In 2017, mathematics education professor Rochelle Gutiérrez wrote that “mathematics operates as whiteness.” Word of this spread quickly, leading to a strong backlash of hate mail and offensive comments on Gutiérrez’s social media [1]. This soundbite is often quoted without context, so here is some context:

“Who gets credit for doing and developing mathematics, and who is seen as part of the mathematical community is generally viewed as White. School mathematics curricula emphasizing terms like Pythagorean theorem and pi perpetuate a perception that mathematics was largely developed by Greeks and other Europeans. Perhaps more importantly, mathematics operates with unearned privilege in society, just like Whiteness.” [2]

In this sense, at least in the U.S., one could certainly argue that mathematics operates as whiteness. In this blog, I would like to pose the question: Can mathematics do otherwise? Can mathematics be antiracist?

Last semester, I developed a class called Inequalities: Numbers and Justice, aimed towards non-majors. My students ranged from undergraduate seniors to students in the local high school, with majors ranging from Government to Chinese to Computer Science. It was the second incarnation of a course I had taught years ago, in which we worked through the ideas in Gutstein and Peterson’s Rethinking Mathematics: Teaching Social Justice by the Numbers, which was written at the middle-school level [3]. In Inequalities, my hope was to develop these ideas into a college-level course.

Over the course of the semester, we explored how notions of fairness and equality have been considered from the point of view of mathematics and economics. What ways were these ideas defined, and given the definitions, how can they be measured? We covered topics ranging from the misuses of statistics to gerrymandering to racial capitalism and climate change. In the end, students were able to appreciate the complexities of fairness, the deep inequities that capitalism produces, and questioned the idea that mathematics is politically neutral.

Can mathematics, specifically beyond the K-12 level, be antiracist? Are critical mathematics pedagogy (the application of critical theory to mathematics education) and “higher” mathematics (college mathematics and beyond) necessarily in opposition to each other? Social justice is a popular phrase these days, even in mathematics circles, but what does it mean? In a recent volume, Mathematics for Social Justice: Resources for the College Classroom, editors Gizem Karaali and Lily Khadjavi describe the work as part of a “national movement to include social justice material into mathematics teaching” [4]. While the volume represents an important effort in bringing discussions around race, gender, class, and power into the college mathematics classroom, I am left wanting more.

Attempts to shoehorn social justice into mathematics curricula perhaps say more about the political leanings of the teacher than anything else. At the same time, we must be wary of diversity initiatives in mathematics which simply reproduce a different class of scientists that perpetuate structures of domination and oppression, in place of work to dismantle the whiteness which mathematics operates as, and to truly equip students for a world of growing inequality and climate catastrophe. After all, would it have been better if it were nonwhite people who developed the atomic bomb? Or the technology to surveil, incarcerate, and deport vulnerable communities?

These small-scale reforms to the system leave the larger problems of capitalism, imperialism, and white supremacy intact. As Piper H. wrote in an earlier post,

“Most of us do not have good role models for what a feminist math department would look like. I have this talk that I give and afterwards, I will often get concerned white men asking me what they can do to fight sexism. But they’re not really thinking about ending sexism. They’re thinking about progress. They want to know which benefits the cis male hoarders-of-power can offer to women so that we don’t feel so bad and complain so much and contribute to such dismal numbers. This is natural, reasonable even, but sexist all the same.”

Indeed, what would a feminist — an intersectional, anti-racist, and class-consciously feminist — math department look like?

Should mathematics be antiracist?

Before we consider the question further, we ought to ask whether mathematics should be doing the work of social justice. Such questions have been asked for some time now in the physical sciences. See the update below.

To be certain, mathematics educators have thought long and hard about the ways in which mathematics education intersects with issues of race, gender, class, and power, at least since Freire’s Pedagogy of the Oppressed [6]. The teaching of mathematics is deeply embedded in politics, and inasmuch as some would prefer to view abstract mathematics as occurring in a vacuum, the social dimension of mathematics education has wide implications.

But what about the majority of college mathematics professors who are not trained in mathematics education but in mathematics? They are highly involved in the production of STEM (science, technology, engineering, and mathematics) majors and the maintenance of power structures in college mathematics classrooms and departments. These mathematicians are not hired primarily based on their pedagogical ability, even at many liberal arts schools.

There are practical and cultural differences between research mathematics and mathematics education (let us admit this binary for the sake of discussion). One could say that mathematics education is concerned about the formation of mathematically literate students, the interplay between oppression, power, and privilege in the context of mathematics education, especially in K-12 settings; whereas in mathematics, we are concerned about mathematics qua mathematics, often as divorced from social reality (except as applied to the physical sciences and engineering). Indeed, in my field, number theory, it is a common boast that the solution of famous problems like Fermat’s Last Theorem are of no immediate practical use. Therefore, simply to attempt to have abstract and socially-engaged mathematics at the same time is to have a kind of a mathematical double-consciousness, and to attempt to bridge the two is a highly non-trivial endeavor.

Nonetheless, one thing is clear: if mathematics is political (and also racial and gendered), then we must be on the side of justice, whatever that may look like. In other words, if mathematics can be antiracist, then it ought to be.

Towards a critical research mathematics

Mathematics education research has made it clear that the teaching of mathematics is a highly political act. But what about the content of mathematics? In other words, what kind of “pure” mathematics might be useful for antiracist mathematics? Is that even the right question to ask? Can the abstractions in college mathematics and beyond, ideas from say, category theory, differential geometry, or abstract algebra open up new ways of critically approaching the social?

In Inequalities, we discussed applications of social choice theory, metric geometry, and random walks to gerrymandering. Some of this follows the work of Moon Duchin’s Metric Geometry and Gerrymandering Group (MGGG) at Tufts and MIT, which is doing exciting work, especially given the upcoming 2020 census. We debated Andrew Hacker’s controversial op-ed, Is Algebra Necessary?, which advocates for replacing the standard mathematics curriculum with “citizen statistics” that would “familiarize students with the kinds of numbers that describe and delineate our personal and public lives.”

We also spent time on fair division, a subfield of behavioral economics initially studied by mathematicians such as Hugo Steinhaus [7], which continues to hold the interest of mathematicians [8]. More complicated fair division problems lead to matching problems in graph theory, for example the Gale-Shapley algorithm in the Stable Marriage problem. The latter was applied to the School Choice problem of matching students to schools, as described in the module [9]. This is an example of a class of problems that construct simplified models of social reality, as one does in the physical sciences, in order to study it.

Another example is the Petrie multiplier, which describes a power law in a model of sexism. The model assumes that men and women are equally sexist, similar to the way that the Schelling model of segregation assumes that people are equally (non)racist, and simply prefer to be with their own kind [10]. One might argue that this approach reveals mathematical laws that force certain phenomena to occur, without discussing how external factors might intervene in reality. Might it be possible for models of social phenomena to account for the complexities of race, gender, class, and nation?

I don’t pretend to have the answers to the questions I am asking. This small sampling suggests a handful of possibilities for mathematics as, say, an intersectional, anti-racist, and class-consciously feminist enterprise. In any case, if we can agree that mathematics can operate as whiteness, then we have a moral duty to ask how mathematics might be otherwise. There is much work left to do. With the strength of our combined mathematical creativity, what might we come up with if we dared to imagine?

Update: (1/2/2020) A previous version cited work of Chanda Prescod-Weinstein that was not yet published. I have removed the reference and apologise for the error. Here is the proper reference. See here, here, here, and here for a sample of the work that is presently published. I readily acknowledge the erasure and antiblack racism perpetuated consciously and unconsciously by nonblack people such as myself, including in science and math, profiting off the work and labour of black people. I’m willing to be called out on that. It was also brought to my attention that there are other people such as Danielle N. Lee, Stephani Page, Raychelle Burks, and Jedidah Isler too who are doing similar work in other realms of science.

References:

[1] Gutiérrez, R. “Why Mathematics (Education) Was Late to the Backlash Party: The Need for a Revolution.” Journal of Urban Mathematics Education 10.2 (2017): 8-24.

[2] Gutiérrez, R. (2017b). Political conocimiento for teaching mathematics: Why teachers need it and how to develop it. In S. Kastberg, A. M. Tyminski, A. Lischka, & W. Sanchez (Eds.), Building support for scholarly practices in mathematics methods (pp. 11–38). Charlotte, NC: Information Age.

[3] Gutstein, E., & Peterson, B. (Eds.). (2005). Rethinking mathematics: Teaching social justice by the numbers. Rethinking Schools.

[4] Karaali, G., & Khadjavi, L. S. (2019). An Invitation to Mathematics for Social Justice. Mathematics for Social Justice: Resources for the College Classroom, 60, 1.

[6] Freire, P. (2018). Pedagogy of the oppressed. Bloomsbury publishing USA.

[7] Steinhaus, H. The problem of fair division, Econometrica 16 (1948), 101–104.

[8] Brams, S.J., M. Kilgour, and Christian Klamler. “Two-person fair division of indivisible items: An efficient, envy-free algorithm.” Notices of the AMS 61, no. 2 (2014): 130-141.

[9] Glass, J., & Karaali, G. (2019). Matching Kids to Schools: The School Choice Problem. Mathematics for Social Justice: Resources for the College Classroom, 60, 155.

[10] Schelling, T. C. (1971). Dynamic models of segregation. Journal of mathematical sociology, 1(2), 143-186.