Category Archives: women in math

On proof and progress in feminism

The recent allegations against several celebrities have led to a broader conversation on how we, as a society, don’t believe women. In a “he said, she said” situation, we trust the man and assume that the woman is either mistaken or lying. “Taking us seriously” means that we are advised of such and offered an explanation for our dismissal instead of simply being dismissed outright. It’s not only personal bias, conscious or not; there are institutional mechanisms perpetuating this state of affairs. No proof is ever sufficient if it comes from a woman. Should she present multiple affidavits, all signed and notarized in triplicate, she’ll be informed that they do not prove her claim; she, on the other hand, probably violated multiple rules and procedures by collecting and presenting her evidence in the first place. She should stop before she gets into more trouble.

Meanwhile, there’s a growing crop of men who, having declared themselves as feminists, proceed to lecture women on how they should go about equity-related matters. At a recent tech conference, a panel of male allies told women that they should just apply themselves a little bit more; another male panelist implored them to wait quietly for their good karma. Closer to home, I’ve been told repeatedly and earnestly that sexism in math would be solved if we only had unmoderated comments on research articles, or anonymous journal submissions, or some such. We’re instructed on what level of anger befits a feminist (low to nonexistent), which fights we can pick without belittling our cause (not many, and most of them were in the past), and how to address men in order to not alienate them (politely and with due deference). We’re offered advice that’s worse than useless in that we have to spend our time rebutting it. We have policies and procedures pushed on us that promote, at our expense, some alien, estranged concept called “women” that does not include us.

This is all of a piece with the culture that casts men as leaders and experts, and women as supporting characters and understudies. In feminism, as in everything else, men believe that their superior knowledge and understanding bestows upon them a natural authority and responsibility. Our equality will be measured, apportioned and dispensed to us by polite, congenial men, men who will invite us to advise and support them as needed, but will always reserve the right to overrule us should they deem it necessary.

Basic things are basic. You spoke over women in committees, silenced them in faculty meetings, denied their requests, and then you don’t understand why they don’t accept your valiant leadership with gratitude? Golly gee, the world can be so unfair. That said, we do need allies. We could use more help. And there are men who, I’m sure, have all the best intentions. And that makes it so much more disappointing when these men dismiss our hard-earned insight in favour of their own solutionism, where each problem has an easy answer and those that do not are declared nonexistent.

Consider the large body of research on unconscious racial and gender bias. Have you also paid attention to the public responses to such studies? Most men, and some women, might read a study on gender bias with astonishment and disbelief, having had no previous intimation that this was going on. They might argue back that not all men do this, and that some women succeed in tech, and women have babies and girls play with dolls. Above all, they will demand more proof. If it’s a lab study, it needs to be repeated and checked against real life statistics. If it’s statistics, then individual cases must be examined for other possible explanations. If it’s individual stories, that’s just anecdata, we need statistics and/or a lab study. To ensure appropriate collegiality, all this must be provided without hurting men’s feelings or contradicting their beliefs.

Many women, meanwhile, respond to the results of the same study with a collective “duh” on social media. It’s hardly news to them that X happens, even if the numbers might still surprise them. They see it all the time; they also see Y, Z, W, and much more. They had talked about it between themselves, thought about it, written about it at length. Nonetheless, they are the first to point out the importance of the study, to praise and publicize it. They do so because it legitimizes their own experience in the eyes of others, opens up a window in which they might be permitted to speak out. It offers evidence other than the flimsy, useless threads of their own words.

None of their knowledge is available to those who insist on conducting every conversation as it if were a criminal trial. There’s no chance of normal discourse. Why did I say “they see it all the time” when there was this one time it didn’t happen? And that other time, too? Who are “they,” anyway? Can we have their names and institutional affiliations? Have we heard the other side of the story? And so women are studied as if we were baboons, endangered for some reason but incapable of articulating what it is that ails us, so that researchers have to rely on statistics, experiments and third-party accounts.

Do you care about proof, or about progress? You can read all the peer-reviewed research, attend all the official panels, and you’ll still only see the tip of the iceberg. You’ll see the isolated facts but you’ll have no idea how to connect them. You’ll see the molehill that can be proved in a scientific paper, but not the mountain that we are forbidden to talk about for confidentiality reasons, and not the one that we stopped talking about because nobody believed us, either.

This post, unlike most of what I write, has no hyperlinks. This is on purpose. There are many related links in my earlier posts, and more in my Twitter feed linked on the sidebar. It’s easy enough to google around and find more. Alternatively, you could entertain the possibility that what I’m telling you is the actual truth of my experience. That would be a good start.

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Diversity and mathematics

bell curve1

Mother Jones, last year:

According to a new psychology paper, our political passions can even undermine our very basic reasoning skills. More specifically, the study finds that people who are otherwise very good at math may totally flunk a problem that they would otherwise probably be able to solve, simply because giving the right answer goes against their political beliefs.

I was reminded of it while reading the article “Does Diversity Trump Ability? An Example of the Misuse of Mathematics in the Social Sciences” in the Notices of the AMS. The author, Abigail Thompson, takes on a well known and widely cited paper:

“Diversity” has become an important concept in the modern university, affecting admissions, faculty hiring, and administrative appointments. In the paper “Groups of diverse problem solvers can outperform groups of high-ability problem solvers” [1], L. Hong and S. Page claim to prove that “To put it succinctly, diversity trumps ability.” We show that their arguments are fundamentally flawed.

Why should mathematicians care? Mathematicians have a responsibility to ensure that mathematics is not misused. The highly specialized language of mathematics can be used to obscure rather than reveal truth. It is easy to cross the line between analysis and advocacy when strongly held beliefs are in play. Attempts to find a mathematical justification for “diversity” as practiced in universities provide an instructive example of where that line has been crossed.

Thompson proceeds to shred both the “mathematical theorem” and the numerical examples from the Hong-Page paper. The actual paper is available here, and I have satisfied myself that Thompson is not unfair in her mathematical analysis. Her article, however, does not exist in a vacuum. It will be read in mathematics departments, organizations and committees where “diversity” is viewed as a bureaucratic imposition made on them by distant administrators who don’t understand research, even as their few women faculty often find themselves alienated and sidelined. That’s why I would like to add a few things.

First, there are many sound reasons for diversity that have nothing to do the article in question. (I will restrict this post to the benefits of diversity per se, independently of how that diversity was achieved. Affirmative action has its own reasons and will get its own post soon.) It should be common sense, not a mathematical theorem, that there are advantages in having a wider perspective and more than one problem-solving approach. Continue reading

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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”:

Continue reading

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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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