The Accidental Mathematician

Women in math, and the overhaul of the publishing system


If you have not yet heard of the Elsevier boycott, you have a lot of reading to catch up on. I’ll wait. I’m not likely to miss traditional commercial publishers when they’re gone, which could well happen within the next decade or so, especially if they and their agents keep asking for it. Think whatever you want about the Cost of Knowledge website, but open access journals have already gained a lot of ground, we have taken charge of the dissemination and advertising of our own research on the internet, and good luck to any journal that tries to stop authors from placing their articles on publicly available webpages and preprint servers.

The better question is: do we still need journals, be it commercial or any other kind, and if not then what will replace them? Among other possibilities, open web-based evaluation systems have been proposed.

This post suggests that a web-based evaluation system would be good for women, the idea being that “women don’t ask” and therefore they are less likely to, say, submit a paper to Annals. I see it exactly the other way around. I’ve talked about some aspects of it already, but not all, and in any case it never hurts to say something more than once, especially when you’re female.

This is not to say that I’m against discussion boards for mathematicians on the internet. I’ll be very happy to have them, as long as they’re not mandatory for everyone and don’t drive out those parts of the current system that function reasonably well. We need more options, not fewer. For instance, I rather like the idea of “evaluation boards” to which authors could submit arXiv papers for validation, without the boards ever pretending to “publish” or “disseminate” the papers. That, if done right, would preserve the advantages of the current system while losing most of its disadvantages. (And it should work just fine for women, I think.)

Now, the details. (This is another one of those long posts. Sorry.)

Proxies. It would be really, really nice if we just evaluated everyone based on the actual merit of their work:

To fix the academic publishing mess, researchers need to stop sending their work to barrier-based journals. And for that to happen, we need funding bodies and job-search committees to judge candidates on the quality of their work, not on which brand name it’s associated with.

Happily, there are signs of movement in this direction: for example, The Wellcome Trust says “it is the intrinsic merit of the work, and not the title of the journal in which an author’s work is published, that should be considered in making funding decisions.” We need more funding and hiring bodies to make such declarations.

If we all did that, there would never be any need ever to worry about either publishing or gender bias. We’d love to be judged purely on merit. Also, everyone should get a pony.

In actual reality, the closest that we come to that ideal is when we solicit expert opinions on the work of candidates for new appointments, promotion, tenure or professional awards. The very existence of such letters testifies to our inability to “just evaluate the intrinsic quality” of the work of someone not in out area of specialization. Still, this is an opportunity for the referees to provide an evaluation that goes beyond the journal titles: what is especially important about this paper, why this other one was a breakthrough, the overall arc of someone’s career and their impact on the development of the field.

Gender bias has been observed in the language used in letters of recommendation, suggesting that a reasonably good and objective proxy (such as a publication list with journal titles) comes closer to measuring the intrinsic merit of our work than an unstructured general evaluation:

In the scholars’ analysis of the words that appeared in the letters of recommendation, they found clear patterns of word use for women’s and men’s letters. Women were more likely to be described with words such as those cited above, as well as “nurturing,” “kind,” “agreeable” and “warm.” Men, in contrast, were much more likely to be described in words classified as “agentive” — words such as “assertive,” “confident,” “aggressive,” “ambitious,” “independent” and “daring.”

What the analysis showed is that letter writers didn’t need to use words like “feminine” to create female stereotypes — and that they did so, time and again, with women who had the same intellectual achievements as their male counterparts.

The study in question analyzed letters of reference of applicants for junior positions. I have not noticed this as much in letters for candidates for tenure, promotion and senior appointments. The candidate will normally have built a substantial body of work by then, and there is a strong expectation for the letters to elaborate on that in specific detail rather than just communicate the writer’s general impression of the candidate.

Let’s assume, then, that reference letters are fair and look at the practical aspects of using them for evaluation purposes.

In my experience, it takes a minimum of 3-4 hours to write a tenure or promotion letter. This can easily expand to a full day if I need to look at a few papers in some depth or check the references. A junior appointment typically requires 3-4 letters of reference. A promotion or tenure case requires 5 or 6, with additional regulations on how many of them must be arms length (no collaborators, no current or former colleagues). Fortunately, most of us don’t get promoted or go on the job market every year. If every faculty member needed to have several expert opinions written about them annually, for instance for the departmental merit pay rankings, we’d never stop writing those letters.

It’s not just the oft-cited “deans and administrators” who need proxies. It’s us. We can pledge all we want to judge everyone on merit. As long as we have to evaluate and rank researchers beyond our own areas of expertise, we’ll use proxies anyway. And there, I would have us use reasonably legitimate proxies (journal rankings, awards, grants, conference invitations) rather than institutional affiliation, race, gender, or my youngish looks. We could in fact use more proxies, not less, to capture those aspects of our careers (such as expository work) that currently tend to get less recognition.

Keeping it professional. The general principle is that women in mathematics benefit whenever there are clear rules and formal procedures for career advancement, and suffer setbacks in the absence of such regulations. The same goes, probably, for every underrepresented minority in every human endeavour where unconscious bias is present.

Equity is of course hard to legislate. Regulations can be ineffective, their interpretation may well depend on who’s doing the interpreting, and I’ve seen policies on diversity that did more damage than good. That said, having a formal procedure with well defined requirements is pretty much always better for women than trusting our colleagues’ gut feelings.

Unconscious bias is unconscious. That’s why we call it that. I have it, too, according to the Harvard implicit association test. No discriminatory intent need ever be involved; it’s just a little bit easier to imagine a leading mathematician as a man, and this often suffices to skew our impulsive, intuitive decisions. A formal procedure prompts us instead to think about specific issues, requirements and criteria. One might not think of a woman as the “natural” candidate for a position or award, but a point by point comparison (when you’re forced to make one) could say otherwise.

The cornerstone of the journal publishing system is the refereeing process. We all know that it’s slow, inefficient and often inaccurate. Suggestions have been made to divorce the evaluation and ranking of papers in terms of their novelty and significance from the painful dance steps of pointing out the typos, little errors, missing or inaccurate references. The former is mostly independent of the latter and can be done much faster, or so the argument would have us believe.

This is where I think the reformers are missing a point. It’s not necessarily the debugging that’s valuable. I’ve found and fixed more bugs in my own papers than the referees ever did. The main thing is, I like that the person who’s being asked to evaluate my paper is also being asked to actually read it. That’s the expectation that the editors have of the referees. Even if the referees only point out a few typos and misspellings, it still prompts them to engage with the content of the paper, or at least to give it a try. That’s much better than, say, summary judgement based on the author’s reputation, institutional affiliation or gender.

What if (for example) the arXiv had a discussion page for each paper? Well, I guess any arXiv user would be able to comment on any paper, regardless of whether they’ve read it or have the expertise to judge it. The boundaries between social and professional interactions might get a little bit blurred, for instance an author might get comments and reviews from colleagues who are part of his social network. (His, because a male mathematician is far more likely to have a substantial social network within the profession than a female one.) Let’s say that a male author posts a paper:

COMMENTER A: Very nice! I really like your Theorem 2 – this is something I would have expected, but when I tried to prove it a few years ago, it was not at all clear how to proceed.

COMMENTER B: I like Theorem 2, too. Do you think that Theorem 3 would extend to the setting of Reference 15? That would be really interesting, because [detailed explanation follows].

MALE AUTHOR: I’ve thought about that, but there’s an obstacle when you try to […].

COMMENTER A: But if that happens, then perhaps you could use Reference 8, which says that […]

and so on.

And if a female author posts a similar paper?

COMMENTER C (2 days later): I think your Theorem 2 is already known, for example it should be in Standard Reference 1.

FEMALE AUTHOR: No, Theorem 2 is new. The difference between Theorem 2 and the results in the existing literature, including Standard Reference 1 and References 9, 10 and 15, is that [details follow]. I explained this in the introduction.

COMMENTER D: Are you aware of Standard Reference 2?

FEMALE AUTHOR: Yes, and I’m citing it in the paper. Do you have any specific questions about it?

COMMENTER E (5 days later): But isn’t your Theorem 2 included in Standard Reference 1 already?

FEMALE AUTHOR: No, and I have already answered that question.

COMMENTER E: Jeebus, why are you getting so emotional about it? I’m only trying to help.

[goes to a different forum and complains about women overreacting to a friendly and polite suggestion]

Yes, really. It doesn’t necessarily happen every time, but it happens often enough. It can get worse. Take a look at the comments on this post about women in math. The author is a professional mathematician with experience in academia and finance who now works at a start-up. Her job as a data scientist involves analyzing statistical data, which makes her especially well qualified to critique typical studies on women in math that rely on statistical arguments. You’d think that her insights on the subject should be taken seriously. Instead, the conversation morphs quickly into an open thread veering from Wall Street to history to Superbowl. Of those commenters who try to keep it on track, only some actually engage with the specific points made in the article. Others never go past the usual stories of bad math teachers, mathematicians with greasy hair, girls liking dolls, and women “just” being different. “Of course girls are different.” “No, they’re not.” “They are, too.” Can we just move past that, please?

In case you were wondering: my blog has a fraction of a fraction of a percent of the readership of Naked Capitalism, but I’ve had comments like that, too, as well as personal attacks. (The worst ones didn’t make it past moderation. There have been some that I approved but perhaps shouldn’t have.) I cited the discussion on Naked Capitalism because it dispels another myth, namely that mass participation will somehow fix all the wrongs and that the best arguments will always float to the top thanks to internet magic.

Women “don’t ask”. More like, we have to pick our battles. This article reports on a study that gets at least one part of it:

Although it may well be true that women often hurt themselves by not trying to negotiate, this study found that women’s reluctance was based on an entirely reasonable and accurate view of how they were likely to be treated if they did. Both men and women were more likely to subtly penalize women who asked for more — the perception was that women who asked for more were “less nice”.

“What we found across all the studies is men were always less willing to work with a woman who had attempted to negotiate than with a woman who did not,” Bowles said. “They always preferred to work with a woman who stayed mum. But it made no difference to the men whether a guy had chosen to negotiate or not.”

Megan McArdle has more, and for once I actually agree with everything she says. I’d add that women are more likely to have to ask, we have to be more persistent in it, and we’re more likely to be told “no”.

It’s generally expected that men will want positions of responsibility, high profile work assignments, or (in academia) that they will want to lead large research groups. It’s also generally expected that women will not want that. We’re less committed, less ambitious, more predisposed to “nurturing” (whatever that means), more family-oriented, or some such. When a man asks for a prestigious work assignment, it’s normal. When a woman does the same, her colleagues might be a little bit disoriented at first before they can muster any other response, because the world they know does not work that way. I’ve seen this, many times over.

Before we say “no” to a man, we’re likely to stop for a moment and consider how it might affect our working relationship. Have I said “no” too many times already? What if I have to ask something of him sometime soon? But a woman should be… easier to work with. Expected to be “kind” and “agreeable”, remember? This, again, is what I have seen in my own experience, along with the surprised looks that a less agreeable woman often gets.

All this said, submitting a paper for publication to a journal is one situation where “asking” is perfectly normal and acceptable, regardless of gender. Men might be somewhat more likely to overshoot wildly, based on what I’ve seen in my experience with refereeing such papers, but such submissions get rejected anyway. This is one point in the process where I do not see much of a problem.

Now, when it comes to getting a fair treatment once the paper is submitted… but that takes us back again to the refereeing process.