On Women in Mathematics

a close reading of the usual take

Laments about the disparity in numbers between men and women in mathematics are so derivative and repetitive that responding to one is responding to them all, so I re-publish this piece on Twitter whenever one is making the rounds (as it is now, in May 2022, after Nature published the most recent iteration of this lament).

The November issue of the Notices of the American Mathematical Society contained a column by mathematician Ruth Haas commenting on the state of women in mathematics. This is a PDF link to her piece.

It’s the usual lament, with calls to “change the culture,” but for some reason I don’t fully grasp, I felt moved to reply via close reading.

So, here it is.

Her piece starts with a recitation of the women who’ve won major mathematical prizes and recognition in the last ten years, all of which are laudable and earned achievements. Her first paragraph ends with, “And yet overall the number of women in our field has stagnated.”

She goes on to list various statistics about the percentage of women in various aspects of mathematical achievement and academia, the most interesting of which is that women earn 39% of doctoral degrees in statistics and 26.8% of other doctoral degrees in mathematics.

Women earning a noticeably higher percentage of statistics doctoral degrees, in an era where “big data” and the ability to correctly interpret information from websites is one of the most lucrative job skills imaginable, strikes me as evidence that women are good at figuring out where their best employment prospects lie. This is not a bad thing.

Most of the other statistics are not hard to interpret in terms other than sexist discrimination. Women drop down or drop out of academia at a much higher rate than men. This should surprise no one who is honest. The half of the species that does 100% of the gestation, delivery, and breastfeeding of offspring, and by necessity (in the very early years) more than half of the hands-on childcare—that half dropping out, at higher rates than the other half, of an intense academic program that typically happens during the prime years for making offspring — imagine that! Whoever could have predicted such a shocking turn of events, huh? It’s almost like people CAN have it all, just usually not all at the same time, and we tend to figure that out when we try.

Next, she cites several programs that aim to prepare women for graduate school mathematics. This is a great idea, and if I ever change my mind and go to graduate school (I won’t) I will likely seek one out. Not because I expect to face discrimination, but because I would prefer a single-sex environment in which to learn some of the “hidden curriculum” of graduate school. These programs are denigrated for having failed to “move the needle,” which is implied to mean achieving parity — 50%.

Here is my question: why is 50% important? Why isn’t “everyone is free to choose what goals they want and work to achieve them” enough?

It's Not Us. It’s Them.

The next section calls for the inevitable “change in the culture,” with these words:

Moreover, it is not just the entry ticket that keeps many women away. It is the system we have in place at every stage. Graduate school in math is often a competitive culture with high stakes exams. A review process that is pervasive in mathematics pretends to be objective, but unconscious bias comes creeping in when we see a female name.

Really? Unconscious bias is being cited here? I would really love to see data indicating that any review process, anywhere, on a university campus has unconscious bias against female names. In my experience, the oppression narrative, with its assertion of the need for allies to be virtuous defenders against the patriarchy, is so strong that the null hypothesis should be the opposite: unconscious bias going in favor of female names. As an undergraduate mathematics major, I regularly wondered if any accolades or compliments I received were genuine or if they were pity bones being tossed to a girl so the professor or TA could reassure himself of his “ally” credentials.

When I used trigonometric substitution to solve a tricky integral or solved an exam problem with a clever proof by contrapositive when a proof by contradiction would’ve been more typical, I always wondered. Would the “good job” next to those problems still have been there if my handwriting were illegible male scrawl instead of girly near-calligraphy?

I didn’t wonder these things because of societal sexism. I wondered them because of a university culture that told me over and over again, explicitly and implicitly, that I was a victim of oppression.

That is my lived experience. Believe me, or don’t.

Actual Differences Between Men and Women

In the next section, she cites some of the studies citing differences between men and women. Men apply for jobs or promotions when they meet just 60% of the qualifications, while women tend to apply only if we meet 100% of the list qualificiations being sought. And competition is not as motivating to women as it is to men. On these topics, she says:

In mathematics, this means women often do not do the self-promotion needed to really get ahead. They are less likely to apply for promotions, or to submit their papers to the highest level journals. And, they may simply tire of an environment where competition is the norm.

These things are all true. I am not significantly motivated by competition. For example—I am presently working out a commitment to walk at least 10,000 steps a day. When I hit that number, I take a screenshot on my step-counting app and send the picture to two of my close friends, both women. They have both been wonderful, encouraging and supportive. It has helped me push through a couple of times when I was at 8900 or 9100 and ready for bed — to get on the treadmill and finish up so I could send my picture to my friends. If we were in some kind of competition, each sending the other a picture of a step total at a prescribed time, I think it would be a lot less motivating and enjoyable. I wouldn’t like feeling like I was trying to “win” so they could “lose.” I would likely have walked a lot less this autumn.

Most male friends I’ve known would feel the exact opposite. Sending pictures without the competitive aspect would not interest them.

And that’s ok. Men and women don’t have to be, think, look, or act the same. We just have to have the same rights and responsibilities — equality under the law and equality of opportunity to the fullest extent we mortals can arrange to make that happen.

What would changing the culture in mathematics look like with regard to competition? I don’t know, but I am reasonably sure that this is something that should be done by persuasion — by winning over mathematicians to belief in a new way of doing things and gaining their enthusiastic support. Not by creating a stultifying climate where the women feel like victims and the men, like their only choice is to be a sexist patriarchal monster or an ally, nothing in between.

Nor am I sure that a less competitive atmosphere would necessarily bring mathematics to 50% women. It might move the needle. But it might not. It might be that women who are high in competitiveness tend to be drawn to mathematics already and they would enjoy the atmosphere less without that, so it could easily be a wash.

She also cites a Washington Post article that argued that women who were elite mathematicians were less likely than men to believe they are elite mathematicians. We’ve all heard of Imposter Syndrome. I certainly have suffered from this. At my current job, a job where I do mathematical analysis, build and test predictive models, and otherwise use mathematics every day, I wondered for months if I was a diversity hire, brought on board so the men could feel virtuous about hiring a female mathematician. It was only being given sole responsibility for something that affected a ton of money and thousands of other people’s jobs that put those worries to rest.

The oppression narrative does not solve this problem; it perpetuates it.

She ends the piece by going over the statistics we have so far about the pandemic causing more women than men to drop out of the workforce. Again, this is unfortunate but hardly surprising. When a national emergency was declared that ended, in many parts of the country, the ability of parents to get childcare through schools, daycare, etc., anyone with the slightest familiarity with evolutionary theory could have predicted this.

Imagine a prophet of old putting this quandary to you:

There will be a great crisis, causing intense fear across the land. The land is occupied by a species of two sexes. One carries, births, and feeds the young from their bodies, a process facilitated by powerful bonding hormones. One plants the seed that results in the young’s creation but is otherwise only as involved as they choose to be. Indeed, in this species many young never know this parent, and many adults of this sex have children of whom they are wholly unaware.

Pop Quiz: when the crisis comes, which of these two sexes will more often end outside pursuits to nest at home to care for the young?

This isn’t hard, people. Fight evolution if you want. Call it oppression if it makes you happy, or happy in your misery. But you’re not going to change it entirely ever, and you’re not going to change it in any noticeable way until you change the material conditions.

What does that mean? Design, use reasoned argument to win support for, and implement a system that accommodates much greater flexibility in terms of hours and career progression. Do this for everyone across the board. Then people can make their own choices.

This study is a great place to start with the reasoned arguments. 10-30% of women and just over half of men are “work centered.” 40-80% of women and the remainder of men are “adaptives,” who want to work but want flexibility — to be able to prioritize their families and other parts of their lives without career setbacks. This study showed that advertising all jobs as flexible caused an increase in female applicants.

Flexibility and the ability to prioritize family as well as career will benefit everyone — men, women, and children.

Am I Saying The “Women In Math” Laments Are Wrong?

No. I’m saying that they’re boring, unnecessary, and largely counterproductive.

I believe that the stories of underrepresented minorities in various fields are important to tell, if only for people who grow up in very deprived circumstances, as I did. When I was a kid, the only educated woman I knew was the pastor’s wife, who went to Bible college. (My teachers were almost entirely moms from the church; I attended an unregulated church basement “school”).

It did help me see myself as a mathematician when I had a woman professor for the first time. That is an undeniable fact, and one I will never short shrift. (If you’re reading this, Dr. M, thanks.)

However, it is equally true that the constant drumbeat of “women in STEM are oppressed!!” was a big part of the reason why my first female mathematics professor made a difference for me just by her example. I was constantly being warned, cautioned, or outright terrified on this topic. There were weeks when I was offered more explicit support from the university for doing calculus with a vulva than for being deaf. (Think about that.)

Largely to stop the chorus in my head that had me terrified in response to their efforts on this topic, for a time, I obsessively researched this topic, which led to the many stories of women mathematicians I wrote as twitter threads and put on their own twitter account, Great Women of Mathematics. Those stories have inspired me and many others, and found their way into homeschooling lessons and classrooms in brick and mortar schools. All of that is valuable.

(Edit: I turned the GWOM account over to the publisher of the Daily Epsilon problem-a-day calendar in January 2022, as I no longer had time for the project.)

What I am saying here is not that the efforts to boost the voices of women mathematicians are or were bad, ill-intentioned, or ineffective.

I’m saying that this fight has been, largely, won. A female child with an interest in mathematics has no systemic barriers in front of her, and in fact has a lot more explicit support than a male child with the same interest. That female child is helped by learning about Katherine Johnson, Maryam Mirzakhani, Emmy Noether, or the other great women of mathematics. But she is even more helped by being given rigorous, challenging mathematics to do by adults who have faith in her ability to do it. She is helped most of all by honesty.

The most honest and helpful words any mathematician ever spoke to me came from a male PhD mathematician who now does other things with his life. He said: “Mathematics is hard. It’s very hard. Not many people can do it at a high level. Maybe you can. Maybe you can’t. I don’t know. You don’t know, either, and you won’t know unless you try very, very hard. Figure out what trying your very hardest looks like for you and then do it. Make sure that if you fail, it won’t be for lack of trying.”

Hearing and responding to the repetitive and boring lament about mathematics not being a 50/50 sex/gender split takes emotional, psychological, and cognitive energy that female would-be mathematicians need to try.

Tell girls (and boys too) about Katherine Johnson — but tell them about the ten years she took off when her kids were little. Tell them about Kathleen Ollerenshaw, another great woman of mathematics, who didn’t just take time off when her kids were little — she was deaf. Tell them about Emmy Noether.

Take advantage of the technology that makes flexible work arrangements easier than ever before.

Then let people make, and live with, their own choices. The way that fully functioning moral agents — adults capable of utilizing their freedom — must do.