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x + y: A Mathematician's Manifesto for Rethinking Gender
Shortlisted for the 2021 Phi Beta Kappa Book Award for ScienceOne of NPR's Best Books of 2020One of the Most Fascinating Books WIRED Read in 2020A brilliant mathematician examines the complexity of gender and society and forges a path out of inequality. Why are men in charge? After years in the male-dominated field of mathematics and in the female-dominated field of art, Eugenia Cheng has heard the question many times. In x + y, Cheng argues that her mathematical specialty -- category theory -- reveals why. Category theory deals more with context, relationships, and nuanced versions of equality than with intrinsic characteristics. Category theory also emphasizes much as a cube can cast a square or diamond shadow, depending on your perspective, so too do gender politics appear to change with how we examine them. Because society often rewards traits that it associates with males, such as competitiveness, we treat the problems those traits can create as male. But putting competitive women in charge will leave many unjust relationships in place. If we want real change, we need to transform the contexts in which we all exist, and not simply who we think we are. Praise for Eugenia Cheng "[Eugenia Cheng's] tone is clear, clever and friendly . . . she is rigorous and insightful. . . . [She is] a lucid and nimble expositor."--- Alex Bellos, New York Times Book Review"Dr. Cheng . . . has a knack for brushing aside conventions and edicts, like so many pie crumbs from a cutting board."--- Natalie Angier, New York Times
268 pages, Kindle Edition
First published July 16, 2020
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About the author
Eugenia Cheng
17 books345 followersEugenia Cheng is a mathematician, pianist, and lecturer. She is passionate about ridding the world of math-phobia. Eugenia’s first book, How to Bake Pi, has been an international success. Molly’s Mathematical Adventure is her first children's book.
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August 24, 2020
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.
Originally posted on Kara.Reviews, where you can easily browse all my reviews and subscribe to my newsletter.
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.
Originally posted on Kara.Reviews, where you can easily browse all my reviews and subscribe to my newsletter.
July 11, 2023
I was incredibly frustrated with this book. I was hoping for something that would give me objective, mathematical ammunition to discuss the subjectivity of gender, critique the gender binary, go into the nuance of gender versus sex- I was instead given a vocabulary lesson in new two words that aren’t given direct and full-fledged definitions.
The author creates two new vocabulary words that she prescribes as the cure to gender inequality. “Congressive” and “ingressive” are established as the central thesis of addressing societal strife, but I spent the book lacking a concrete concept for each that didn’t just align with the much simpler, already existing dichotomy of either masculine/feminine or individualistic/collective.
The author states that these new words will create a blank slate for peoples’ understanding of gender and open their minds to an unbiased discussion of gender expectations, but fails to recognize that these words align too closely with already existing, loaded concepts. We do not exist in a vacuum and introducing these new concepts will not suddenly erase the bias already present in those learning the new words or open them up to new ideas about eliminating sexism.
It is fine to create new words to discuss sexism and gender, but focusing on finding new words to erase the context and assumptions of those that would otherwise doubt your argument is essentially tone policing. This is catering to those that do not want to listen to the argument while not even proving that doing so would even be beneficial to the cause overall. To me, this is the most glaring flaw in the entire argument. Why should these new words actually convince people of the necessity to change when they mean things that everyone already associates with gender or political ideology?
The author creates two new vocabulary words that she prescribes as the cure to gender inequality. “Congressive” and “ingressive” are established as the central thesis of addressing societal strife, but I spent the book lacking a concrete concept for each that didn’t just align with the much simpler, already existing dichotomy of either masculine/feminine or individualistic/collective.
The author states that these new words will create a blank slate for peoples’ understanding of gender and open their minds to an unbiased discussion of gender expectations, but fails to recognize that these words align too closely with already existing, loaded concepts. We do not exist in a vacuum and introducing these new concepts will not suddenly erase the bias already present in those learning the new words or open them up to new ideas about eliminating sexism.
It is fine to create new words to discuss sexism and gender, but focusing on finding new words to erase the context and assumptions of those that would otherwise doubt your argument is essentially tone policing. This is catering to those that do not want to listen to the argument while not even proving that doing so would even be beneficial to the cause overall. To me, this is the most glaring flaw in the entire argument. Why should these new words actually convince people of the necessity to change when they mean things that everyone already associates with gender or political ideology?
August 5, 2020
An interesting take on gender disparities in society that attempts to solve the problem by completely sidestepping it: gender is correlated with traits that are valued in current society (and that society is set up to reward), thinking those traits are natural or perfectly related to gender (or to skills like math that are valued!) is a logical mistake, and it makes more sense to make society equitable for people with different levels of these traits. As another reviewer put it "Cheng is not arguing that all people are the same with the same abilities but takes issue with the division of character traits into “masculine” and “feminine”. She proposes instead a spectrum of character using two neologisms: “ingressive” (“going into things”) and “congressive” (“bringing things together”)."
I think Cheng has some work to do to prove that these traits are the important ones and there is a LOT of work to be done to make society value both congressive skills as much as ingressive (Cheng sketches out some of these in the last part of the book, but I think going into these suggestions could have been a full book by themselves).
Cheng is very good at explaining mathematical concepts and how they may relate to perceptions of differences between categories. The book is also a nice primer on logical thinking. On the whole an interesting, breezy read.
I think Cheng has some work to do to prove that these traits are the important ones and there is a LOT of work to be done to make society value both congressive skills as much as ingressive (Cheng sketches out some of these in the last part of the book, but I think going into these suggestions could have been a full book by themselves).
Cheng is very good at explaining mathematical concepts and how they may relate to perceptions of differences between categories. The book is also a nice primer on logical thinking. On the whole an interesting, breezy read.
June 2, 2020
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.
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.
February 16, 2021
I came across this book in a bookstore following an evening of my bloviating about how math and “absolute truths” are inherently sexist. It was an absurd argument that I only somewhat believed but followed out to its logical ending for the sake of argument (I know, Cheng would HATE this). So when I stumbled across this book the next day I simply had to buy it— it was incredibly topical and two of my greatest academic interests are math and gender studies. You can imagine my disappointment when this self-proclaimed “mathematician’s manifesto for rethinking gender” did not rethink gender in the slightest and used math metaphorically rather than as its methodology. I do not think that one can “rethink gender” by not thinking about it at all. And to present gender as binary (VERY occasionally acknowledging it is not but for the most part using language of “male vs female,”— even the cover and title present 2 opposing genders) is to completely fail in an analysis of gender.
Cheng’s thesis was almost entirely about how collaboration is better than competition and ignores the topic of gender because to acknowledge it would be “divisive.” I am all for collaboration and mitigating the competitive definition of success in our society but I do think that necessitates a class analysis and discussion of capitalism itself— which this book fails to provide. One of Cheng’s 7 chapters is entirely about “leaning out” and why Sheryl Sandberg’s capitalist conception of feminism cannot succeed. Yet Cheng still conceives of success as female CEOs and presidents— she just contends that we should achieve those positions through collaboration. Even in Cheng’s example of collaborative education in Finland— which she presents as an ideal method of teaching— she acknowledges that sexism and gender imbalances remain. Cheng herself shows that teaching children to be more collaborative cannot itself remedy patriarchy. Yet this is her broad solution to “rethinking gender.”
In her final chapter, she brings up “congressivity” as a solution to American incarceration. If we simply collaborate more, people won’t commit crimes and then won’t have to go to prison!! This is where she completely lost me. Cheng’s idea of collaboration cannot stand on its own and simply educating people to collaborate more will not solve the “ingressive” or competitive elements inherent in a capitalist society. On the next page, she discusses how European colonization of America was an instance in which society went, Cheng “would say: from congressive to ingressive.” I’m sorry but to use made up words to discuss violent colonization and genocide feels incredibly offensive. We have words to describe oppression— words which Cheng sprinkles throughout the book, but then rejects due to their “divisive nature.” If we view the problems with our society, as Cheng does, simply as the divide between collaboration and competition, we fail to recognize actual oppressive forces at play and then will never be able to remedy them.
Aside from my pretty clear problems with the central arguments of this book, I also did not like the way it was written. The overuse of metaphor made it hard to remember what the actual point she was making was and as I got later in the book, sentences started to feel like exact repetitions of sentences I had read earlier. The concept of this book was very intriguing but the execution was disappointingly subpar.
Cheng’s thesis was almost entirely about how collaboration is better than competition and ignores the topic of gender because to acknowledge it would be “divisive.” I am all for collaboration and mitigating the competitive definition of success in our society but I do think that necessitates a class analysis and discussion of capitalism itself— which this book fails to provide. One of Cheng’s 7 chapters is entirely about “leaning out” and why Sheryl Sandberg’s capitalist conception of feminism cannot succeed. Yet Cheng still conceives of success as female CEOs and presidents— she just contends that we should achieve those positions through collaboration. Even in Cheng’s example of collaborative education in Finland— which she presents as an ideal method of teaching— she acknowledges that sexism and gender imbalances remain. Cheng herself shows that teaching children to be more collaborative cannot itself remedy patriarchy. Yet this is her broad solution to “rethinking gender.”
In her final chapter, she brings up “congressivity” as a solution to American incarceration. If we simply collaborate more, people won’t commit crimes and then won’t have to go to prison!! This is where she completely lost me. Cheng’s idea of collaboration cannot stand on its own and simply educating people to collaborate more will not solve the “ingressive” or competitive elements inherent in a capitalist society. On the next page, she discusses how European colonization of America was an instance in which society went, Cheng “would say: from congressive to ingressive.” I’m sorry but to use made up words to discuss violent colonization and genocide feels incredibly offensive. We have words to describe oppression— words which Cheng sprinkles throughout the book, but then rejects due to their “divisive nature.” If we view the problems with our society, as Cheng does, simply as the divide between collaboration and competition, we fail to recognize actual oppressive forces at play and then will never be able to remedy them.
Aside from my pretty clear problems with the central arguments of this book, I also did not like the way it was written. The overuse of metaphor made it hard to remember what the actual point she was making was and as I got later in the book, sentences started to feel like exact repetitions of sentences I had read earlier. The concept of this book was very intriguing but the execution was disappointingly subpar.
August 29, 2022
If you really want to make justice, then start with the truth.
September 6, 2020
I thought this book was ok - I am empathetic to the concepts "congressive" and "ingressive," although given how central they are to the book, they are rather vaguely defined and very rough around the edges. Even though they aren't meant to be opposites of one another, they are often used in a sort of "congressive good, ingressive bad" way. I feel like there are some assumptions about gender disparities in this book that I think are totally believable, but still I would've liked some more academic backing for them. That said, it was a nice read and I'll definitely try to implement the last part of the book, about how to be more congressive, in my personal life.
February 21, 2024
Nearly all PhD programs in mathematics in the United States begin by requiring students to pass some set of preliminary or qualifying exams to demonstrate they have a knowledge of the fundamental subjects of mathematics. They usually must be completed in the first two years of the PhD program, and at some schools they purposely serve as a tool to "weed out." students.
As someone currently in a first year math PhD program, this is my life right now. Literally the only thing that matters right now is passing these exams. Thankfully, I am at a school where I have multiple chances to pass these exams, and which do not construct them to purposely remove students from the program. However, I have still found it to be an overwhelming culture shock. And in x+y, Eugenia Cheng has given me the language to express what I have been trying to for months.
Coming from a small, liberal arts college, I was struggling with the mental shift that has been required for me to be successful on these exams. I have learned that, essentially, the way to pass the exams is to memorize as many things as possible. You can have a perfectly fine fundamental understanding of the concepts, but because you are only asked to solve problems which you have seen before, literally the only way to pass these exams is to have the mental recall of solutions which you never would have come up with on your own. There are little to no problems where you "follow your nose" to the answer by applying the fundamentals. Instead, you just have to memorize all the critical proofs.
This has irked me because personally, I do not consider mental recall to be a huge part of being a mathematician. Yes, you should have an understanding of the basics, especially in your chosen field, because you don't want to always be looking things up. You want to just know things. But in my experience, the knowing things comes from using them over and over, not from purposely memorizing them. And in the end, you can always look things up. It also bothers me because I feel the skills that my undergraduate education focused on - collaborative mathematics, how to write proofs well, how to present math to experts and non-experts, and, most importantly for actual math research, problem solving - don't matter in this system at all.
Cheng explains that the educational methods which focus on tests and memorization are ingressive, a term she coins to refer to aggressive, competitive, and self-centered behavior, while the undergraduate education I received was ingressive, a term to describe behavior which is more collaborative and community-focused.
The main thesis of x+y is that we have been mapping character onto gender, and in order to actually fix gender inequality, we need to quit thinking about gender and think on a different dimension: that of ingressive and congressive character.
As a gender expansive person, I was initially concerned Cheng would simply be replacing one false binary with another. And while she does hedge that everything is a spectrum and nothing is binary, it still felt at times that she was treating it in that fashion. However, I can't deny that the idea of thinking on a completely different dimension from gender is appealing. And Cheng is unflinchingly inclusive, repeatedly bringing trans and nonbinary people into her discussions of gender, and she demonstrates a large amount of intersectionality, speaking at length how being a person of color can affect relationships with gender, and the discrimination people face.
And while I have my qualms about the book (Cheng seems to say that we need to convert all the ingressive things in our society to congressive things, which is a point I am skeptical of as someone who feels that there must be a balance to things) I cannot deny that this language has been incredibly useful. I would genuinely love for the terms ingressive and congressive to catch on (maybe in the math community at least they will?) because I find them to be an illuminating and productive way to describe the world around me. I would definitely recommend this book to anyone, math nerd or otherwise, who is interested in looking at the world through a new lens. Or, should I say, in a different dimension.
As someone currently in a first year math PhD program, this is my life right now. Literally the only thing that matters right now is passing these exams. Thankfully, I am at a school where I have multiple chances to pass these exams, and which do not construct them to purposely remove students from the program. However, I have still found it to be an overwhelming culture shock. And in x+y, Eugenia Cheng has given me the language to express what I have been trying to for months.
Coming from a small, liberal arts college, I was struggling with the mental shift that has been required for me to be successful on these exams. I have learned that, essentially, the way to pass the exams is to memorize as many things as possible. You can have a perfectly fine fundamental understanding of the concepts, but because you are only asked to solve problems which you have seen before, literally the only way to pass these exams is to have the mental recall of solutions which you never would have come up with on your own. There are little to no problems where you "follow your nose" to the answer by applying the fundamentals. Instead, you just have to memorize all the critical proofs.
This has irked me because personally, I do not consider mental recall to be a huge part of being a mathematician. Yes, you should have an understanding of the basics, especially in your chosen field, because you don't want to always be looking things up. You want to just know things. But in my experience, the knowing things comes from using them over and over, not from purposely memorizing them. And in the end, you can always look things up. It also bothers me because I feel the skills that my undergraduate education focused on - collaborative mathematics, how to write proofs well, how to present math to experts and non-experts, and, most importantly for actual math research, problem solving - don't matter in this system at all.
Cheng explains that the educational methods which focus on tests and memorization are ingressive, a term she coins to refer to aggressive, competitive, and self-centered behavior, while the undergraduate education I received was ingressive, a term to describe behavior which is more collaborative and community-focused.
The main thesis of x+y is that we have been mapping character onto gender, and in order to actually fix gender inequality, we need to quit thinking about gender and think on a different dimension: that of ingressive and congressive character.
As a gender expansive person, I was initially concerned Cheng would simply be replacing one false binary with another. And while she does hedge that everything is a spectrum and nothing is binary, it still felt at times that she was treating it in that fashion. However, I can't deny that the idea of thinking on a completely different dimension from gender is appealing. And Cheng is unflinchingly inclusive, repeatedly bringing trans and nonbinary people into her discussions of gender, and she demonstrates a large amount of intersectionality, speaking at length how being a person of color can affect relationships with gender, and the discrimination people face.
And while I have my qualms about the book (Cheng seems to say that we need to convert all the ingressive things in our society to congressive things, which is a point I am skeptical of as someone who feels that there must be a balance to things) I cannot deny that this language has been incredibly useful. I would genuinely love for the terms ingressive and congressive to catch on (maybe in the math community at least they will?) because I find them to be an illuminating and productive way to describe the world around me. I would definitely recommend this book to anyone, math nerd or otherwise, who is interested in looking at the world through a new lens. Or, should I say, in a different dimension.
November 15, 2022
“Sono una matematica, e come tale scriverò questo libro, formulando teorie da matematica ed esplorandole da matematica. Proporrò una riformulazione del discorso sul gender che consiste nel focalizzarsi sui tratti caratteriali invece che sul genere, introducendo una nuova terminologia che può aiutarci a entrare in questa nuova dimensione. [...] È un problema su cui si è scritto tanto, senza però suggerire una soluzione.” – Pag. 19
L’autrice di questo saggio, che si presenta molto ambizioso già nelle prime pagine, è Eugenia Cheng, insegnante in una scuola d’arte di Chicago, appassionata di musica e molto altro, ma prima di tutto una matematica, esperta di teoria delle categorie. È attraverso le nozioni fondamentali di questa teoria che Cheng vorrebbe andare oltre la dicotomia “maschile/femminile” per superare i problemi di disparità di genere di cui è affetta la nostra società in tutti i suoi campi, dall’istruzione e la ricerca fino alla giustizia e alla politica.
Essendo io ingegnera, matematica e femminista, la quarta di copertina di “X+Y” mi ha incuriosito molto. Mi sono quindi approcciata a questo saggio con due obiettivi principali: scoprire qualcosa di più sulla teoria delle categorie, di cui non sapevo nulla, e comprendere come questa possa essere applicata per incentivare la parità di genere. Ahimè, sono stata delusa su entrambi i fronti: non penso di avere imparato nulla della teoria delle categorie e trovo parecchi difetti nella soluzione presentata da Cheng. Lo stile adottato poi lo definirei “accademicamente ridondante”: in diverse parti mi è sembrato di leggere le classiche frasi da articolo come “In questa sezione, prima mostrerò come… poi descriverò… etc”, con tantissime ripetizioni: il saggio avrebbe potuto essere lungo un quarto.
La teoria delle categorie viene introdotta brevemente a pagina 23, in questo modo: “La teoria delle categoria ha un diverso punto di partenza [rispetto alla teoria degli insiemi, ndr]: le relazioni. Si basa sull’idea che possiamo capire molto di una cosa o di una persona osservando i modi in cui si relazione con ciò che la circonda“. Segue poi un esempio illustrato per indicare i fattori di 30 come un sottoinsieme dei numeri naturali o come una categoria, cioè “una collezione di elementi con una rete di frecce che ne mostrano le relazioni”. Praticamente, si usa un grafo diretto dove i vertici sono i fattori di 30, e c’è un arco da un vertice n1 a un vertice n2 se n2 è un divisore di n1. Ma fin qui sto usando nozioni base di teoria dei grafi: in cosa si distingue la teoria delle categorie? Purtroppo, andando avanti nella lettura, questo non viene approfondito, così come non vengono mai approfonditi i concetti di “funtori”, “morfismi” o le più generiche “trasformazioni”, che si trovano nella pagina di Wikipedia dedicata alla teoria delle categorie (https://it.wikipedia.org/wiki/Teoria_...). Essendo questo un libro rivolto al grande pubblico e non a una nicchia ristretta di persone esperte di matematica, posso anche comprendere l’assenza di termini e definizioni esplicite, ma ci fosse almeno qualche cenno! In “X+Y” sono presenti solo diagrammi, mappe, implicazioni logiche e altre schematizzazioni utili a rappresentare delle relazioni, ma la divulgazione in questa direzione per me finisce qui (o non l’ho proprio compresa).
Passando al cuore del saggio, Cheng suggerisce di “scollegare la personalità dal genere, e poi riflettere più attentamente sui ruoli che i diversi tratti caratteriali possono giocare” (pag. 73), osservando che “È possibile che questi comportamenti siano in qualche modo correlati con l’essere uomini o donne, ma è un’osservazione che può arrivare in un secondo momento, non un principio guida. E in ogni caso non si tratta di qualità innate, ma acquisite tramite il condizionamento della società, e che quindi possono essere modificate” (pag. 124). Su questo sono perfettamente d’accordo: molte caratteristiche che vengono etichettate come “femminili“ o “maschili” in realtà non dovrebbero avere genere. Per scardinarle dal genere, Cheng introduce due nuovi termini: “ingressivo” e “congressivo”. Il primo riassume tutte le caratteristiche tipiche di coloro che sono individualisti e competitivi, mentre il secondo racchiude quei tratti di chi è più portato alla collaborazione e alla cooperazione per raggiungere scopi di bene comune. Cheng dedica poi molto spazio a raccontare diversi casi di studio (tra cui la sua esperienza) secondo i quali un atteggiamento congressivo sarebbe preferibile a uno ingressivo. La tesi principale di Cheng è quindi la seguente: per ottenere risultati, in termini non solo di parità di genere ma bensì di “parità umana” (pag. 124), bisogna dimenticarsi del genere per concentrarsi solo su questa nuova dimensione, incoraggiando la congressitivà. E questo è completamente impossibile, secondo me, almeno adesso. A regime sì, se e quando si raggiungerà la parità di genere, il genere potrà e dovrà essere tralasciato, ma non siamo ancora in quel punto. E la stessa Cheng lo conferma quando specifica, in diverse frasi, che il genere va sì dimenticato a meno che non sia necessario. Il genere è parte del problema: non può essere ignorato finché non lo si risolverà.
Un'altra criticità di questa tesi, come sottolineato anche in altre recensioni, è che il binomio ingressivo/congressivo incarna lo stesso limitato binarismo di maschile/femminile: mi aspettavo sinceramente di più, che l’introduzione di due soli poli, e la quasi totale assenza di considerazione di altri generi al di fuori del maschile e del femminile. Cheng rimarca che alcune caratteristiche si riscontrano spesso negli uomini o nelle donne, ma non sono proprie di tutti gli uomini o di tutte le donne: d’accordissimo, peccato che poi negli esempi descritti sono quasi sempre le donne a essere presentate sotto una luce migliore.
Cheng prova infine a descrivere come potrebbe cambiare la società adottando una mentalità congressiva. Sulla carta è tutto molto bello, ma rimane un’utopia. Per quanto il linguaggio sia determinante e i principi proposti siano validi, non è sufficiente a rovesciare una realtà non così pura.
Inoltre, sempre nel capitolo conclusivo, Cheng scrive: “Questa è la mia risposta a tutti i libri femministi che esortano a cambiare il sistema senza spiegarci come farlo. Credo che ora, con le nuove idee introdotte nella seconda parte del libro, siamo pronti a farlo. In particolare, sono convinta che saremo in grado di affrontare i problemi esposti nella prima parte, legati ai limiti di un pensiero monodimensionale e di genere. Eravamo bloccati ad analizzare le differenze tra uomini e donne, e distratti dal chiederci se fossero innate o acquisite. E così ricadevamo in una falsa dicotomia fra varie idee genderizzate su come cambiare lo status quo.” – Pag. 196
Usando la sua stessa terminologia, ho trovato la prima frase un po’ ingressiva, nel senso di arrogante: a parte i suggerimenti di come adottare un approccio più congressivo nel privato, sul lavoro e nella vita in generale, non sono stati descritti strumenti specifici e concreti per affrontare il problema della parità di genere. In quale modo starebbe quindi dando una “sua risposta a tutti i libri femministi”? Rimane tutto astratto e lontano, nell’iperuranio dove le idee sono perfette, ma non replicabili così nel mondo reale. Però, visto che comunque il problema della parità di genere è di comune interesse, ci tengo a rendere congressiva anche questa mia recensione: sono convinta che, in fondo, Cheng volesse accendere questa discussione, e l’intenzione c’era, anche esplicita: a pagina 41, infatti, Cheng scrive: “Nella matematica bidimensionale disegniamo grafici nelle due dimensioni x e y. Ma y non deve necessariamente essere contrapposta a x: x e y possono essere sommate in modo da creare una dimensione nuova e un nuovo modo di pensare“. In questo caso, x è il genere, y è la congressività: x+y sarebbe stata la dimensione corretta da indagare. Purtroppo Cheng si è persa nella dimensione nuova da lei definita. Sarebbe interessante sentire cos’avrebbe da dire in merito alla dimensione somma.
L’autrice di questo saggio, che si presenta molto ambizioso già nelle prime pagine, è Eugenia Cheng, insegnante in una scuola d’arte di Chicago, appassionata di musica e molto altro, ma prima di tutto una matematica, esperta di teoria delle categorie. È attraverso le nozioni fondamentali di questa teoria che Cheng vorrebbe andare oltre la dicotomia “maschile/femminile” per superare i problemi di disparità di genere di cui è affetta la nostra società in tutti i suoi campi, dall’istruzione e la ricerca fino alla giustizia e alla politica.
Essendo io ingegnera, matematica e femminista, la quarta di copertina di “X+Y” mi ha incuriosito molto. Mi sono quindi approcciata a questo saggio con due obiettivi principali: scoprire qualcosa di più sulla teoria delle categorie, di cui non sapevo nulla, e comprendere come questa possa essere applicata per incentivare la parità di genere. Ahimè, sono stata delusa su entrambi i fronti: non penso di avere imparato nulla della teoria delle categorie e trovo parecchi difetti nella soluzione presentata da Cheng. Lo stile adottato poi lo definirei “accademicamente ridondante”: in diverse parti mi è sembrato di leggere le classiche frasi da articolo come “In questa sezione, prima mostrerò come… poi descriverò… etc”, con tantissime ripetizioni: il saggio avrebbe potuto essere lungo un quarto.
La teoria delle categorie viene introdotta brevemente a pagina 23, in questo modo: “La teoria delle categoria ha un diverso punto di partenza [rispetto alla teoria degli insiemi, ndr]: le relazioni. Si basa sull’idea che possiamo capire molto di una cosa o di una persona osservando i modi in cui si relazione con ciò che la circonda“. Segue poi un esempio illustrato per indicare i fattori di 30 come un sottoinsieme dei numeri naturali o come una categoria, cioè “una collezione di elementi con una rete di frecce che ne mostrano le relazioni”. Praticamente, si usa un grafo diretto dove i vertici sono i fattori di 30, e c’è un arco da un vertice n1 a un vertice n2 se n2 è un divisore di n1. Ma fin qui sto usando nozioni base di teoria dei grafi: in cosa si distingue la teoria delle categorie? Purtroppo, andando avanti nella lettura, questo non viene approfondito, così come non vengono mai approfonditi i concetti di “funtori”, “morfismi” o le più generiche “trasformazioni”, che si trovano nella pagina di Wikipedia dedicata alla teoria delle categorie (https://it.wikipedia.org/wiki/Teoria_...). Essendo questo un libro rivolto al grande pubblico e non a una nicchia ristretta di persone esperte di matematica, posso anche comprendere l’assenza di termini e definizioni esplicite, ma ci fosse almeno qualche cenno! In “X+Y” sono presenti solo diagrammi, mappe, implicazioni logiche e altre schematizzazioni utili a rappresentare delle relazioni, ma la divulgazione in questa direzione per me finisce qui (o non l’ho proprio compresa).
Passando al cuore del saggio, Cheng suggerisce di “scollegare la personalità dal genere, e poi riflettere più attentamente sui ruoli che i diversi tratti caratteriali possono giocare” (pag. 73), osservando che “È possibile che questi comportamenti siano in qualche modo correlati con l’essere uomini o donne, ma è un’osservazione che può arrivare in un secondo momento, non un principio guida. E in ogni caso non si tratta di qualità innate, ma acquisite tramite il condizionamento della società, e che quindi possono essere modificate” (pag. 124). Su questo sono perfettamente d’accordo: molte caratteristiche che vengono etichettate come “femminili“ o “maschili” in realtà non dovrebbero avere genere. Per scardinarle dal genere, Cheng introduce due nuovi termini: “ingressivo” e “congressivo”. Il primo riassume tutte le caratteristiche tipiche di coloro che sono individualisti e competitivi, mentre il secondo racchiude quei tratti di chi è più portato alla collaborazione e alla cooperazione per raggiungere scopi di bene comune. Cheng dedica poi molto spazio a raccontare diversi casi di studio (tra cui la sua esperienza) secondo i quali un atteggiamento congressivo sarebbe preferibile a uno ingressivo. La tesi principale di Cheng è quindi la seguente: per ottenere risultati, in termini non solo di parità di genere ma bensì di “parità umana” (pag. 124), bisogna dimenticarsi del genere per concentrarsi solo su questa nuova dimensione, incoraggiando la congressitivà. E questo è completamente impossibile, secondo me, almeno adesso. A regime sì, se e quando si raggiungerà la parità di genere, il genere potrà e dovrà essere tralasciato, ma non siamo ancora in quel punto. E la stessa Cheng lo conferma quando specifica, in diverse frasi, che il genere va sì dimenticato a meno che non sia necessario. Il genere è parte del problema: non può essere ignorato finché non lo si risolverà.
Un'altra criticità di questa tesi, come sottolineato anche in altre recensioni, è che il binomio ingressivo/congressivo incarna lo stesso limitato binarismo di maschile/femminile: mi aspettavo sinceramente di più, che l’introduzione di due soli poli, e la quasi totale assenza di considerazione di altri generi al di fuori del maschile e del femminile. Cheng rimarca che alcune caratteristiche si riscontrano spesso negli uomini o nelle donne, ma non sono proprie di tutti gli uomini o di tutte le donne: d’accordissimo, peccato che poi negli esempi descritti sono quasi sempre le donne a essere presentate sotto una luce migliore.
Cheng prova infine a descrivere come potrebbe cambiare la società adottando una mentalità congressiva. Sulla carta è tutto molto bello, ma rimane un’utopia. Per quanto il linguaggio sia determinante e i principi proposti siano validi, non è sufficiente a rovesciare una realtà non così pura.
Inoltre, sempre nel capitolo conclusivo, Cheng scrive: “Questa è la mia risposta a tutti i libri femministi che esortano a cambiare il sistema senza spiegarci come farlo. Credo che ora, con le nuove idee introdotte nella seconda parte del libro, siamo pronti a farlo. In particolare, sono convinta che saremo in grado di affrontare i problemi esposti nella prima parte, legati ai limiti di un pensiero monodimensionale e di genere. Eravamo bloccati ad analizzare le differenze tra uomini e donne, e distratti dal chiederci se fossero innate o acquisite. E così ricadevamo in una falsa dicotomia fra varie idee genderizzate su come cambiare lo status quo.” – Pag. 196
Usando la sua stessa terminologia, ho trovato la prima frase un po’ ingressiva, nel senso di arrogante: a parte i suggerimenti di come adottare un approccio più congressivo nel privato, sul lavoro e nella vita in generale, non sono stati descritti strumenti specifici e concreti per affrontare il problema della parità di genere. In quale modo starebbe quindi dando una “sua risposta a tutti i libri femministi”? Rimane tutto astratto e lontano, nell’iperuranio dove le idee sono perfette, ma non replicabili così nel mondo reale. Però, visto che comunque il problema della parità di genere è di comune interesse, ci tengo a rendere congressiva anche questa mia recensione: sono convinta che, in fondo, Cheng volesse accendere questa discussione, e l’intenzione c’era, anche esplicita: a pagina 41, infatti, Cheng scrive: “Nella matematica bidimensionale disegniamo grafici nelle due dimensioni x e y. Ma y non deve necessariamente essere contrapposta a x: x e y possono essere sommate in modo da creare una dimensione nuova e un nuovo modo di pensare“. In questo caso, x è il genere, y è la congressività: x+y sarebbe stata la dimensione corretta da indagare. Purtroppo Cheng si è persa nella dimensione nuova da lei definita. Sarebbe interessante sentire cos’avrebbe da dire in merito alla dimensione somma.
June 24, 2021
I've thought a lot about this book and how to review it. I'm not sure I can give it the review it deserves and I'm not sure I have given it the star rating it deserves, but I can always edit both later.
For now, here are my fragments:
The info in the book was great. Cheng has some fantastic historical tidbits. For example, I had no idea Florence Nightingale was a mathematician whose use of statistics was instrumental in the changes she enacted as a nurse, and Cheng's illuminating discussion on a female coder who created a company that specifically to employ young women with children and paid them on a job done basis, not a per hour basis, to allow them flexibility and encourage job efficiency. It worked, her business boomed.
I also think Cheng's discussion on how unsupportive environments favour confident people, while supportive environments favour less confident people (I'm oversimplifying her arguments) was absolutely fascinating. It paints a picture of men creating a society in which everyone struggles needlessly, solely because a difficult environment elevates a handful of such men who--under better circumstnaces--would be *over* confident and overly aggressive. I have thoughts on that which aren't suitable for a review but suffice to say, it's interesting to think about. It would also explain the situation above (re jobs and women.)
She offers a general analysis that there is no point forcing 50/50 m/f participation unless we ALSO set up the environment to support women, because women will continue to underperform even when appropriately represented. That's fair and probably true, and feeds into the insidious myth that women haven't "earnt" the equality men so reluctantly give them.
But fundamentally, I do not think gender can be discussed in a mathematical way, and that's where the book falls down for me.
The problem of gender as a construct (and it is a problem, there is little that is uniformly positive about gender) is one which is linguistic and philosophical in nature.
Cheung says she set out to essentially define and create what "genderfree" feminism looks like. There is no such thing. And in any case, feminism is not about destroying gender or supporting gender; it is not about equality and it is not about finding solutions which "don't upset" the men (one of her goals.)
Feminism is about centering women in a world and society which centers men, however that centering may look, however you define men or women. It is about rejecting the context and structures and frameworks that give patriarchy an unfair, unethical, and illogical dominance in society, and which harm the vast majority of humans (regardless of gender or sex or background or whatever.) Most people will benefit from feminism, but feminism does not fight for most people primarily; it fights for women. If others benefit, fine, but that wasn't the goal.
This is an unpopular view, because people are stuck in patriarchal mindsets which make anything outside that seem threatening and evil. There is actually nothing wrong with a cause being focused. No one approaches cancer charities and screams at them for not collecting money to end Alzheimer's, and in a similar vein to the example above, if a cancer charity stumbles on research which benefits other sicknesses, cool! But that wasn't its goal. Get your pitchforks ready for cancer research, eh?
Likewise there is zero reason to scream at feminism because it doesn't carry a torch for every civil rights cause. (The concept of rights itself is patriarchal, but that's a whole other bag of shite.)
In summary, for me this interesting and earnest and lovely little book carries a fundamental flaw: mathematics is, I feel, a science of idealism, a world of imaginary numbers and abstract theories. Real life doesn't stop for such idealism, though, and the depth and complexity of this discussion cannot be carried by maths alone, as has been attempted here.
I'm going to regret this review later I'm sure.
For now, here are my fragments:
The info in the book was great. Cheng has some fantastic historical tidbits. For example, I had no idea Florence Nightingale was a mathematician whose use of statistics was instrumental in the changes she enacted as a nurse, and Cheng's illuminating discussion on a female coder who created a company that specifically to employ young women with children and paid them on a job done basis, not a per hour basis, to allow them flexibility and encourage job efficiency. It worked, her business boomed.
I also think Cheng's discussion on how unsupportive environments favour confident people, while supportive environments favour less confident people (I'm oversimplifying her arguments) was absolutely fascinating. It paints a picture of men creating a society in which everyone struggles needlessly, solely because a difficult environment elevates a handful of such men who--under better circumstnaces--would be *over* confident and overly aggressive. I have thoughts on that which aren't suitable for a review but suffice to say, it's interesting to think about. It would also explain the situation above (re jobs and women.)
She offers a general analysis that there is no point forcing 50/50 m/f participation unless we ALSO set up the environment to support women, because women will continue to underperform even when appropriately represented. That's fair and probably true, and feeds into the insidious myth that women haven't "earnt" the equality men so reluctantly give them.
But fundamentally, I do not think gender can be discussed in a mathematical way, and that's where the book falls down for me.
The problem of gender as a construct (and it is a problem, there is little that is uniformly positive about gender) is one which is linguistic and philosophical in nature.
Cheung says she set out to essentially define and create what "genderfree" feminism looks like. There is no such thing. And in any case, feminism is not about destroying gender or supporting gender; it is not about equality and it is not about finding solutions which "don't upset" the men (one of her goals.)
Feminism is about centering women in a world and society which centers men, however that centering may look, however you define men or women. It is about rejecting the context and structures and frameworks that give patriarchy an unfair, unethical, and illogical dominance in society, and which harm the vast majority of humans (regardless of gender or sex or background or whatever.) Most people will benefit from feminism, but feminism does not fight for most people primarily; it fights for women. If others benefit, fine, but that wasn't the goal.
This is an unpopular view, because people are stuck in patriarchal mindsets which make anything outside that seem threatening and evil. There is actually nothing wrong with a cause being focused. No one approaches cancer charities and screams at them for not collecting money to end Alzheimer's, and in a similar vein to the example above, if a cancer charity stumbles on research which benefits other sicknesses, cool! But that wasn't its goal. Get your pitchforks ready for cancer research, eh?
Likewise there is zero reason to scream at feminism because it doesn't carry a torch for every civil rights cause. (The concept of rights itself is patriarchal, but that's a whole other bag of shite.)
In summary, for me this interesting and earnest and lovely little book carries a fundamental flaw: mathematics is, I feel, a science of idealism, a world of imaginary numbers and abstract theories. Real life doesn't stop for such idealism, though, and the depth and complexity of this discussion cannot be carried by maths alone, as has been attempted here.
I'm going to regret this review later I'm sure.
November 3, 2020
A great idea for a book. The concept to replace gendered language with novel adjectives is worth the effort put in. But the execution is not clear or helpful enough. Ingressiveness and congressiveness are for most of the book stacked against each other as if they were opposite sides of the same dimension, while in some more detailed parts they are presented as semi-independent dimensions. I felt that such generic a term (and a half) does not enable the discussion as much as the author hopes (as even the author often just uses it interchangeably with gendered-adjectives).
Also the book is quite repetitive. It feels like the same introduction and conclusion is repeated in each chapter.
Also the book is quite repetitive. It feels like the same introduction and conclusion is repeated in each chapter.
July 24, 2020
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.
Thanks to the publisher and NetGalley for providing me with an advanced reader copy in exchange for an honest review.
July 29, 2024
"When I reconsider the behaviours I learnt during my time in mainstream academia, I wonder if some of them were valuable. Perhaps being able to be uncowed by aggressively dominant people is a genuinely useful skill to have learnt, but it’s only useful because aggressively dominant people exist. If they didn’t exist it wouldn’t be a useful skill at all"
It hard to know how to describe or respond to this book. Judged by the merits for which Cheng claims for it, it is really that successful. Cheng doesn't replace feminism here - for starters, she does not discuss how social and economic power works, nor the thorny issue of domestic labour and to whose benefit it is, nor reproductive rights, nor secual violence. Her focus is firmly on bias and prejudice, how this impacts on women in the workplace and education, and yes, how this intersects with other forms of bias and prejudice. She tackles the whole problem of gender inequality as if no-one benefits from it, and therefore, largely as if it is more accident than anything else. In reality, she views it a byproduct of a society designed to reward ïngressive"(selfish) behaviour over congressive (supportive and empowering) behaviour*.
However, within the limitations of this being a book about how behaving more generously might also create a world with more equality and just more actual comfort and happiness, which also takes some deadly side swipes at stupid sexist arguments, it is fantastic. Cheng uses the language of maths to demonstrate, devastatingly, how arguments morph from "stats show men are slightly better at x skill" to "almost all mathematicians should be men" by shifting the meanings in the formulations one by one until something entirely different is concluded. I would hope it is a very effective teaching method, to help people understand how things can seem proven, when in practice they are anything but." The stories she chooses of women leaders who chose different pathways are a mixed bunch, but Emmy Noether's, for example, was fantastic. (I am a huge fan of promoting the work of Rosalind Franklin, not only because of her brilliance, but because of the appalling way she was treated by Watson in particular, but nothing I've read makes her seem anything like the paragon of collaboration).
Cheng also writes movingly of her own experiences in the fields of academia and mathematics, and what led her to teach maths in an art school, to seek her joy in helping the terrified find their feet, rather than in the hypercompetitive world of specialist disciplines. Some of her anecdotes - a beloved professor noting that "women are so vain" when she checked her hood at her graduation, really are pretty awful. But her leap from her to that all sexism could be managed or minimised with more empathic and inclusive behaviours isn't really something I could endorse more generally. Her clarion call, which could be summarised as "focus less on changing the glass ceiling and more on building an open forum where everyone gets a say" is admirable, and should be heard. The maths parts, at the beginning of the book, work well to understand category theory as well as to better pick apart many sexist myths. And frankly, she is very funny and very warm and a pleasure to spend a book with.
*While as shorthand, Cheng summarises ingressive as "going more into things" and congressive as "bringing things together". However the full description she provides is noticeably less neutral "ingressive: Focusing on oneself over society and community, imposing on people more than taking others into account, emphasising independence and individualism, more competitive and adversarial than collaborative, tendency towards selective or single-track thought processes. congressive: Focusing on society and community over self, taking others into account more than imposing on them, emphasising interdependence and interconnectedness, more collaborative and cooperative than competitive, circumspect thought processes.""
It hard to know how to describe or respond to this book. Judged by the merits for which Cheng claims for it, it is really that successful. Cheng doesn't replace feminism here - for starters, she does not discuss how social and economic power works, nor the thorny issue of domestic labour and to whose benefit it is, nor reproductive rights, nor secual violence. Her focus is firmly on bias and prejudice, how this impacts on women in the workplace and education, and yes, how this intersects with other forms of bias and prejudice. She tackles the whole problem of gender inequality as if no-one benefits from it, and therefore, largely as if it is more accident than anything else. In reality, she views it a byproduct of a society designed to reward ïngressive"(selfish) behaviour over congressive (supportive and empowering) behaviour*.
However, within the limitations of this being a book about how behaving more generously might also create a world with more equality and just more actual comfort and happiness, which also takes some deadly side swipes at stupid sexist arguments, it is fantastic. Cheng uses the language of maths to demonstrate, devastatingly, how arguments morph from "stats show men are slightly better at x skill" to "almost all mathematicians should be men" by shifting the meanings in the formulations one by one until something entirely different is concluded. I would hope it is a very effective teaching method, to help people understand how things can seem proven, when in practice they are anything but." The stories she chooses of women leaders who chose different pathways are a mixed bunch, but Emmy Noether's, for example, was fantastic. (I am a huge fan of promoting the work of Rosalind Franklin, not only because of her brilliance, but because of the appalling way she was treated by Watson in particular, but nothing I've read makes her seem anything like the paragon of collaboration).
Cheng also writes movingly of her own experiences in the fields of academia and mathematics, and what led her to teach maths in an art school, to seek her joy in helping the terrified find their feet, rather than in the hypercompetitive world of specialist disciplines. Some of her anecdotes - a beloved professor noting that "women are so vain" when she checked her hood at her graduation, really are pretty awful. But her leap from her to that all sexism could be managed or minimised with more empathic and inclusive behaviours isn't really something I could endorse more generally. Her clarion call, which could be summarised as "focus less on changing the glass ceiling and more on building an open forum where everyone gets a say" is admirable, and should be heard. The maths parts, at the beginning of the book, work well to understand category theory as well as to better pick apart many sexist myths. And frankly, she is very funny and very warm and a pleasure to spend a book with.
*While as shorthand, Cheng summarises ingressive as "going more into things" and congressive as "bringing things together". However the full description she provides is noticeably less neutral "ingressive: Focusing on oneself over society and community, imposing on people more than taking others into account, emphasising independence and individualism, more competitive and adversarial than collaborative, tendency towards selective or single-track thought processes. congressive: Focusing on society and community over self, taking others into account more than imposing on them, emphasising interdependence and interconnectedness, more collaborative and cooperative than competitive, circumspect thought processes.""
August 24, 2024
Trite, doesn’t add anything to the conversation about gender
This book does a bang-up job of responding to things no one but right-wing internet trolls have argued for at least 40 years. For example, there are many pages devoted to arguing men are not biologically superior at science. Right, agree, but this is not new information.
The other part of the book consists of “wouldn’t it be nice if we prized nurturing over aggression” ideal worldbuilding and once again, I agree, but it just felt hollow and unhelpful.
Also, the math angle added nothing lol
This book does a bang-up job of responding to things no one but right-wing internet trolls have argued for at least 40 years. For example, there are many pages devoted to arguing men are not biologically superior at science. Right, agree, but this is not new information.
The other part of the book consists of “wouldn’t it be nice if we prized nurturing over aggression” ideal worldbuilding and once again, I agree, but it just felt hollow and unhelpful.
Also, the math angle added nothing lol
September 5, 2024
I like the way that Cheng uses mathematics to reposition how we should think about gender, but find that she still falls into a binary thinking in much of her analysis. Her framing of gender within a multi-dimensional scope and treatment of gender and behavior as independent variables was quite insightful, but didn’t feel as novel or radical as she claimed.
Engaging, quick read from CA to IL. Overall I’d give this about 3.75 stars (rounded up to be nice 😇).
Engaging, quick read from CA to IL. Overall I’d give this about 3.75 stars (rounded up to be nice 😇).
July 28, 2020
More of a 3.5. I'll try and write a review when I have more of my thoughts together, but I do think this is an interesting exploration of gender dynamics and what society needs to succeed as a whole. There's a lot of food for thought that I'd like others to feast on. :)
February 4, 2022
I’ll admit that I’m not the target audience for this book, but I was very looking forward to it, and was disappointed. I’m a professor who studies gender and has a strong background in statistical methodology, so a mathematician analyzing gender seemed right up my alley, maybe even counting towards “keeping up with the literature.”
When the book started off with a description of the mathematical concepts behind defining sets and connections, I was there for it. As the author points out, gender and sex can’t be defined by any individual trait or set of traits; though they seem clear cut to most of us most of the time, they’re fuzzy categories, and someone using the math of fuzzy categories to look at gender seems like a great idea.
But this isn’t that book.
The author’s big idea is that we should re-label gendered traits, stop calling them “masculine and feminine,” and instead call them “ingressive and congressive.” This new dimension doesn’t seem different than a proposed masculine-feminine dimension, just re-labeled to be decoupled from sex. Is there any sense here that gender is a multi-dimensional construct, that masculine and feminine traits can, and generally do, co-exist? Not really. Are there traditionally feminine “ingressive” traits? Nope. Nor the reverse. Is this ground breaking and progressive? If anything, treating gendered traits as unidimensional, even if it makes measurement easier, is theoretically regressive, and hardly what we’d expect from a book on gender in 2021. Does she engage with the social science literature on gender? Nope- she cites a couple of well worn studies, but mostly sticks to pop psych books. Pro tip: when a scholar starts citing TedX talks that changed their way of thinking, you can stop paying attention.
Of course, that wouldn’t fill up a book. So we get some memoir, which is the best and most interesting part of the book, about the author’s shift from a competitive academic environment to a more inclusive and rewarding one. Is that content for everyone? Not really, but I’m an academic, so it speaks to me.
Aside from that, we get a lot of self help pablum. Some of this I liked, too: mostly the parts where she talks about how to make academic presentations and q and a sessions more inclusive (and shut up the old white guys who tend to dominate them).
I have no doubt that the author could write an amazing book about the deep math of connections and gender, and I hope to read it. But this is shallow, overly simple, a waste of time and effort.
(Why two stars instead of one? I liked the academic content. YMMV)
When the book started off with a description of the mathematical concepts behind defining sets and connections, I was there for it. As the author points out, gender and sex can’t be defined by any individual trait or set of traits; though they seem clear cut to most of us most of the time, they’re fuzzy categories, and someone using the math of fuzzy categories to look at gender seems like a great idea.
But this isn’t that book.
The author’s big idea is that we should re-label gendered traits, stop calling them “masculine and feminine,” and instead call them “ingressive and congressive.” This new dimension doesn’t seem different than a proposed masculine-feminine dimension, just re-labeled to be decoupled from sex. Is there any sense here that gender is a multi-dimensional construct, that masculine and feminine traits can, and generally do, co-exist? Not really. Are there traditionally feminine “ingressive” traits? Nope. Nor the reverse. Is this ground breaking and progressive? If anything, treating gendered traits as unidimensional, even if it makes measurement easier, is theoretically regressive, and hardly what we’d expect from a book on gender in 2021. Does she engage with the social science literature on gender? Nope- she cites a couple of well worn studies, but mostly sticks to pop psych books. Pro tip: when a scholar starts citing TedX talks that changed their way of thinking, you can stop paying attention.
Of course, that wouldn’t fill up a book. So we get some memoir, which is the best and most interesting part of the book, about the author’s shift from a competitive academic environment to a more inclusive and rewarding one. Is that content for everyone? Not really, but I’m an academic, so it speaks to me.
Aside from that, we get a lot of self help pablum. Some of this I liked, too: mostly the parts where she talks about how to make academic presentations and q and a sessions more inclusive (and shut up the old white guys who tend to dominate them).
I have no doubt that the author could write an amazing book about the deep math of connections and gender, and I hope to read it. But this is shallow, overly simple, a waste of time and effort.
(Why two stars instead of one? I liked the academic content. YMMV)
January 1, 2021
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.
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.
June 23, 2022
3.5 stars
The general topic of this book, and the argument it was making, I actually liked quite a bit. I appreciated that the author created language to separate out gender and those feelings attributed to gender from the topics being discussed. I also really appreciated being walked through breaking down and questioning the "logic" of very gendered statements. (Men are typically good at A, A is a skill often needed in B, therefor men are better at B) and really questioning these statements and logic.
What I struggled with, was that the main actionable step for "rethinking gender" is the change to non-gendered language, and that only was introduced half way through. And the subtitle is slightly misleading. It's less about rethinking gender, and more about rethinking language and attributing character traits to specific gender, and how that's unhelpful to feminism and society in general.
I did get a lot of "Quiet: the power of introverts" by Susan Cain vibes, and think these two books complement each other.
The general topic of this book, and the argument it was making, I actually liked quite a bit. I appreciated that the author created language to separate out gender and those feelings attributed to gender from the topics being discussed. I also really appreciated being walked through breaking down and questioning the "logic" of very gendered statements. (Men are typically good at A, A is a skill often needed in B, therefor men are better at B) and really questioning these statements and logic.
What I struggled with, was that the main actionable step for "rethinking gender" is the change to non-gendered language, and that only was introduced half way through. And the subtitle is slightly misleading. It's less about rethinking gender, and more about rethinking language and attributing character traits to specific gender, and how that's unhelpful to feminism and society in general.
I did get a lot of "Quiet: the power of introverts" by Susan Cain vibes, and think these two books complement each other.
Read
December 26, 2023very intriguing and fruitful read! i do think so much of cheng’s work has merit but, as she acknowledges, it is very utopian. i laughed at the ingressive/congressive exchanges at the end because as a sarcastic person it was hard not to realise i love to be a bit cheeky. but she’s right in her conclusion that no matter how impossible a world that isnt hierarchical and oppressive seems, there’s no harm in trying to change things no matter the scale or impact. be the change and all!
May 30, 2021
In this book Eugenia Cheng attempts to use some of the techniques of category theory in mathematics, her specialty, to reassess gender in terms of character traits, instead of gender terms and it’s roles and norms. Her main stab at this is in terms of ingressive and congressive behaviors. She would categorize the use of “stab” as ingressive. Ingressive behavior is competitive often fought under zero-sum, win-lose, terms. Ingressive behavior is most associated with males, but also can describe female behavior too. Congressive behavior is done in cooperative ways, and win-win, nonzero sum terms. Congressive behavior is associated mostly with female behavior, although some males may behave in this manner as well. Her basic analysis is that in today’s world ingressive behavior is seen as the best way to gain success in it. She would like to see it move in a more congressive manner, and she makes and share some ways to do it. By making the world more congressive we can accommodate more woman into the mix of successful higher level positions, since it is typically, but not exclusively, female behavior.
Here are a few comments based on notes as I was reading the book. Numbers in brackets [] refer to Kindle page locations.
[97] “. . . I wonder whether that competitive behavior I learned was important even for academia, where I learned it. Was there another way to be successful in that environment? More radically, was there another way for that environment to be?” I thought of the compulsive collaborator in mathematics, Paul Erdős, who had a total of 507 different co-authors. He was seen as an excellent example of a mathematician.
[127] ”Language is important. It can help us clarify our thoughts about something, even if we were already thinking about that thing before we had a word for it. Having a word for a concept is a way of making it more convenient to carry around in our brains.” This brings me back to my philosophy blog days, where I argued that we do not think in language—language is just an aid like Cheng is talking about here.
[240] “She [Paula Gunn Allen] describes tribal societies as egalitarian, organizing events and phenomena not by hierarchies, as in white (Christian) societies, but with everything related to everything else in a harmonious or unified way. She even writes of traditional war that it was “not practiced as a matter of conquest or opposition to enemies” but instead was a ritual to gain the attention of supernatural powers.” First, I question the accuracy of this statement. But mainly, if that was the case maybe they would have had no wars if they didn’t have supernatural beliefs.
[242] “It is possible that this [not having a parliamentary form of government] is why it is taking much longer to get a woman president of the United States than a woman prime minister of the United Kingdom or a woman chancellor of Germany.” But, Margaret Thatcher was pretty ingressive, and Angela Merkle seems ingressive as well.
So how much help is category theory in the analysis of gender or character traits. I do not propose to answer. Cheng’s ingressive/congressive split does however seem a possible solution in part, as that alone would not probably eliminate the gender divide we face. In practice I am not sure how it would play out though. Still I felt the book to be pretty good. As you might expect information category theory was mainly descriptive, as the book’s main focus was feminism, and a possible way forward. She also supports all gender identities, whether cisgender identities or transgender identities. I can give the book a solid 4 stars.
If you are interested in feminism, particularly a different approach from the usual, this would be a good book to read. I cannot see any benefit for those that oppose feminism or transgender feminism (albeit there is not a whole lot about it in the book), although I cannot honestly see these types of people reading it in the first place. If you are looking for a mathematical exploration of category theory you will be disappointed.
Here are a few comments based on notes as I was reading the book. Numbers in brackets [] refer to Kindle page locations.
[97] “. . . I wonder whether that competitive behavior I learned was important even for academia, where I learned it. Was there another way to be successful in that environment? More radically, was there another way for that environment to be?” I thought of the compulsive collaborator in mathematics, Paul Erdős, who had a total of 507 different co-authors. He was seen as an excellent example of a mathematician.
[127] ”Language is important. It can help us clarify our thoughts about something, even if we were already thinking about that thing before we had a word for it. Having a word for a concept is a way of making it more convenient to carry around in our brains.” This brings me back to my philosophy blog days, where I argued that we do not think in language—language is just an aid like Cheng is talking about here.
[240] “She [Paula Gunn Allen] describes tribal societies as egalitarian, organizing events and phenomena not by hierarchies, as in white (Christian) societies, but with everything related to everything else in a harmonious or unified way. She even writes of traditional war that it was “not practiced as a matter of conquest or opposition to enemies” but instead was a ritual to gain the attention of supernatural powers.” First, I question the accuracy of this statement. But mainly, if that was the case maybe they would have had no wars if they didn’t have supernatural beliefs.
[242] “It is possible that this [not having a parliamentary form of government] is why it is taking much longer to get a woman president of the United States than a woman prime minister of the United Kingdom or a woman chancellor of Germany.” But, Margaret Thatcher was pretty ingressive, and Angela Merkle seems ingressive as well.
So how much help is category theory in the analysis of gender or character traits. I do not propose to answer. Cheng’s ingressive/congressive split does however seem a possible solution in part, as that alone would not probably eliminate the gender divide we face. In practice I am not sure how it would play out though. Still I felt the book to be pretty good. As you might expect information category theory was mainly descriptive, as the book’s main focus was feminism, and a possible way forward. She also supports all gender identities, whether cisgender identities or transgender identities. I can give the book a solid 4 stars.
If you are interested in feminism, particularly a different approach from the usual, this would be a good book to read. I cannot see any benefit for those that oppose feminism or transgender feminism (albeit there is not a whole lot about it in the book), although I cannot honestly see these types of people reading it in the first place. If you are looking for a mathematical exploration of category theory you will be disappointed.
May 10, 2025
Like a few reviewers on here I was frustrated with this book. Initially I found the idea to develop a framework for talking about character outside of gender and using ideas from mathematical formalisation to do it interesting and novel. I forgave the slightly weak examples of logical fallacy in the promise of new ideas from a clearly intelligent and STEM trained author. However, the definitions of ingressive and congressive never feel fully complete and I struggled to see how they were any different than the authors presentations of masculine and feminine. I waited for an example to be presented that made the distinction but this never came. By the end of the book I was questioning whether ingressive was just a term for behaviour the author personally doesn’t like and the final chapter does even include a model of congressive education which addresses the authors “pet peeves”. Many of the examples and anecdotes of behaviours could be easily reversed with a different point of view but these are not explored despite an example of “congressive ingressivity” being presented in the context of raising questions. There is an assumption throughout the book that congressive behaviour is better for both individuals and society but this is never really fleshed out. A simple example of team sports seems to be a rebuttal to this. Many of the arguments in the final chapter are based on singular examples. Native American social structures are discussed as congressive and therefore the author claims we need to reclaim this but the exact opposite argument could be written for native Australians who have well defined power structures based on elders with men still largely dominant. The discussion of external validation is an example where the narrative seems just plain confused. In one chapter external validation is an ingressive trait based on winning, later it is necessary for congressive people to thrive and ingressive people “base their confidence on nothing”. It would seem that you can simultaneously receive grades, awards and promotions and still be basing your confidence on nothing. Overall I was left frustrated at the lack of development of ideas and consideration of different perspectives even as a thought experiment. The author never stops to ask why people might be ingressive. I’d suggest a lot of it comes from poverty where you have to exhibit selfish behaviour to survive. Ironically I came to the conclusion that adapting your life to be congressive is likely only possible from a place of privilege.
December 15, 2025
This had an interesting and novel framework that ultimately disappointed me. I like the way Dr. Cheng uses her research field in non-math contexts like this and I am forever impressed by her dedication to making math/science education accessible to all. Some of her descriptions rang true to my experiences as a woman in a highly male-dominated field in a way that made me feel very seen. Unfortunately, it went downhill from there.
I don’t necessarily dislike Cheng’s ingressive/congressive framework specifically, and I can see its value in divesting from masculine/feminine terminology. I had hoped that she’d continue to build out a vision of how these behaviors and characteristics can coexist.
However, the way she actually builds this framework feels reactionary and reductive. It ends up just constructing a new morally charged good/bad dichotomy in which traditional ingressive behaviors (which are not well defined, but rather seem to be behaviors that Cheng personally dislikes or that don’t come naturally to her) are demonized. I am a woman in engineering who has a mix of what Cheng would describe as ingressive and congressive behaviors, including some so-called ingressive traits like competitiveness and ambition that I LIKE in myself and that are already stigmatized in women. Instead of resonating with me as someone who has a lot of congressive traits in an ingressive field, this sharp dichotomy ended up just alienating me, and I imagine it might do the same to many other readers.
I am pretty much the target reader for this: a woman in a heavily male-dominated stem field, a staunch feminist, and a person invested in making STEM more equitable and inclusive. But this still ended up putting me off because it seemed to veer so hard into moral judgments and black and white thinking. At a certain point, the mathematical reasoning behind this framework seemed to be dropped entirely, veering off into a rant of personal opinion. I felt that this framework could have had potential had Cheng not taken it in this direction.
I don’t necessarily dislike Cheng’s ingressive/congressive framework specifically, and I can see its value in divesting from masculine/feminine terminology. I had hoped that she’d continue to build out a vision of how these behaviors and characteristics can coexist.
However, the way she actually builds this framework feels reactionary and reductive. It ends up just constructing a new morally charged good/bad dichotomy in which traditional ingressive behaviors (which are not well defined, but rather seem to be behaviors that Cheng personally dislikes or that don’t come naturally to her) are demonized. I am a woman in engineering who has a mix of what Cheng would describe as ingressive and congressive behaviors, including some so-called ingressive traits like competitiveness and ambition that I LIKE in myself and that are already stigmatized in women. Instead of resonating with me as someone who has a lot of congressive traits in an ingressive field, this sharp dichotomy ended up just alienating me, and I imagine it might do the same to many other readers.
I am pretty much the target reader for this: a woman in a heavily male-dominated stem field, a staunch feminist, and a person invested in making STEM more equitable and inclusive. But this still ended up putting me off because it seemed to veer so hard into moral judgments and black and white thinking. At a certain point, the mathematical reasoning behind this framework seemed to be dropped entirely, veering off into a rant of personal opinion. I felt that this framework could have had potential had Cheng not taken it in this direction.
March 15, 2022
HEHEHEHEHEHEHEHEHEHEHEHE I FINALLY FINISHED!!!!!!!!
I have this burning need to meet Eugenia Cheng. She would be such a great individual to talk to and learn from. There's been so much in this book that's just expanded my little mind and viewpoint, and I just have a really strong desire to know more about her unique understanding of the world.
ALSO IT FEELS SO REFRESHING TO READ ABOUT A MATHEMATICIAN WHO GENUINELY WANTS MAJOR SUPPORT FOR ARTSY PEOPLE. LIKE HELL YES YOU BREAK THOSE STUPID STEREOTYPES.
Her introduction into the idea of ingressivity and congressivity has gotten all the cogs turning in my brain (even if they're complaining about all the other work that school demands). Both words are actually new pieces of terminology she's created to separate previously gendered thinking about characteristics from arguments that inevitably end in circles of "not all men" and "not all women" and man.... it's genius. I loved it. I got so involved in this concept and I'm lowkey inspired.
To be completely honest reading x + y: A Mathematician's Manifesto for Rethinking Gender didn't feel like other math-related books I've read. Sure, some ~concepts~ were explained in the first half, albeit surprisingly sparingly, but it was more so that a sound analogy could be provided so that more emotionally-charged examples can be analysed. And I was fully okay with that as school may or may not be melting my brain at this point. Also, mathematics and academia provided quite a few examples of why change is needed and what that change could look like, and I particularly found this fascinating.
All in all, such a good and balanced read for anyone interested in feminism/arguments centred around gender and mathematics being used to explain abstract concepts.
I have this burning need to meet Eugenia Cheng. She would be such a great individual to talk to and learn from. There's been so much in this book that's just expanded my little mind and viewpoint, and I just have a really strong desire to know more about her unique understanding of the world.
ALSO IT FEELS SO REFRESHING TO READ ABOUT A MATHEMATICIAN WHO GENUINELY WANTS MAJOR SUPPORT FOR ARTSY PEOPLE. LIKE HELL YES YOU BREAK THOSE STUPID STEREOTYPES.
Her introduction into the idea of ingressivity and congressivity has gotten all the cogs turning in my brain (even if they're complaining about all the other work that school demands). Both words are actually new pieces of terminology she's created to separate previously gendered thinking about characteristics from arguments that inevitably end in circles of "not all men" and "not all women" and man.... it's genius. I loved it. I got so involved in this concept and I'm lowkey inspired.
To be completely honest reading x + y: A Mathematician's Manifesto for Rethinking Gender didn't feel like other math-related books I've read. Sure, some ~concepts~ were explained in the first half, albeit surprisingly sparingly, but it was more so that a sound analogy could be provided so that more emotionally-charged examples can be analysed. And I was fully okay with that as school may or may not be melting my brain at this point. Also, mathematics and academia provided quite a few examples of why change is needed and what that change could look like, and I particularly found this fascinating.
All in all, such a good and balanced read for anyone interested in feminism/arguments centred around gender and mathematics being used to explain abstract concepts.
December 3, 2022
this was one of the best books I've read all year; I gained a new appreciation for math, a novel way of understanding gender and gender differences, and got concrete, actionable tips for self-improvement. One would think that a book covering all of those topics would feel a bit disjointed, but they dovetailed into each other surprisingly well.
One thing I absolutely loved was the fact that she explained her argument in quite mathematical terms. Often, when reading books (especially the feminist non-fiction I've been reading recently), they state their point like it's a foregone conclusion, not giving enough evidence about exactly how they got there. This book's emphasis on a mathematical approach (at least at the beginning, it got much less so as it progressed) was undoubtedly one of its greatest strengths. She debunked flawed arguments about the supposed inherent superiority of men in certain areas, exposing that their reasoning made unnecessary assumptions.
From this, she concluded that it is character traits, not necessarily gender, that leads to success, and her dream of a post-gender world, in which character traits and gender are decoupled, strikes me as being lowkey gender abolitionist, which I think is a pretty cool point of view to hold. Instead of categorising behaviour as masculine or feminine, Cheng argued that we should be more specific, and add another dimension (another prime example of mathematical thinking shining)coining the terms "ingressive" and "congressive". Initially, I believed that her claims made at the beginning of the book were a bit overhyped, but I was gladly proven wrong. This new way of thinking absolutely blew my mind, providing answers to questions I didn't know that I had, and is definitely something I have to consider in my personal life.
I wholeheartedly agree that we should do whatever we can to fight for a more congressive world, and I liked all her examples of ways in which our current world rewards ingressive thinking, and how it can be radically changed to promote congressivity.
One thing I absolutely loved was the fact that she explained her argument in quite mathematical terms. Often, when reading books (especially the feminist non-fiction I've been reading recently), they state their point like it's a foregone conclusion, not giving enough evidence about exactly how they got there. This book's emphasis on a mathematical approach (at least at the beginning, it got much less so as it progressed) was undoubtedly one of its greatest strengths. She debunked flawed arguments about the supposed inherent superiority of men in certain areas, exposing that their reasoning made unnecessary assumptions.
From this, she concluded that it is character traits, not necessarily gender, that leads to success, and her dream of a post-gender world, in which character traits and gender are decoupled, strikes me as being lowkey gender abolitionist, which I think is a pretty cool point of view to hold. Instead of categorising behaviour as masculine or feminine, Cheng argued that we should be more specific, and add another dimension (another prime example of mathematical thinking shining)coining the terms "ingressive" and "congressive". Initially, I believed that her claims made at the beginning of the book were a bit overhyped, but I was gladly proven wrong. This new way of thinking absolutely blew my mind, providing answers to questions I didn't know that I had, and is definitely something I have to consider in my personal life.
I wholeheartedly agree that we should do whatever we can to fight for a more congressive world, and I liked all her examples of ways in which our current world rewards ingressive thinking, and how it can be radically changed to promote congressivity.
July 14, 2020
This was a really interesting book that takes a different spin on the male-dominated social structure systems and how to better adapt them to individual needs, taking note of other texts like Invisible Women and the work of Cordelia Fine.
The idea that congressive thinking and actions could be more productive, inclusive and successful than ingressive strategies isn't something I have come across before; it shows the impact that these ways of thinking can have on the way we conduct ourselves and how we interact with others. I'm heartened to read (or listen to, thanks Netgalley!) yet another nonfiction book on gender that says a woman doesn't necessarily have to 'act like a man' in order to progress in their career and to be respected... that a more measured approach can work just as well.
The idea that congressive thinking and actions could be more productive, inclusive and successful than ingressive strategies isn't something I have come across before; it shows the impact that these ways of thinking can have on the way we conduct ourselves and how we interact with others. I'm heartened to read (or listen to, thanks Netgalley!) yet another nonfiction book on gender that says a woman doesn't necessarily have to 'act like a man' in order to progress in their career and to be respected... that a more measured approach can work just as well.
December 27, 2021
There're quite interesting points in this book, but ironically they are not the ones gender related.
The most stimulating part is when Cheng introduces the difference between "ingressive" (characterized by individualism, imposition, competitiveness) and "congressive" (focused on interdependence, community, collaboration and cooperation ). Two neutral and genderless neologisms (to describe, and not to prescribe to, people, things or situations), that she uses to delineate social power structures (she mainly focuses on the education and career systems).
The idea that society favors ingressive people and environments, to the detriment of congressive people, is the actual observation point of the book.
Pretty much a good book, but it's a bit repetitive and even if the ideas exposed by Cheng are quite right, they are in fact not related to gender, at least not in a pragmatic way.
The most stimulating part is when Cheng introduces the difference between "ingressive" (characterized by individualism, imposition, competitiveness) and "congressive" (focused on interdependence, community, collaboration and cooperation ). Two neutral and genderless neologisms (to describe, and not to prescribe to, people, things or situations), that she uses to delineate social power structures (she mainly focuses on the education and career systems).
The idea that society favors ingressive people and environments, to the detriment of congressive people, is the actual observation point of the book.
Pretty much a good book, but it's a bit repetitive and even if the ideas exposed by Cheng are quite right, they are in fact not related to gender, at least not in a pragmatic way.
November 17, 2024
I loved the premise of this book, and the first half had me hooked- I find myself interpreting life through the lens of ingressivity and congressivity almost immediately! I specifically enjoyed hearing about her background in academia and reading how she described abstract statistical concepts for a common reader. As a PhD student myself really interested in science writing, this was a great example of that.
It started dragging on a bit as she started going into examples in the latter part of the book. Maybe this is ingressive of me, but I kind of thought "I get it" at a certain point and only really hot ducked back in during the appendix where she gave practical advice on how to be congressive.
This would make a great book club book at a university, or good pre-reading for a teacher education course.
It started dragging on a bit as she started going into examples in the latter part of the book. Maybe this is ingressive of me, but I kind of thought "I get it" at a certain point and only really hot ducked back in during the appendix where she gave practical advice on how to be congressive.
This would make a great book club book at a university, or good pre-reading for a teacher education course.
August 10, 2023
I made my expectations before reading this book and that was a mistake. Having read The Art of Logic and Beyond Infinity from Dr. Eugenia Cheng I expected much more maths in this book. Unfortunately for my expectations it was not the case and that deceived me. It is not the authos fault though, but mine. Don't get me wrong, it is not a bad book, but one with rather interesting proposals to change our current paradigms in many environtments. It made me think a lot though more philosophically than mathematically.
If you are looking for an alternative to the current gendered world, I totally recommend this book to you.
If you are looking for an alternative to the current gendered world, I totally recommend this book to you.
October 17, 2020
Yes! Yes x infinity to the power of infinity
I love how little I needed to know math to understand this book. And I loved how it touched very gently but in a relevant way all the subjects that matter. The book was written in March 2020 so it’s current and important and yes can we start doing that right now?
One thing that I wish it would have been addressing more is how that proposed theory would work in languages that are extremely gender specific but I guess it can be discussed further in an extended edition later in the process.
I love how little I needed to know math to understand this book. And I loved how it touched very gently but in a relevant way all the subjects that matter. The book was written in March 2020 so it’s current and important and yes can we start doing that right now?
One thing that I wish it would have been addressing more is how that proposed theory would work in languages that are extremely gender specific but I guess it can be discussed further in an extended edition later in the process.
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