Category Archives: women in math

A postscriptum on diversity and learning a language

“The man of the East cannot take Americans seriously because they have never undergone the experiences that teach men how relative their judgments and thinking habits are. Their resultant lack of imagination is appalling. Because they were born and raised in a given social order and in a given system of values, they believe that any other order must be “unnatural,” and that it cannot last because it is incompatible with human nature. But even they may one day know fire, hunger, and the sword.”

— Czesław Miłosz, The Captive Mind

I grew up in Europe, on the other side of the Iron Curtain. I’ve often had to try to explain my country of origin to those born and raised on this side of the Atlantic. Facts can be learned. It’s the lack of imagination that can be the greater problem. It’s disbelief that learning is in fact needed. It’s making assumptions instead of asking questions. It’s demanding a simple picture where the truth is complex. It’s presuming social or political homogeneity where the reality is ripe in conflict and discord. It’s failing, or perhaps not wanting, to understand just how far the circumstances of a different time and place might be from the here and now. and to accept that, were we placed there and then, we would likely behave the same way as those who were in fact so placed.

I’m neither a historian, nor a social scientist, nor willing to accept an unpaid second job. I can only do it in small steps, for my own pleasure. Even just for that, I needed a language that I could use. I needed examples and templates, in English, that I could try to work with. For a long time, I could not find what I wanted. English-language history books, for the most part, neither understood nor cared much about our life down on the ground. At the same time, I had too little in common with those Eastern European writers whose goal in writing was to distance themselves from their own background before witnesses who shared that background and, often, the distancing. That was not the argument I wanted to have. History has already passed judgement on communism and I’m satisfied enough with its verdict. I do, however, want to argue with those who view us with a mixture of pity and condescension, who consider the details of our history unimportant, who dismiss without looking the artistic and intellectual accomplishments of the Eastern Bloc as “couldn’t possibly have been any good,” who bounce the word “communism” here and there like a beach ball but have no idea how that system actually worked.

If you are reading this, you may have already seen my last post on the legacy of Communist and Soviet symbols in Poland:

I learned to give little thought to the walled-off parts of the city. The [Soviet] soldiers were easy to ignore in my daily life: they marched through our streets on their way to or from exercises, but otherwise they and their families stayed within their gated communities. I grew up mocking the unkempt buildings with newspapers in place of window curtains, but also reading children’s books from the Russian bookstore, which was open to the public; as a university student, I returned there for mathematical monographs unavailable in Polish. We resented that the Soviet food stores were well stocked even when ours were empty. Poles, especially children, would sometimes sneak in and shop there: a guard might look the other way, a Russian woman might allow a Polish kid to come in with her. I dreamed of travelling the world, becoming a scientist or an astronaut, but did not know and probably could not imagine what it might be like to live in a city without the Soviet army.

For comparison, here’s an article on how living with Confederate flags and statues in the south of the US was “like having a crazy family member.”

For those of us not born and bred below the Mason-Dixon, it can be really jarring to encounter symbols of the Old South sprinkled all over the place, as though by a casual hand. But given the ubiquity of these symbols, it makes sense that you’d kind of have to let them fade into the background, or you might never leave your house. […]

Everyone deserves to have local pride; it’s just that for a lot of black people in the South, getting to do that means having to swim in the racial messiness that comes with civic life there. The cultures of Southern black folks and Southern white folks have always been defined by a peculiar, complicated familiarity. That might explain why so many black folks have — by necessity — come to look on displays of the Confederate flag with something subtler than apoplexy, why Naima just rolled her eyes at the flags on her campus and moved on. Like a lot of black Southerners, she clearly had a lot more practice holding all of these ideas in her head at once than we Northerners do. The flag matters to her. Of course it matters. It’s just not the only thing that matters.

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Gender, conferences, conversations and confrontations

My departmental colleague Greg Martin has posted a paper entitled “Addressing the underrepresentation of women in mathematics conferences.” A comment and a bibliographical reference on page 9 of the text inform us that the paper is intended for publication in the Notices of the AMS. [Update, 3/20: I have been informed by the Notices of the AMS that they did not solicit the paper and will not publish it.] In the acknowledgement at the end, the author thanks “other friends and colleagues, too numerous to list here, for their encouragement and inspiration.” Given that we are employed in the same department, and that I often write here about gender, one might ask whether that large number included me. I would like to make it clear that it did not. Had anyone asked for my opinion, I would have discouraged it and, instead, encouraged the Notices to solicit a very different article.

I would have told them that such an article needs to be grounded in extensive firsthand knowledge of our practices related to conference organizing in mathematics. For that reason, it should be written by someone–better yet, by a group of authors–with broad experience in organizing conferences and an established record of promoting women and minorities in that context. It is not enough to point to the discrepancy between the gender proportions at the bottom and the top of the pyramid, and fall back on studies of gender bias in other fields for an explanation. It is necessary to diagnose the mechanisms that lead to it, addressing directly and specifically our actual practices. That requires experience and access to information including confidential and protected material. If a recommendation is made, it should first be tested in real-life conference organizing, and the results of such attempts should be analyzed. I would also insist that it should be written by a woman or a team of authors including women, and not only because women have direct knowledge of gender bias that men cannot have. Were the Notices to publish an article on the subject, it is likely that this would be suggested as a resource for prospective conference organizers; I know of at least one such attempt before the paper was even submitted. I do not believe that the article can have the necessary moral authority without a woman’s name on it.

Martin starts with, “In the context of mathematics conferences, the subject of gender is somewhat of a taboo. Certainly, bringing up the subject at all during a conference would be deemed outside the norm.” This is not true in my experience. I have organized many conferences. The NSF “broader impact” criteria include “broadening the participation of groups underrepresented in science, mathematics, engineering and technology,” and this carries disproportionate weight in mathematics as other ways of meeting these criteria are rarely available to research mathematicians. Mathematics institutes, in addition to being funded by the NSF and therefore accountable to it, often have their own diversity mandates. The organizers of conferences held under their auspices must report explicitly the number of women speakers and are often asked to increase that number. I have also attended many conferences. I have not found it uncommon, or outside the norm, for the participants to talk about gender-related issues in the space reserved for unstructured interactions. I have had many such conversations myself and have witnessed many more.

It is possible that Greg Martin’s experience has been different. He and I rarely attend the same conferences or talk to the same people. But these sentences point to a deeper issue, and not just with this article: the common belief that the gender problem in mathematics could be fixed if we only talked more about it. I disagree. I have said that I witnessed many conversations on gender at mathematics conferences. I did not say that they were all part of the solution. “Bringing up the subject” can mean complaining about the NSF diversity requirements, pointing out this woman or that one who was clearly only invited because of affirmative action, or explaining how we would all gladly invite more women if only they were a little bit better, even as we reassure everyone within hearing range that we totally believe in gender equality. We sure talk about gender. In terms of pure volume, we may be close to the saturation point already. It is not clear that this is helping.

There follows a long overview of literature on implicit bias and gender discrimination. None of these studies or findings are new to me. I’ve seen them on many feminist blogs and Twitter feeds, have linked to them and written about them here. Still, there is no shortage of people who are less familiar with the subject, and I will be glad if such a reading list is delivered to the mailbox of every mathematician in America and beyond. That is long overdue.

Unfortunately, the original research is problematic. It includes an analysis of the gender make-up of two conferences, the 2014 International Congress of Mathematicians in Seoul and the 2014 Joint Mathematics Meetings of the AMS and the MAA in Baltimore. For both meetings, Martin sets the target benchmark for female participation at 24%, based on the fact that at least 24% of doctoral degrees in mathematics at U.S. institutions were granted to women in each year since 1991.

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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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Filed under academia, feminism, mathematics: general, 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.


Filed under mathematics: people, women in math

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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