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

Eugenia Cheng
Basic Books
Publication Date: 
Number of Pages: 
[Reviewed by
Mary Beth Rollick
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Eugenia Cheng, a Ph.D. mathematician, often is asked about her experience being a woman in a male-dominated field. When she began her career she was not interested in this issue but eventually, she felt a need to address the topic of gender. In this book, Cheng applies mathematical thought processes as a tool to reframe the problem of gender inequality.
As a category theorist, Cheng researches relationships. She uses this focus on relationships to address the problem of the divisiveness of arguments around gender equality. She abstracts the ideas and reframes the discussion based on relevant character traits that she demonstrates do not have to be linked to gender.  She looks for assumptions that have been made, seeks to discard them, and discovers fundamental relationships. In order to better articulate these relationships, she invents new terminology as a way of preventing futile divisive arguments. These new terms are ingressive and congressive. She defines ingressive behavior as “going into things” where the focus is on the self and is more competitive, individualistic, and adversarial. She defines congressive behavior as “bringing things together” where the focus is on community and is more collaborative, interdependent, and cooperative.  She gives many examples to illuminate her definitions.
Cheng’s writing style is clear and concise with a light touch of humor. She prepares the reader for her main ideas by a careful use of examples so that even the explanation of category theory would be easily understood by a general audience. Her use of stories keeps a reader captivated.
This is not a mathematics book so it doesn’t seem to fit with the books on the MAA Booklist and yet Cheng asserts that it does apply to professionals who teach mathematics. Category theory was briefly described so that Cheng could explain her way of addressing the issue of gender. Her manifesto is to transform society into a congressive and unified world where it is x + y and not x versus y.  One of her target audiences is teachers of traditionally ingressive subjects like mathematics. She wants to encourage them to think differently about the meaning of success. She envisions teaching mathematics in a collaborative manner using explorations and a non-cumulative curriculum with the aim of nurturing interest and appreciation for mathematics. Cheng is deeply interested in making mathematics accessible to everyone.
Mary Beth Rollick ( is Professor Emerita at Kent State University in Kent, Ohio. She continues to be involved in mathematics education. She has been tutoring undergraduate students and enjoys helping them to understand the “why” as well as the “how” of mathematics.
The table of contents is not available.