Category Archives: academia

A seminar room of our own

Following my last two posts on women in mathematics and the internet, I was challenged to turn my crystal ball sideways and look at it again. I have talked about what I oppose (comments on the arXiv). I have talked about initiatives that are successful but labour-intensive and difficult to pull off (research conferences for women). Are these the only choices we have? Must the internet disadvantage women in math?

The fact is, the positive impact of the internet on my own career would be hard to overestimate. I had long-distance collaborations by email that kept me going when I was isolated at my institutions of employment. I made new mathematical contacts over the internet. I do not need the departmental coffee room to keep track of research developments or professional opportunities. I get my news from blogs, social media postings and online discussions.

It might be too much to claim that, without the internet, my isolation would have killed my research career. Remote communication existed long before computers, even if it was less efficient. It is also possible that, in other circumstances, I might have made different career choices. Yet, the particular career I did have was largely shaped by the internet, and, given that women are especially likely to be isolated within their institutions, it should be safe enough to say that my experience was not unique. It is easy to overlook this kind of impact when it’s all around us, uncontroversial and taken for granted. Still, it’s there, a vital lifeline to those of us who might otherwise have been left stranded with no way back in.

We should not forget career advice. Perhaps you’re negotiating a job offer. Articles and blog posts can tell you about the process: the timeline, the framing and manner of speech, the range of what might be expected. You can ask about your specific case in a trusted discussion forum. But when I first went on the market, I did not even know that one was supposed to negotiate at all. Somehow, I’m still here. I’m not always sure how that even happened. The withholding of information has always been a means of control, and the internet is the best antidote to it that we have.

We can, and should, go much further. In recent years, I have been making a conscious effort to avoid those environments that I consider suboptimal for me, and to spend more time instead in feminist spaces, many of them online, with people who share deeper ties with me than mere geography and profession. As my commitment and involvement there increased, as I learned and grew in these spaces, as I began to pay more attention to how they were optimized for growth and learning, I found that this also affected the ways I approach mathematics and especially mathematical collaborations. I found the advantage that has been missing from my mathematical career all along.

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Filed under academia, feminism, women in math

The mathematics of wheel reinvention

The first talk I attended at this year’s JMM in Seattle was Tim Gowers’s lecture on how the internet and mass communication might change mathematics. Tim started out by listing some of the more dysfunctional features of how we do mathematics today, then suggesting how they might be improved. I very much agree with that part, and I would like to mention a few points from it here.

Our basic and most important unit of discourse is a research article. This is a fairly large unit: effectively, we are required to have a new, interesting and significant research result before we are allowed to contribute anything at all. Any smaller contributions must be bundled and packaged into units of acceptable size, or else they go unacknowledged. A comparison that came to my mind was having to conduct all transactions in twenty-dollar bills. Whatever your product is, you would have to sell it for $20 or else give it away for free, with nothing in between. It should not be difficult to see why this would not be am ideal environment for doing business. We should have smaller bills in circulation. It should be possible to make smaller contributions–on a scale of, say, a substantive blog comment–and still have them count towards our professional standing.

Our culture is extremely competitive. We value beating others more than we value helping them. All that matters is getting “there” first and scooping everyone else on our way. Intermediate results are worth far less. Additionally, this prioritizes one specific type of contributions over all others, even in those cases where a different order of priorities might be more reasonable. A good expository paper might have more impact on its area of mathematics than a middling research article; and yet, expository work is rarely, if ever, taken seriously by funding agencies and tenure committees.

We spend a great amount of time and energy on reinventing the wheel. A mathematician working on a problem might start with relatively small reductions, observations and lemmas that, by themselves, do not qualify as journal-publishable units; if that effort is not successful, these smaller contributions are lost and the next person working on the same problem has to reprove them all over again. Moreover, information such as “this method didn’t work, and here’s why” might be very useful to that next person. If nothing else, a great deal of time might be saved that would otherwise be spent on trying out unsuccessful approaches. Yet, there is currently no system in place to circulate such information and reward those who provide it.

Consider also how we work and collaborate. We are all gifted in different ways: some are better at imagining new ideas, some at asking questions, some at turning informal sketches into rigorous proofs, some are walking encyclopedias of the relevant literature. Yet, we have decided that each of us has to be self-sufficient and do all of these things equally, instead of allowing people to focus on what they do best and forming collaborations based on complementary skills. (I’d add that such collaborations obviously exist, including in my own experience. We just pretend, at least in official paperwork, that this does not happen.)

I agree with all of this, and I’d love to see us abandon the old ways and adapt new ones. We are far too invested in forcing everyone to fit the same mould. In a profession we like to call creative, I’d love to see more diverse and varied career paths and modes of expression. I’d love to see the flow of information a little bit less hampered by our ambition and competitive instincts. Think of all the theorems we could prove if we allowed more people into the field and, instead of hampering their intellectual power, harnessed it to the full.

I do not believe, however, that such changes are inevitable, and I have very little faith that they will be forced by the internet and other means of mass communication. It takes more than technology to change the culture. The early evidence is not encouraging. The basic discourse unit is still the research paper, except that we now post these on the arXiv. Other types of research contributions are still not being counted towards career progress, even as the subject comes up in discussions over and over again. We are as competitive and territorial as ever. The Polymath projects came and went; one was successful, another one was somewhat productive, others fizzled out. They did attract more participants than conventional math collaborations, but they never became truly “massive” as originally envisioned. People still ask questions on Math Overflow, and sometimes they get useful answers, but it never became the universal communication and collaboration platform that some of its early enthusiasts seemed to imagine. Other, smaller discussion boards went mostly unnoticed. There’s not much actual research that gets done on public blogs or social networks.

At the end of the talk, someone raised the diversity point in a question. The participants in Polymaths, Math Overflow and other similar projects are even less diverse than the general population of research mathematicians. Is there a reason why women and minorities tend to stay away from such venues? What can mathematicians do to ensure that all of us feel welcome to participate? I do not feel that Tim really answered that. He said (and I hope that I’m summarizing it fairly) that all those changes are just going to happen, like it or not, because they bring a more efficient way of doing mathematics and nobody will want to give up on that. It is an unfortunate fact that some people feel less comfortable on the internet, but in the end we will all just have to get over it.

I would like to suggest a different answer.

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Filed under academia, mathematics: general

A response to Scott Aaronson

Scott Aaronson has been kind enough to respond on his blog to a couple of my tweets. I would like to thank him for his interest and engagement, and encourage everyone to take the time to read his entire post. There is also an excellent discussion in the comments.

Much of the discourse focuses on the use and misuse of jargon in social and physical sciences, and specifically on words such as “privilege,” “delegitimization,” or “disenfranchised.” I’ll address that in a moment, but let me first say that my main reason for objecting to the comment that started this discussion was the phrase “This isn’t quantum field theory” at the end. I understood this, in the context of that comment and the comment to which Aaronson was responding, and in light of the similarity to the well known phrase about rocket science, to imply that social sciences do not have the same complexity as quantum field theory and should not need a multilayered structure where concepts are defined, compared, then used to define further concepts, whereupon the procedure is repeated and iterated, so as to make advanced discourse possible and manageable. Aaronson has now explained that this would be an oversimplification of his position, and I’m glad to stand corrected.

I also would like to speak to some of the other points that he makes about language, feminism, social science, and clarity of writing. I’ll try not to repeat the arguments that his commenters have already made, perhaps better than I could have done it. Still, I have no desire to hide (as some have suggested) behind Twitter’s 140-character limit and avoid making my case at more length. And so, here we are. I will just quote the last two paragraphs from Aaronson’s post, but please do go to his site to read the rest:

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Filed under academia, feminism, writing

ICERM postdoctoral positions

I’m co-organizing the program Dimension and Dynamics at the Institute for Computational and Experimental Research in Mathematics┬áin Spring 2016. (Yes, this means that I hope to participate in the program. Details to follow when they are finalized.) ICERM has several postdoctoral positions associated with the program, one for the full academic year and four for the semester. Applications should be submitted via MathJobs. There is also funding for program visitors and workshop participants; the ICERM webpage has more details on that.

The program covers various aspects of dimension theory and dynamics, from ergodic theory to hyperbolic dynamics to computation. In my own research, I’ve been increasingly attracted to connections between dimension theory and dynamical systems on one hand, and harmonic analysis and additive combinatorics on the other. I look forward to doing more work in that direction in the next few years.

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Filed under mathematics: research, recruitment

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

Thanks, U of T Math

I’d like to thank the University of Toronto mathematics department (my doctoral alma mater) for the nice news item on its front page mentioning my ICM invitation. (It was posted a while ago, but I only saw it now.)

Being invited to speak at the ICM is often regarded as one of the highest honours that a mathematician can receive. It is a truly international recognition of the depth and ground breaking impact of their research.

UBC, meanwhile? Nope. It’s not that they don’t update their webpage, either – the page has been updated since the announcement.

This is of course the season for graduate and postdoctoral applications. Departments go out of their way to compete for the top candidates, and one part of it is showcasing the accomplishments of their faculty (to get the prospective students and postdocs interested in working with them) and their former postdocs and students (hey, this could be you). UBC Math has 3 session speakers at the 2014 ICM: Kai Behrend, Jun-cheng Wei, and myself. Additionally, Ben Green (who was a postdoc here for a year) is a plenary speaker. Is there some reason why UBC Math would not want to advertise it?

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Filed under academic politics

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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Filed under academic politics, feminism, women in math