation theory.

The talk was originally presented in 1975 at a seminar on “Mathematics, Mathematicians and Society” in the Math department of what is today the University of Paris-Saclay at Orsay.

My thanks to Michèle Vergne for permission to publish this translation on my blog. The original talk, published as an article in French, may be found on her website:
https://webusers.imj-prg.fr/~michele.vergne/

Note: To read the first part of my translation of Vergne’s talk, click HERE.

The talk translated, part II

My warrior initiation

I was an advanced master’s student studying under Claude Chevalley, who had no idea of the psychological isolation that I experienced as a woman. It was the period of my warrior initiation, a rite of passage that pretty much all young researchers undergo: a period of self-doubt, of ordeals to be undergone by oneself alone. I cite here Colette Audry, who wrote of the difficulties that young writers encounter. What she says explains how I felt during this period:

“but these arid inner quibblings, this doubt cast on oneself as an individual creator, are all that the writer shall know if he is born male; when the writer is a woman, added to these is the wholesale questioning of her very belonging to the category of creator. The simple interrogation of the individual ends in the latter’s being put to the test: nothing is given beforehand; risks must be run. However, the questioning of the category to which one belongs blocks everything since such questioning brings into play predestination: everything is given beforehand; the activity is not worth the effort.”¹

I spoke to no one. I had been very talkative in my classes with girls but suddenly, confronted by men upon completing high school, I found myself tragically silenced. I was scared to talk. Even today, before I speak in public at a seminar, I experience several moments of panic. If a fellow came near me while I was studying at the library, it was horrible. I immediately hid my notes so that he would not be able to see what I had written (and, in fact, I am still like this). If I asked for an explanation of some mathematical point, my voice trembled with fear. If some guy spoke to me of mathematics, my ears filled with a buzzing sound. I understood nothing and was rendered incapable of responding with a single intelligent word. To be more precise, I scarcely heard what he said. Instead, I heard the words, “No woman will ever be a genius. Go on, show me one. For instance, answer this mathematical question… Well, in any case, there’s nothing to be done. It’s biological, it’s Nature.” And I, I interiorized the imposed stereotypes as per which I would surely never be capable, mathematical ‘creation’ being impossible for me as it was for all girls. And I began to take classes in the History of Mathematics, which my adviser considered a perfectly reasonable thing for me to do.

“Don’t worry if you aren’t able to do it!”

And so I was prepared for failure and received no support from any peer group or protective clique, the benevolence of the group towards a young woman manifesting itself in general in the following terms: “But don’t worry if you aren’t able to do it!” Towards young men by contrast it was: “But don’t worry, of course you will be able to do it!”

And so, cut off from all living communication, from all mathematical culture, from all real relations with my object of study, I effectively understood Nothing. Astonishing as it may sound, as I recall, I understood Nothing in the classes I attended. Since, in general, the professors passed quickly over the details of proofs, and since I did not understand the references they made to well-known, classical ideas, I could not spot the missing markers. They said, “By a standard reasoning, it is proved that…” And I was reduced to a state of utter abjectness at my inability to divine what that standard reasoning was. I think that when professors do not make an effort to explain from where their ideas, their intuitions come, they are being racist and sexist, whether deliberately or not, towards those who belong to categories that are not immersed in a mathematical culture, and who have no other means, classes apart, of knowing from where the ideas arise. I say this because I no longer believe that men are predestined to knowledge from the cradle on, or that I was predestined to ignorance.

And all that I describe—that fear, that isolation, that difficulty to imagine, that impossibility to speak, to have confidence in myself, to belong to a group—I do not think those were merely my own inner burdens that I carried around within myself. And I do not think that, had I been less shy, prettier, less this, more that, everything would have been much better. No, all that is false. I think I was just confronting reality. I think that women live in a society where, overtly or covertly, they are despised and threatened, whether mentally or physically. Women do not interiorize irrational fears: if one is afraid, it is with reason. And like all of society that surrounds it, the mathematical milieu is profoundly misogynistic: if a girl speaks in class or in a seminar, or rather if she does not speak because she is afraid, well then, she is right to be so, because, in effect, she risks a great deal. If the question is stupid, the entire class will immediately arrive at a stereotypic image of her—a stereotype of a woman, and this is always a negative stereotype, which will stick close to her skin, which will suit her perfectly. In the best of cases, they might say, “Yes, she is cute alright, but she would do well to spend her time on other, less boring matters, because life has so many more interesting things to offer, especially to women.”

And I know that I myself, for a long period, despised all the young women who presented bad work—all the young women who reflected back at me a negative image of women, one that I did not want to accept.

To love and be loved

I began to come out of this quite by accident. I got to know, and subsequently married, a man who was very reassuring and who helped me a great deal. Besides, psychologically, it was a fundamental change to be married: “Yes, I am not as stupid and ugly as all that because I too have been able to find myself one …”

I had all manner of complexes about my physique at the time. And for a young woman, social relations and her relationship with herself are mediated in the first instance by her physique. For a young woman to please and to be pleased, to love and be loved, what matters above all is her physique. I still recall with pain my father’s reaction—perhaps he was simply teasing—when I succeeded brilliantly at the École Normale Supérieure entrance exam: “Well then, what would you like as a reward? Plastic surgery perhaps?”

On the other hand, it was in that milieu that I met, quite by accident, a young woman named Monique Lévy-Nahas, who consciously called into question the milieu’s elitist values, which was exceedingly rare at the time. She spoke to me. She did not try to valorize herself through me for someone else. We actually spoke to one another—not while waiting for or instead of someone else who was ‘better,’ nor out of frustration at not being listened to by some fellow who was more ‘popular.’ At last, I could speak to someone about math without that buzzing sound in my ears. She gave me a certain degree of self-confidence. She studied theoretical physics. We began to work together. I also met a young Algerian man who helped me greatly. I was finally able to abandon algebraic geometry and switch to the study of Lie groups without feeling like a complete failure. I completely surmounted that feeling of failure, and felt capable of studying the subject with a reasonable degree of certitude that I would be able to understand it perfectly. Before, I had had a psychological block that I had interiorized as an intellectual block. And I think I would not have managed to overcome it had I not decided, with their help, to study other things. I think their help was absolutely decisive. For once, society’s negative stereotypes helped me: faced with a young woman and an Algerian, I felt as if I was in full possession of all my means. I realized, always with surprise, that at times I too was intelligent. Between these moments of surprised joy were gaping black holes. Nevertheless, slowly, the psychological problems I experienced as a young woman changed in nature. I began to feel more self-confident, though I remained entirely dependent on the appreciation of others. I had to please them because that was what I had been taught was my raison d’être.

Among the men though there was a lot of aggression towards women, and no solidarity. A young woman’s success was always doubted: “Well, let her prove herself. We’ll see afterwards if we consider her to be inferior or not!”

I have horrible memories of the Bourbaki seminar at which I spoke in 1969. I was very nervous, very anxious to know what impression I had made. And, of course, the first views that I heard represented to me the definitive view of everyone. There were three fellows discussing the seminar among themselves. The first—and he was the kind one—said, “Well, what a discovery! There are women mathematicians who are sexy!” The second, who was rather old, said (and I quote), “Ah, it was technical. It was so clearly a woman talking. All those petty, precise calculations, and not one big idea.” And the third, a student the same age as me, said, “I heard Serre and Thom talking. They said your talk was really bad.” I had a tough time getting over these views that sent me back inexorably into my predestined category, that sordidly destroyed the little self-confidence that I had managed to acquire despite everything. I felt better last June when I was asked once more to speak at the Bourbaki seminar. The invitation made me feel that that third remark had been a mere lie invented by a frustrated young man, something that I had known rationally to be the case all along. I confess though that I faced my second talk with about the same anxiety as the first. And immediately after, I encountered the very same remarks as the first two I had encountered all those years ago. And I think, this time round, both sets of remarks were justified after a fashion!

To be continued in A portrait of the mathematician as a young woman, Part III.