"x + y" was an interesting read, but I'm not sure whether the author made a great argument.
The author argues for degendering discussions by not talking about typically female or male characteristics and instead talking about congressive and ingressive behavior to make the conversation less divisive and more inclusive. Overall, this is a good idea, but then the author continuously goes back to talking about women "emulating ingressive behaviour" thereby implying that ingressive = masculine and congressive = feminine behaviour which somewhat undermines her own argument.
Also, there were a lot of repetitions and general arguments. I think the book could have profited from giving more examples to illustrate the argument.

The blurb caught my attention but after that I lost my interest and didn't read this book. MAybe next time.

I enjoyed Chengs first book, “How to bake Pi”. This book was just as good. He aim of ending gender wars, ooof that's a toughy. This book really got me thinking, and debating with friends. I recommend this to others. Quite a thought provoking piece of writing.

I have to preface this review by urging everyone to pick up this book and read it and by saying that it has become one of my favourite non-fiction books to ever exist on this planet!!!!

Okay, now back to your normally scheduled review...
I started this book as an audiobook ARC, but the format didn't work for me and I'm glad I managed to catch an e-book copy. Can't wait to get my hands on the physical one as soon as possible, so I can adnotate and underline and note the f out of this amazing piece of knowledge.
Although it may surely seem like it, this book is not about feminism, nor how to evolve as a female or any stuff like that. It is about equality, about changing the environment, leaving gendered thinking behind and how to start assessing people based on their abilities rather than their ingrained qualities.
I loved every piece of information in this book, but I think I didn't really enjoy the first half of it so much as a consequence of having read it audibly. The second part, however, turned into me highlighting and taking notes all throughout it, hands why I can not wait to reread it and make the most of it physically.
Besides introducing me to the 2 new terms of ingressive and congressive, the book also provided support for change, with examples of how you can change the environment, rather than the person, so as to suit both ingressive and congressive people.
I don't really know what else I could say, other than that I really recommend this book for absolutely everyone, but mostly for people that currently feel like they aren't going to succeed in life. You can and you will, you just have to change your environment.

This book provides a different outlook of gender roles by looking at character traits independently of gender. Among other things, it shows how character traits are often unfairly and baselessly attached to gender and how statistics can be used to manipulate data to support or oppose a desired point. The author therefore encourages readers to separate behavior/character from gender (unless when absolutely necessary) by instead considering characteristics in the context of being ingressive (All about self) or congressive (collaborative, team work). Cheng continues by furnishing readers with several real life examples of congressive and ingressive behaviors and strongly nudges readers to embrace congressivity and neutralize ingressivity.

While this book was thought-provoking, I was rather underwhelmed by the writing style and struggled to read through to the end. I often felt like I was reading a research paper and I simply was not engaged. However, I finished reading with an awareness of the spaces that I occupy in my daily life and the type of behavior and characteristics that are fostered and encouraged there, and with a desire to embrace congressivity and neutralize ingressive behavior. I appreciated Cheng's use of real life examples throughout this book, to which, I am sure, many people who occupy spaces specifically in academia can relate. I do feel that, intentionally or not, this book equated ingressive to bad and congressive to good without consideration for people who might be naturally ingressive or ways/situations in which ingressive behaviors may be appropriate or even beneficial. Still, I completed this book with new insight and a lot to contemplate on.

Disclaimer: This is not the type of book I would normally read. I’ve not been into gender (more on that below) and I don’t think of mathematics if I can help it. But still, this sounded interesting enough, and it was available on Netgalley.

So, it did actually turn out to be interesting, although, what the author speaks of is common sense, and she doesn’t actually redefine gender per se, but people along non-gendered lines. As in, women and men are recategorized into congressive (collaborative, mellow) and ingressive (me, me, me) people. Now if one sounds more feminine than the other that’s on you. She contends that being congressive is more beneficial to the society on the whole, because really the only thing ingressivity benefits is the person themselves. Any accidental boons are accidental.

I can’t argue with that. But there are a few times in the book that I felt that congressive and ingressive were themselves gendered, and it was assumed that women who are currently successful at their careers, especially in male-dominated ones, happen to be so because they have successfully learned to emulate male qualities. As in, they’re aggressive and pushy, but they are so because they’ve learned to do this. This isn’t a great assumption - it is as false as assuming that all men are aggressive and pushy.

I also couldn’t help but wonder if it was just replacing one discrimination with another. What about naturally ingressive people? Do they fit in nowhere? And if they do try and fit in, but are still more pushy and want to win more than the collaborative people in their group, do they take over because congressives are less likely to fight over this? In any case, are ‘no girls in stem’ a western thing? Because, I studied to be an engineer in a class that was equal parts girls and guys, and this was true across the board. Some branches of engineering didn’t have the same cutoff, true, but it had started to even out more by the time I graduated. I faced discrimination later, when I was employed, but never when I was still studying. This is probably seen through the lens of my own minor experience, but it true that a lot of girls in India are engineers or doctors (who end up facing a bunch of discrimination, don’t get me wrong, it’s not utopia, but academics itself is slightly decoupled from gender).

But this was still an interesting read that made me think along lines I wouldn’t normally have.

Thanks to Netgalley and the publisher for the ARC .

I’m really sorry but I did not finish this one at 12% in. I struggled to get into it. The writing style felt like an academic paper and it wasn’t an enjoyable read for me. I like nonfiction but this one wasn’t for me. The start of the book was mostly describing what the book was about the describe and I wanted it to go straight in. As a math teacher, I knew most of the mathematic foundation but I understand it was to make it accessible to all readers. I found that part very slow and boring personally. Overall, the style was too much like an academic paper for me and not a leisurely informative read.

Redefining Our Categories
Kenneth Silber
Mathematician Eugenia Cheng tackles gender.

Eugenia Cheng is a mathematician, Scientist in Residence at the School of the Art Institute of Chicago, and author of four books. I reviewed her third, The Art of Logic in an Illogical World, two years ago, finding it a valuable effort “to explain the tools of logic as used by mathematicians and demonstrate their relevance in everyday life—and particularly in helping think through divisive political and social issues.”

Whereas Cheng’s first two books, How to Bake Pi and Beyond Infinity, hewed more closely to math, her new work, X + Y: A Mathematician’s Manifesto for Rethinking Gender (Basic Books), continues her more recent delving into the sociopolitical, in this case focusing on fraught issues of men and women in the workplace and beyond. Her approach is shaped by her research focus, category theory, a field that’s spread from pure math to computer science, physics and other areas, burgeoning in importance while remaining little-known to the public.

Category theory is highly abstract, the “mathematics of mathematics,” as Cheng called it in How to Bake Pi. Relying on diagrams filled with arrows, category theory emphasizes relationships among abstract elements. By contrast, set theory, familiar from K-12 education, puts items into collections based on their characteristics. Both theories are “foundational,” in that they can be used as frameworks for organizing and understanding diverse mathematical concepts.

Inspired by the category-theory approach, Cheng looks for a more fluid, context-oriented way of thinking about gender, instead of seeing male and female as clear-cut in their attributes. This translates into skepticism about gender differences being innate and unchanging, or that such differences can justify unequal job statuses and incomes. At the same time, Cheng dislikes “leaning in,” where women seek success by adopting presumed male traits; she recalls with distaste a female executive who immediately bragged about her $5 billion budget.

To reframe discussion of gender issues, Cheng introduces new terms: “ingressive” and “congressive.” Etymologically, the former is for “going into”; the latter for “bringing together.” She defines ingressive thus: “focusing on oneself over society and community, imposing on people more than taking others into account, emphasizing independence and individualism, more competitive and adversarial than collaborative, tending toward selective or single-track thought processes.” Congressive, by contrast: “focusing on society and community over self, taking others into account more than imposing on them, emphasizing interdependence and interconnectedness, more collaborative and cooperative than competitive, tending toward circumspect thought processes.”

Upon reading the above, I came up with other terms that would convey similar meaning, such as “autogressive” and “allogressive.” But since it’s Cheng’s book, which includes a section about “mansplaining,” I’ll adopt her terminology. Importantly, she acknowledges the two tendencies are “not a clean dichotomy,” since people behave in ways that mix them. She presents a diagram with “ingressive” and “congressive” as perpendicular arrows, such that behavior can fall anywhere in between.

Such terminology enables focusing more on behavior than on gender; and recognizing that correlations of behavior with gender have numerous exceptions and change over time. Cheng writes that “men are currently more ingressive” and that “society favors ingressive behavior, with the result that men are more successful and powerful.” Such behavior is broadly harmful, she contends, and so the goal becomes getting individuals and institutions to be more congressive, not “separating men from women and erasing non-binary people in the process.”

X + Y offers various suggestions for reforms. Cheng would make classrooms more collaborative; in math, that would include more “high ceiling, low floor” questions that set few limits on who can contribute or how much they can learn. She’d like to see academic research shared freely, with grants and prizes spread broadly and peer-reviewed journals going by the wayside. She wants workplaces to link promotions to mentorship. She’d like elections that have ranked voting among multiple candidates, rather than a zero-sum contest between the top two.

I don’t share Cheng’s negativity toward competition, at least in degree; my karate school, among other organizations I’m familiar with, adeptly combines competition with collegiality. And I was nonplussed by her seeming amenability to “contemporary definitions of sexism” where “it only counts if it’s by the group that holds power (men) against the group that doesn’t (women).” It’s apparent to me the arrow can go both ways. Yet Cheng also criticizes the “oppression olympics,” discussions where people compete to be the most downtrodden.

As in recent contretemps about 2 + 2 = 5, any effort to employ math in issues that fall under the rubric of “social justice” is bound to cause controversy, as irrelevant or potentially undermining of standards. I suspect X + Y will have some detractors in that regard, as was the case with Cheng’s The Art of Logic. However, if politics can reshape math, math can also reshape politics, injecting rigor and precision where previously was only ideology and rhetoric. Cheng’s two latest books do an admirable job of moving contentious debates in that beneficial direction.

—Kenneth Silber is author of In DeWitt’s Footsteps: Seeing History on the Erie Canal and is on Twitter: @kennethsilber

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.

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.

Thank you to NetGalley and Basic Books for a chance to read an early copy of this book, finishing it up just in time for its release this coming Tuesday! It is a great conversation starter that puts forward some very thought-provoking arguments.

The blurb makes it sound pretty dry -- blah blah blah category theory blah blah blah dimensionality blah blah blah. But I actually found it very readable! Essentially she is saying is that we should move away from a "set theory" way of thinking and examining intrinsic traits -- what do ALL women or ALL men have in common (to say nothing of nonbinary or gender-fluid people) and toward a "category theory" approach of thinking about relationships, how do certain character traits group humans together -- these may have cultural association or statistically observed frequency in one gender or another, but are not exclusive to a certain gender. Specifically, what do people who prize the individual over community have in common, and what do people who prize community over the individual have in common. This gets away from "not all men are competitive," "not all women are shy about speaking up in class," and other arguments about innate vs socialized gender, into a more productive way of thinking about where independence and competition are useful vs where collaboration and cooperative behavior are useful, and realizing how power structures currently favor competition and winner take all approaches, and will continue to reward people who take on those behaviors.

This idea of community vs self, and her argument that being cooperative is ultimately better for society is....pretty relevant to a global pandemic. The book was written before all that happened, though she does have a preface and postscript from March, pointing out the early example of that basketball guy making fun of COVID and touching all the microphones...then turned out to have COVID and got the NBA shut down. And, well, I think we all can see how the mask debate applies.

Many of her examples are in education, as she is a math professor, and she makes a convincing argument that fostering appreciation and curiosity in a field rather than emphasizing memorize and regurgitate yes-or-no answers will not only help make it more accessible to everyone as part of a school curriculum, it will encourage a wider range of people and personalities to become experts in that field, and thus help alleviate existing imbalances, gender or otherwise.

I would say that this book does get a little repetitive. However, part of this is because I JUST read another book by her, THE ART OF LOGICAL THINKING IN AN ILLOGICAL WORLD [my tl;dr there is it's a great and accessible introduction to logic in its basic examples, but the political examples she uses are very much "here is why conservatives are illogical and wrong" and I'd already tired of seeing these arguments play out on social media dozens of times], and some of the content is still the same. Also, the book takes a while to build up to its main argument. She talks about her idea for new vocabulary to move away from gender for the whole first half of the book, but doesn't introduce the terms until the end of chapter 4 of 7. I found that frustrating, but I already think and read about gender a lot, so I did not need very much convincing, while working through moving away from arguments about what feminism means or whether women can mansplain might be useful for other readers.

I know a $28 hardcover is pretty steep these days but this book was really cool and offers a very productive and timely argument for moving away from gender-based disagreements toward thinking about character traits and reshaping the structures of our world bit by bit to make it a more inclusive place. I'm really looking forward to talking with other people about this book!

Thank you to NetGalley for the opportunity to read this book in exchange for an honest review!
I’d like to start by saying I was only able to read this book through the NetGalley app, as before it all appeared white and without text.
This is an interesting approach to gender although I must admit it wasn’t my favorite and not my entire cup of tea.

Using mathematics, and specifically Category theory, the author explores gender and inequality. It is a really unique lens to explore this much-researched topic and although it gets a bit dry and essay-ish, it is an interesting thought provoker!

Thanks to the publisher and NetGalley for providing me with an advanced reader copy in exchange for an honest review.

I love this approach to gender- and what a better way to do this than to use one of the all time subject that most women have been put down for. Oh, how I wish I could buy this book and send it as presents to those teachers who kept telling me that boys are better at math than girls!
It took me a while to read this book, because it's not the kind you read like fiction- or a thriller, turning page after page, but rather one that you will enjoy as it unpacks gender and the approach feminism has taken over the years.
Thanks Netgalley for the eARC.

So, this is a funny review to write. Because I really enjoyed what the book tried to do, playing with mathematics and gender roles. However, I was not the target audience for it.
It is a more niche book, which is fine. But I feel like, to many, it can be a bit hard to get through.

I absolutely loved this book, which offers a perspective on gender inequality and identity from the perspective of mathematics and math principals. The author's main premise is that a lot of what we see as gender inequality comes from a flawed idea of feminism, which assumes that women should act more like men to active equality, or that women can, and should, do things that men do to empower themselves. This, however, assumes that a direct correlation can be made between character/personality traits and gender when often society just values socially constructed masculine traits and qualities, which then leads to men having more social and economic advantages. She provides an alternative model that challenges this modern feminist framework.

The only qualm I have with this book is that I wish her proposed model had as much data behind it as the premise and lead up did. Overall great read though and very thought-provoking for anyone in the gender and sexuality studies fields.