Review of x + y: A Mathematician's Manifesto for Rethinking Gender by

Book cover for x + y: A Mathematician's Manifesto for Rethinking Gender

At first I admit to some scepticism about the idea that we could use mathematics to rethink our conversations around gender. I was apprehensive because science, and even to some extent mathematics (or at least more applied subsets of its, like statistics) have been misused and abused in service of gender stereotype fallacies. Indeed, Eugenia Cheng points this out herself, and this, along with her careful and patient exposition of her topic, eventually won me over. X + y: A Mathematician’s Manifesto for Rethinking Gender is a good example of how an interdisciplinary approach to gender issues can often yield interesting new ideas. Cheng has clearly taken a lot of time to consider how to model and talk about disparities in our society when viewed through the lens of gender. Her conclusion? Sometimes when we think we’re talking about gender, we aren’t, and that creates too much confusion for us to make effective change.

I received this as an eARC from NetGalley and the publisher in exchange for a review.

Cheng’s central argument goes like this. We spend a lot of time observing differences between men and women in various aspects of society (professional life comes up a lot as an example). Some people hold that these differences are innate. Otherwise believe the differences are caused by environment—that is, structural inequities. And the truth, probably, is somewhere in between. But as Cheng points out, researching innate gender or sex-linked differences is very hard and every time someone purports to have sorted it, people come along and very easily poke holes in the findings. Similarly, we have this tendency to refer to certain behaviours as masculine or feminine, yet that association is not as useful as we think: there are plenty of women who behave in so-called masculine ways, and likewise there are many men who exhibit so-called feminine attributes.

As a side note, I have struggled with these terms myself lately as I transition. Technically anything I do, as a woman, is feminine by definition. Yet in everyday language, when I discuss how I dress, wearing makeup, etc., I talk about “expressing my femininity” and “being feminine.” I do this because I have an idea in my mind about how to express myself as a woman, but that idea is wrapped up in what we have been socialized to believe is feminine as a result of our society. For me, as a woman, wearing makeup is a feminizing act—but if a man wears makeup, is that feminine or feminizing? I would argue that context matters greatly here: some men put on makeup to feminize themselves (e.g., drag); others do it merely to hide a blemish or look better, just as many women do, and in that context I would argue that wearing makeup is in fact a masculine behaviour, if we are defining masculine as something done by men.

Hopefully you can see how this quickly becomes confusing! Cheng points this out and then tries to help us make sense of it by falling back on her experience as a mathematician. If you were hoping to escape any mathematics in this book, you’ll be disappointed, but you also don’t need to understand the mathematics Cheng references to understand her point. Basically, math is good at definitions. Math is also very good at contextual definitions: infinity means something different depending on which mathematical world you’ve chosen to play in. Finally, Cheng argues that her particular field, category theory, is of supreme usefulness in this discussion because it tries to discuss different items in terms of relationships rather than membership/attributes.

Now, in this particular case I don’t think Cheng is on to anything new. Plenty of people before and after Foucault have written about social justice from the point of view of power dynamics. If all she brought to x + y was some category theory, I don’t think this book would be very useful or successful. However, the discussion of category theory merely lays the ground work for Cheng’s main thesis. This goes back to what I discussed above about the equivocating around the terms masculine and feminine. Cheng proposes two new terms: ingressive and congressive. I’m not going to explain it as well as she does, but the gist goes like this: ingressive actions look inwards, centreing the individual; congressive actions work to bring the community together.

When I first heard these terms, I immediately thought, “is this just a rehashing of individualism versus collectivism? In some ways, perhaps, but I will credit Cheng with building atop such concepts. My next thought was, “this is a nice attempt, but won’t people just use ‘ingressive’ as a synonym for ‘masculine’ and ‘congressive’ as a synonym for ‘feminine’?” I didn’t think Cheng was intending it, but I can see how someone who isn’t being careful might view this as a one-to-one mapping. Cheng makes it clear that this isn’t the case, going so far as to outline her journey from acting ingressively to keep up as a research mathematician to realizing that she truly preferred to foster a congressive environment while teaching mathematics. Lest you think that this is merely semantic sophistry to chronicle her journey from trying to act like one of the guys to reclaiming her femininity, Cheng tries to help us understand that this is not, in her opinion, a matter of gender.

What these terms allow us to do, she argues, is discuss our ways of relating to one another without making stereotypical statements about gender. When someone jumps to ask a question that highlights their own expertise, that’s not “typical masculine behaviour”; it’s ingressive. People of all genders can do this. Likewise, if someone is trying to build consensus and help everyone get on to the same page, that’s not the empathetic behaviour of a woman—it’s congressive, and again, people of all genders can do this. So we can challenge the dominance of ingressivity in areas like academia in a way that removes the complication of talking about gender.

Great, right? I’m not sure.

I do like the new terminology, and I see the value in what Cheng proposes. I agree that sometimes our focus on gender can obscure the true power dynamics at work. Cheng demonstrates this aptly by referring to critiques of “lean in” feminism as trumpeted by Sheryl Sandberg. Cheng understands, and I agree with her, that merely putting women in positions of power within the current system is insufficient. It ignores intersectionality and the idea that there may be other marginalizations at work (race, class, etc.) that contribute to oppression or unequal power dynamics. Her solution is to restructure parts of our society to encourage congressivity, presumably because a congressive social order would allow people to participate more equitably regardless of their identities.

It’s a nice vision. I want to acknowledge that it’s not entirely pie in the sky, that Cheng takes her time to lay out how we can build a congressive future from the ground up. That’s more than some dreamers do in their books where they try to explain why their one neat trick for saving society is the one we should enact.

I hesitate to endorse this fully, however. Cheng tries hard to be congressive here, to encourage us to rethink our discussions around gender because she doesn’t want us to be “divisive.” She offers up competing definitions of feminism and slogans like “smash the patriarchy” as examples of how current thinking on gender polarizes the conversation and prevents true progress. I am sympathetic to this view. Yet I think there is an appropriate time and place for polarizing or divisive messages.

Let’s take transgender people, for example. (And I note that Cheng makes every effort to be inclusive here, using cis and trans appropriately and acknowledging that, for example, some trans men are capable of becoming pregnant.) We trans people are, just by existing in current society, polarizing. TERFs or gender-critical feminists or whatever you want to call them (I prefer the simple transphobe label) would really rather prefer we don’t exist at all. No amount of re-labeling or rethinking the gender conversation will change this fact, because at the end of the day, this is not about how trans people behave or even about how transphobes behave: it is, ultimately, an ideological divide. It is not one that can be argued away. For trans people to be safe and able to participate fully in society, we and our allies must fight, passionately and aggressively, against discrimination. I, personally, hope that some transphobic people, if they are exposed to more trans people and come to know us and understand that we are not a threat, will change their tune. In that respect I do not think this is an “us vs. them” situation. Nevertheless, this is an example of how some aspects of gender-linked discrimination cannot be rectified through new labels.

If you come to x + y expecting a totally revolutionary blueprint for how to think about gender, you might be disappointed. I came to this book with sceptical expectations, however, and I was pleasantly surprised. This book reminds me of Beyond Trans: Does Gender Matter?, in which trans man Heath Fogg Davis argues that there are many areas of society where gender doesn’t matter even though, at the moment, we insist it does. Cheng and Davis would probably agree on a lot of points, I think, as do I with both of them. I see value in critiquing the epistemology of gender, and I like that Cheng tries to apply the rigor and flexibility of mathematics. However, her arguments and ideas here can only take us so far. This is a great contribution to the ongoing meta-discussion.


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