A multidimensional approach to mathematics and gender

Melita Wiles

Science & Environment Editor

 

After starting her career in mathematics, a male-dominated field, and then transitioning to art, a female-dominated field, Eugenia Cheng — mathematician, musician and author — has had much time to consider ideas of gender and success in different professional settings. She has written a book called, “x+y: A Mathematician’s Manifesto to Rethinking Gender,” in which she uses math to explain new ways of exploring gender and success.

Cheng is a category theorist, meaning that she studies mathematical structures. When explaining this area of math herself, she describes it as the “flexibility of thinking” or “the mathematics of mathematics.” Although her work is abstract, she believes that because abstractness is further removed from life, it also becomes more inclusive.

We are more accustomed to thinking in one dimensional space. Cheng wants to challenge us to think in more dimensions. She thinks it would be beneficial to create descriptive characterization words of people’s behaviors and interactions instead of classifying people by gendered terms like feminine, masculine, grandmother or uncle, but rather by intrinsic characteristics. By ignoring the specific individuals and focusing on their behaviors, Cheng proposes two new words: ingressive and congressive. Ingressive is defined as focusing on oneself and being individualistic, independent, competitive and adversarial, while congressive focuses on collaboration and interdependence, accounts for others and emphasizes society and community. Cheng clarifies that she is not advocating for “gender blindness” because it is important that we address all forms of bias and exclusion.

Cheng supports both congressive learning and living. She believes, especially in the U.S., that we favor ingressive learning and working styles, which create toxic environments for success and productivity. In education specifically, she believes that more people would be interested in math if they were taught in a more congressive way. Cheng tested this while teaching math to art students at the School of Art Institute of Chicago. She says by taking a congressive approach, she saw more students realize that math is more than a right or wrong answer; it is about how to think. Teaching in a congressive way creates a more inclusive environment, where students can investigate, discover and uncover relationships. Cheng describes it as “low floor/high ceiling,” where the expectation is low to start, but the reward is very high in the end. Conversely, ingressive learning focuses more on right and wrong, facts and rules and competition. With ingressive learning there is less time to explore and be creative, which is what math is all about to Cheng. Category theory is innately congressive. It focuses on relationships and understanding structures and gives us different ways in which things may be similar or not.

With these terms we can categorize how people behave and their interactions with each other, instead of focusing directly on intrinsic gendered characterizations. Cheng’s philosophy supports the idea of congressive living, in which we can create an inclusive, multidimensional world where all people feel heard, valued and successful.