Category Archives: women in math

Maryam Mirzakhani makes history

The IMU has just announced this year’s Fields medal winners. For the first time ever, a Fields medal has been awarded to a woman, Maryam Mirzakhani. I will have the honour of attending the ceremony this morning.

The official press release on Mirzakhani’s research is available, as are the citations for the other Fields medalists. I’d like to speak to what the selection of a female Fields medalist means to me as a woman and a mathematician. In that, I would like to paraphrase something that Melissa Harris-Perry has said about the election of President Obama. Mirzakhani’s selection does exactly nothing to convince me that women are capable of doing mathematical research at the same level as men. I have never had any doubt about that in the first place, and I have said so here many times. What I take from it instead is that we as a society, men and women alike, are becoming better at encouraging and nurturing mathematical talent in women, and more capable of recognizing excellence in women’s work. I’ve said here before that the highest level of achievement within the age limit set for the Fields medals requires a confluence of both exceptional talent and favourable circumstances. Talent must be recognized, nourished, directed in productive ways, accomplishment must be acknowledged and promoted. Among the setbacks I experience every day and hear about from other women, Mirzakhani’s award offers a reason for guarded optimism, a point of evidence that sufficient dents have been made in the many layers of glass ceilings that a woman could break through all of them to the highest level.

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The human factor

A recent Telegraph article suggests that “females, as a whole, are not hugely engaged by science.” Emphasis mine:

The problem with science is that, for all its wonders, it lacks narrative and story-line. Science (and maths) is about facts, and the laboratory testing of elements. It is not primarily about people. Women – broadly speaking – are drawn to the human factor: to story, biography, psychology and language.

This self-proclaimed people specialist keeps referring to women as “females,” the noun more often than the adjective. For instance: “Biology and nature, he suggested, will generally nudge females away from [science and engineering].” Here’s to biology, I guess. And to consistency.

Here’s one good rebuttal, with further links. This essay in particular matches a great deal of my own experience. But I also want to question the “science is not about people” line from a different angle–the one that scientists adapt enthusiastically and unquestioningly in every funding application, from individual grants with a training and/or collaborative component, to conference funding, to large institute grants. For example:

The mandate of PIMS [Pacific Institute for Mathematical Sciences] is to:

  • promote research in and applications of the mathematical sciences of the highest international caliber
  • facilitate the training of highly-qualified personnel at the graduate and postdoctoral level
  • enrich public awareness of mathematics through outreach
  • enhance the mathematical training of teachers and students in K-12
  • create mathematical partnerships with similar organizations in other countries, with a particular focus on Latin America and the Pacific Rim.

NSERC pays 1.15M per year for this, and that amount does not include provincial funding or support from participating institutions. I suppose one might argue about the precise meaning of “primarily,” but the “human factor” does not exactly seem unimportant. You could also look at the webpages of individual institute programs:

The purpose of this programme is to bring together researchers in these diverse areas of mathematics, to encourage more interaction between these fields, and to provide an opportunity for UK mathematicians to engage with an important part of the mathematical computer science community.

This is very standard language. Every conference, workshop and institute program aims to bring together researchers, encourage interactions, promote the exchange of ideas, contribute to training, engage the community. Every conference proposal and grant application emphasizes it. Every funding agency demands it. Every mathematics institute derives its very existence from this notion.

And how do women score here? In light of their natural, biologically determined talents and inclinations, surely we should be looking for women scientists in particular to manage all those human interactions, or at least to participate in them significantly? PIMS has never had a female director or deputy director. Among the more than 120 participants in the program I linked above, there are 3 that I recognize as women. There are many more such examples, more that I could ever have the time to list. Women are often underrepresented at conferences (read the comment section for testimonials), both as speakers and as organizers, and when they are represented proportionally or better, this is often framed as an affirmative action gimmick rather than genuine appreciation of their contributions.

We sing the importance of communication, interaction and connection-making at the bean counters, then ignore it in our own deliberations. We take pride in choosing conference speakers based on “scientific merit,” defined as a best paper contest with an all-male jury, even when good arguments can be made that the “human factor” should in fact count towards scientific merit. And heavens help anyone who might raise the idea of inviting more women to conferences based on their alleged skills in interpersonal communication. And I don’t see women being overrepresented among institute directors, deputy directors, or other high profile research facilitators, all positions for which women should be particularly well qualified by the virtue of biology and nature.

Consistency, indeed.

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G.H. Hardy and Mrs. Ellis

David, by Michelangelo. Image: Wikimedia

David, by Michelangelo. Image: Wikimedia

If you haven’t yet read this classic essay by Linda Nochlin on the question of why there have been no great women artists, I recommend it very highly. The essay is from 1971, but Nochlin’s points remain very much relevant to today’s arguments about why there have been so few great women philosophers, or mathematicians, or whatever.

Nochlin starts out by questioning the common notion of a “great artist” as a singularity that exists independently of society and history. The truth is, it takes at least a village. Great artists are enabled by the society they live in, draw on its artistic traditions, engage in a dialogue with other practitioners. Indeed, if artistic greatness depended only on innate talent, it would be very difficult to explain what Nochlin calls “conditions generally productive of great art,” such as must have existed, for instance, in the 15th century Florence and Rome, or in France in the second half of the 19th century. (We’ll note here that much of the same can be said of mathematics.)

The society also establishes standards for what qualifies as “great art,” and what does not. In the pre-impressionist Europe, historical painting– understood broadly so as to include biblical scenes, Greek and Roman mythology– was considered the highest and most prestigious form of art. Landscapes, still-lifes, portraits, and other suchlike were deemed less worthy. To wit:

Until the 20th century, Mona Lisa was one among many and not the “most famous painting” in the world as it is termed today. Among works in the Louvre, in 1852 its market value was 90,000 francs compared to works by Raphael valued at up to 600,000 francs.

“Great art,” going back to ancient Greece and Rome and then again starting with Renaissance, more often than not depicted naked and partially naked human bodies. Think Michelangelo, Raphael, Titian, Botticelli, Rubens. Even when the figures are clothed, the paintings still display a thorough knowledge of human anatomy. Such knowledge was usually gained through extensive study of the nude model, a practice that continues to be a mainstay of art programs. And yet, as Nochlin explains in detail, nude models (both male and female) were forbidden to women painters before the end of the 19th century. That right there explains completely why there has been no female Michelangelo or Raphael.

Nochlin cites many other ways in which the society refused to enable women artists: the apprenticeship system, access to academic educational institutions such as the Ecole des Beaux-Arts, opportunities to establish suitable relationships with art patrons, and more.

But the part I want to highlight here is the prevailing attitude to “the lady’s accomplishment”:

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Eternal sunshine of the progressive mind

Leszek Kolakowski, 2007. Photo: Mariusz Kubik

Leszek Kolakowski, 2007. Photo: Mariusz Kubik

Every now and then, I’m instructed to have more faith in the progressive tendencies of humanity. Racism and sexism, I’m told, are relics of the past, and especially so in science and tech. Progressive, open minded people are against discrimination. Scientists and tech geeks are open minded almost by definition, therefore progressive, therefore against racism and sexism, which therefore are no longer a problem. I should just look around and see how many Chinese and Indian immigrants work in tech and science; clearly, this means that the field is not racist. And if there aren’t so many women around, that’s obviously because they’re not interested – or, as the progressive feminist Steven Pinker explains, maybe it’s just the innate differences. Progress! We’re all in this together! Let’s forget our differences, join our hands and work together for a better future.

Except I’ve seen it before: the unquestioning conflation of all possible good causes, the expectation that good intentions alone guarantee progress and enlightenment. Take, for example, the Western New Left in the 1950s and 60s. Leszek Kolakowski in “My correct views on everything: A rejoinder to Edward Thompson’s ‘Open letter'” from 1974:

[S]ocialist writing [...] amounts to saying that the world should be good, and not bad, and I am entirely on your side on this issue. I share without restrictions your (and Marx’s, and Shakespeare’s, and many others’) analysis to the effect that it is very deplorable that people’s minds are occupied with the endless pursuit of money, that needs have a magic power of infinite growth, and that the profit motive, instead of use-value, is ruling production. Your superiority consists in that you know exactly how to get rid of all this and I do not.

Eastern Europe, meanwhile, was being subjected to a practical implementation of that wondrous dream of progress and unity. If the Party represents everything that’s good and progressive, why would anyone ever want to oppose it? Who would need other political parties? Why, indeed, should any organizations be independent of the Party and government – surely, progressive and well-meaning people would want to associate themselves with the historic forces of good? Who could possibly be against world peace? The logical consequences are obvious. Kolakowski again:

… we got rid of this fraudulent bourgeois device of the division of powers and we achieved the socialist dream of unity, which means that the same apparatus has all legislative, executive and judicial power in addition to its power of controlling all means of production; the same people make law, interpret it and enforce it; king, Parliament, army chief, judge, prosecutor, policeman and (new socialist invention) owner of all national wealth and the only employer at one and the same desk-what better social unity can you imagine?

Clearly, if some Eastern Europeans were unhappy with this arrangement, this was just because they didn’t understand. They had “false consciousness,” in the language of the Marxist-Leninist theory, and therefore needed to be told what was really good for them, and beaten into submission if necessary. Not to say that the system was perfect, of course:

… you, not unlike most of both orthodox and critical communists, believe that everything is all right in the Communist system as long as the leaders of the party are not murdered. This is, in fact, the standard way of how communists become “critical”: when they realize that the new alternative socialist logic does not spare the communists themselves and in particular party leaders. Did you notice that the only victims Khrushchev mentioned by name in his speech of 1956 (whose importance I am far from underestimating) were the Stalinists pur sang like himself, most of them (like Postychev) hangmen of merit with uncountable crimes committed before they became victims themselves? Did you notice, in memoirs or critical analyses written by many ex-communists (I will not quote names, excuse me) that their horror only suddenly emerged when they saw communists being slaughtered?

I’m thinking of the progressive folks who believe that the main focus, always and in all matters, should be on them. I’m thinking of the men testifying on feminist blogs that they, too, have to prove their merit all the time, and there was even this committee meeting three years ago when someone interrupted them twice. I’m thinking of the journalism genre that “treats race as an intellectual exercise – a low-stakes cocktail party argument between white liberals and white conservatives over their respective racial innocence.” I’m also thinking of how the same people, when asked to stop and listen for a moment, respond with “I’m listening” followed by yet another barrage of words on how their arguments are really superior. Which of course they must be, seeing how eagerly they are accepted and applauded by the important target audience of other like-minded progressives. If someone like me continues to dissent, that’s my false consciousness speaking. Or maybe I’m simply too emotional and pessimistic. I should just continue to do my good work and we’ll all benefit, as I’ve been told many times. Kolakowski again:

… the spontaneous and almost universal mistrust people from Eastern Europe nourish towards the Western New Left. By a strange coincidence the majority of these ungrateful people, once they come to or settle in Western Europe or in the US, pass for reactionaries. These narrow empiricists and egoists extrapolate a poor few decades of their petty personal experience (logically inadmissible, as you rightly notice) and find in it pretexts to cast doubts on the radiant socialist future elaborated on the best Marxist-Leninist grounds by ideologists of the New Left for the Western countries.

Czeslaw Milosz:

I lived through two phases in Paris. In 1950, I was an attaché of the Polish embassy and attended parties with Paul Éluard and Pablo Neruda. The following year, after breaking with the Polish Communist regime, I came to live there as a refugee. At that time, French intellectuals were completely in love with Communism and Stalin. Anyone who was dissatisfied and who came from the East like myself was considered a madman or an agent of America. The French felt that their so-called ideés générales were valid for the whole planet—beautiful ideas, but hardly realistic. At that time the political climate of Europe was dismal; millions of people were in gulags; their suffering contaminated the aura, the air of Europe. I knew what was going on. The West had to wait for Solzhenitsyn to write The Gulag Archipelago to learn about it.

I’ve never been a fan of sloppy comparisons to communism, and I want to be very specific here. My beef is with those who say, “I’m a nice, progressive person, therefore I can’t be doing anything wrong and your complaints are not valid.” It’s with those who believe in the theory and refuse to see the evidence. It’s with those progressives who feel that every “good” cause, by virtue of their self-identification with it, is about them; and that their opinions trump everyone else’s experience because they, sensitive and enlightened as they are, would obviously notice any signs of injustice or discrimination; and that, when such experience is presented to them, the proper answer is to point to the bright future that is sure to descend on us soon like a state of grace.

Progressive minds such as those like to be unburdened by history and evidence. For all the talk of “inevitable historical forces” in Marxist theory, socialist writing rarely respects history as history. Instead, it invokes history as the future, the promise and the fairytale. “Historical determinism” was then, as “progress” is now, the magic wand that would forge a perfect world out of the fairy dust of good intentions. Forgive me if I’m a little bit skeptical.

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Leaning back and smelling the roses

Now that the list of next year’s ICM invited speakers has been posted, I’m pleased to be able to say here that I will be speaking in Section 8: Analysis.

It gives me far less pleasure to say that the UBC mathematics department did not approve any graduate courses in harmonic analysis for this year. My proposal for a 600-level (topics) course was rejected. This is not an isolated incident: I have been at UBC since 2000 and I still have not taught a single 600-level course.

For comparison, the department had one ICM speaker in 2006, two in 2010, and there are two others (in addition to me) in 2014. One of those was only hired last year. Of the remaining 4, each taught at least one 600-level course in 2009 or later. They all boast large research groups, each with several full professors and at least 2-3 graduate courses each year in their research areas. Meanwhile, I’m still the only full professor in my group. As it happens, I’m also the only woman among the UBC ICM speakers. Make of that what you will.

In the past, I might have given lectures anyway on the same topics, or offered a working seminar instead that students could take for credit as a reading course, in addition to my assigned course load. I have in fact done that, back when my teaching load was reduced thanks to the UFA award. Not any more. If the university does not want my topics course, it will not have it.

When I see women being admonished to “lean in” to advance their careers, I think back on the time when I actually tried to do that. “Internalize the revolution.” Be ambitious. Take risks. Seek out opportunities. Don’t hold yourself back. Above all, accept the relentless and accelerating career demands, because that’s good for you, because of course it is. Except when it’s not.

I gave reading courses. I supervised 4-5 graduate students as early as 2005-06, back when I was still the only active harmonic analyst in the department. When the local PIMS institute offered no support, I organized a program at the Fields Institute instead. I accepted a good deal of administrative work at and beyond UBC. I served 3 years on the Putnam problem-setting committee.

Tenure-track and tenured positions tend to have no clear job description. Only the course teaching load is fixed, more or less. In popular imagination, this means just a few hours of work per week. In reality, tenure, promotion and pay increases depend on meeting the institution’s “standards,” which in turn are established via a rat race between faculty members. Two parallel rat races, actually: one to achieve more in science, one to ascend to a position of enough influence in departmental politics to push one’s own interpretations of the outcomes of the first race. Clearly, I’ve done better in one of those than in the other, as was my preference all along.

Of course achieving is easier when one’s work is supported by one’s institution, in a variety of ways that are never written into any contract but nonetheless make a world of difference. Some groups here (probability, number theory) have 6-8 faculty; of course it’s easier for them to attract graduate students and postdocs, or to offer several graduate courses each year with the department’s blessing. Of course it’s impossible to function in a similar manner when you’re isolated, as I was for many years. You try anyway, “leaning in” and hoping that it will get noticed, seeking external leverage when it doesn’t, as wise colleagues keep lecturing you on how everyone else’s needs are greater and priorities more important than your own.

But now? I have nothing left to prove here. I’m a known quantity and have been for some time. My research is going better than ever. There can be no doubt as to whether I’m capable of building a group or advising graduate students.

My employers are more than welcome to lean in and take advantage of that. Even just with the current faculty, we could have an excellent graduate training program in harmonic analysis here, one of the best in the world. Just give us one or two guaranteed graduate courses each year. Stop insisting on the false alternative where we either have to teach the same syllabus every 1-2 years in our graduate courses or give them up altogether, because smaller groups really need more flexibility than that. Cut back on those degree requirements that serve no purpose I can think of, or that prop up the largest groups but are not relevant to the thesis work of everyone else’s students. And please please cut down on the bureaucracy, both within the department and at the university level, because I’m tired already of having to deal with that.

But if not, then, well, not. Or nought, if that’s your fancy. Life is too short to be spent on a hamster wheel, even as colleagues throw wrenches in it and the only reward is more time on the same hamster wheel back again. That stretch of my career is over and done with.

I’ll lean back in when you do. Make of that what you will.

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Gender Bias 102 For Mathematicians: Merit

A long time ago, I promised a follow-up to my Gender Bias 101 post. One thing I’ve found out the hard way is that I can’t promise to post anything here on a regular schedule, or according to deadlines. Paid work takes precedence, as does vacation time and my other interests – that’s one problem. The other one is that I don’t really have much to say about gender that’s not complicated. That’s why, instead of one follow-up, you’ll get several “Gender Bias 102″ posts on different topics. This is the first one. The rest will follow… oh, whenever I get around to it. I did mention a paid job that takes precedence.

I’ve said already that this is complicated. That’s my main point here. There’s no such thing as a complete explanation of sexism that will fit in a single post. You shouldn’t assume that you can learn everything you need to know from me, either. There’s a lot of women out there, with different experiences, and none of us have all the facts or answers. What I’m aiming for is this. When the subject of gender bias comes up, well-meaning colleagues like to offer one-sentence explanations and simple solutions, for instance (today’s example) that we should “just” evaluate everyone based on merit and not gender. I’ll try to give you reasons to stop and think about it twice. Once you do that, it’s not hard to find further reading, should you be so inclined.

Deal? OK, let’s get started.

MYTH: We should just evaluate everyone based on objective merit, regardless of gender, race, or other similar considerations.

FACT: Wouldn’t it be nice if we could actually do that. Unfortunately, it’s much easier said than done.

First, we do not evaluate people or their work objectively, even when we think we are doing just that. Gender is a known risk factor. I cited this Yale study last time, and an older one with similar conclusions can be found here (PDF):


In the present study, both male and female academicians were significantly more likely to hire a potential male colleague than an equally qualified potential female colleague. Furthermore, both male and female participants were more likely to positively evaluate the research, teaching, and service contributions of a male job applicant than a female job applicant with an identical record. These results are consistent with previous research that has shown that department heads were significantly more likely to indicate that they would hire female candidates at the assistant professor level and male candidates with identical records at the associate professor level (Fidell, 1970).

Incidentally, if you believe you have no gender bias, then statistically you are in fact more likely to be biased. That’s not self-help mumbo-jumbo, that’s Nate Silver.

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Gender Bias 101 For Mathematicians

The great enemy of the truth is very often not the lie—deliberate, contrived and dishonest, but the myth, persistent, persuasive, and unrealistic. Belief in myths allows the comfort of opinion without the discomfort of thought.

- JFK

MYTH 1: Sexism is perpetrated by a small number of men, typically close to retirement age, who are “against women.” Most academics, especially mathematicians, are open-minded people who are against discrimination.

FACT: Please read this study on gender bias in science hiring:


In a randomized double-blind study (n = 127), science faculty from research-intensive universities rated the application materials of a student—who was randomly assigned either a male or female name—for a laboratory manager position. Faculty participants rated the male applicant as significantly more competent and hireable than the (identical) female applicant. These participants also selected a higher starting salary and offered more career mentoring to the male applicant. The gender of the faculty participants did not affect responses, such that female and male faculty were equally likely to exhibit bias against the female student. Mediation analyses indicated that the female student was less likely to be hired because she was viewed as less competent.

See also summaries and discussion here and here, and my own posts here and here. This is not an isolated study, either. See, for example, this study on gender and blind auditions in music. I’ve seen the same exact thing in my own experience and heard about it from colleagues. Statistical evidence from my own university confirms it.

The bottom line is, we are all biased. We all tend to think of women’s work as somewhat smaller, derivative, inferior. We do so unconsciously and involuntarily. We are not aware of it, nor do we notice it in others. That’s what all these studies are saying. It’s as if everyone is wearing glasses with the same tint. You’re wearing them even if you’re “open-minded” or “against discrimination”, even if you start your sentences with “I’m not against women, but…”

It is not, and never has been, only about a few individuals who forgot to catch up with the times. It’s not about trolls who say horrible things about women on unmoderated blogs. It’s about you, and me, and everyone we know. It’s about the nice, polite, progressive people who just wish that their female colleague down the hall didn’t try to be more ambitious than is good for her. (She’s clearly good, but does she really think she’s equal to X and Y? And she doesn’t have the same leadership quality, either.) It’s about that paper by two female authors that’s just not quite as groundbreaking as this other paper written by two men. In other words, you need to start by examining your own bias.

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