Supremum/Supremacy

I’m going to say something political that some of you may not like. In the spirit of The Oatmeal, http://theoatmeal.com/comics/believeI’m going to ask you to read to the end before you decide that I cannot possibly have said what I think I said (paraphrasing Rebecca Goldstein, who is summarizing Wittgenstein on Gödel). Thanks, I appreciate it.

Here it is: mathematics is political. In this post I’m going to reflect on what this means, why I believe it, why I think it matters, and what we might do as a result.

The most common reaction to this claim is quintessentially mathematical: please define political. For the purposes of this post, I mean that math is a cultural institution that interacts with systems of power and identity. The next most common reaction is to suggest that I’m sullying mathematics with this thought, hence the request above to suspend judgement.

I’m asking you to trust me, so I should start by talking about my own path to this issue. Some of you may know that I’m on sabbatical this year. My PhD is in mathematics (algebraic geometry), but this year has essentially been a PostDoc in mathematics education research (RUME). I think of myself as bi-disciplinary, and I can code switch between these two communities, though I suspect that I have an “accent” in both communities. With a foot in two separate disciplines, I can’t help but notice the differences in approach, especially around justice, equity, and power. Education research often starts from the assumption that the whole endeavor is about justice, so it goes without saying that we should care about equity and power, though this common value doesn’t always rise to the surface in discussions. Mathematics, in contrast, often starts from the assumption that our work is purely abstract, so when questions of justice are present, they are completely explicit. In my experience, both communities are evolving, heading in good directions with respect to the ways they handle justice; perhaps I want them to converge.

I’ve also been an observer of cultural institutions my whole life. My parents seem to think of themselves as northern transplants who raised children in the south; I certainly never identified as a southerner. They tried to raise me in the Jewish community, though that didn’t take either. Part of this culture is a self-framing as other from the larger culture, and I studied at a bilingual school for years in a language I couldn’t speak outside of school. But I think that the strongest reason that I end up looking at culture like a participant observer is that I’m queer (gay and mildly gender non-conforming, as I see it). The expectations of masculinity, which seem invisible like the rest of culture to many people, have always seemed like rampaging elephants in the room to me. I see lines of power everywhere, from the privilege offered to me as a (white) male to the tariffs that attempt to restrict my behavior in order to support this system. I have, on occasion, been jealous of the people who seem able to move through this world without being so conscious of how they are participating in it.

There are lots of things I like about mathematics, but mostly that it is a thing of beauty to which we all have access by virtue of our humanity. There’s something extremely egalitarian about math: you don’t need permission to think about concepts; other than time, you don’t need expensive spaces or objects to do most of the work; and we each have the authority to validate arguments independently. https://mathbabe.org/2015/01/16/representation-of-women-and-the-genius-myth/Or at least, that’s how I want it to be. I think that these potentially egalitarian facets of mathematics might explain why math is above the trend-line in this famous graph of gender representation in PhDs vs the myth of genius. Of course, the whole point of this graph is that this egalitarian hope is not realized. Many thinkers who have come before me have noticed that declaring math to be independent from identity and power is a double-edged sword. Students in some ongoing empirical work by Matt Voigt of SDSU (@twistedcubic) articulated the fundamental “paradox” of being in STEM: if the work is independent of identity, anyone can do it, but as a result it is also hostile to discussions of identity and hence to people who don’t fit the default image of the field.

We’ve come to the point that will be hardest to hear: regardless of our intentions, when we try to maintain mathematical spaces as apolitical, we are making them hostile. This applies to both professional spaces such as conferences and educational spaces such as our classroom. I know many mathematicians who consciously choose to try to make their classroom spaces safe by keeping them silent on controversial issues, under the assumption that students want a space where they don’t have to think consciously about, for example, their minority status. But my understanding is that this is simply not how it works for our students. Mathematics is centered on cisgender, straight, white males, and our silence allows that default to dominate. In our culture, there are comedians and female comedians; in academia, there is American History and African-American History; in our discipline, there is mathematics and ethnomathematics. It might be tautologous in mathematical logic that black women are black and women, but we know from intersectionality that claiming this identity is simply the sum of its parts has real, negative costs for actual people. Perhaps mathematics is the reine vernunft, pinnacle of pure reason, but this purity excludes people practically and illogically; math is both a supremum and supremacist.

Math is political because it is done by groups of people. Those people construct the narratives of our discipline, and telling any story involves selecting characters and emphasizing a plot; the one I learned is almost exclusively about European men. Groups of mathematicians also have to make decisions together, which is a struggle in many departments. Even at the Institute for Advanced Study, the mathematicians couldn’t come to agreements with Gödel, so they made him the sole member of the logic group to get around their issues.

Math is political because it is shaping our world. Cathy O’Neil argues in Weapons of Math Destruction that “big data” is inequitable and threatens democracy. Mathematical algorithms are filtering the kinds of information that breaks into our personal bubbles, and more subtly our world (especially our hand-held devices) are built around math that has gone from powerful to invisible, meaning they drive our culture when we aren’t watching. Ranking algorithms for image searches literally make diversity invisible. Governmental decisions are made using quantitative reasoning skills that don’t seem reliable, and rejecting the interpretation of data without grounds has become an ideological move. Ironically, we also know that people are disproportionately influenced psychologically by the inclusion of quantitative information in arguments. While I think that quantitative reasoning and math are separate phenomena, we must help lead this nation in the discussion this kind of reasoning as part of citizenry.

Math is political because it is learned by people. School is a cultural institution that, in part, seeks to recreate culture. Math is a critical access point for future opportunity, but it has been a very effective barrier. Inside our classrooms, how do some voices, ideas, and questions become central while others are dismissed or made peripheral? Who has mathematical authority and autonomy? Perhaps math is some abstract thing, but we do math through language often without questioning which language we are using and what that means in terms of our reasoning and the access it affords for individuals. I believe math can be approached from any language, but that reasoning is not done on problems as stated by experts; it is done on the interpretation of those problems made by learners. Declaring that some fields are political while others are not implies that people who care about power and identity belong in some spaces and others do not, and existing in our classrooms without considering power and identity is a privilege offered to only a few students.

I am not the first mathematician to view our discipline as political. GH Hardy’s “A Mathematician’s Apology” wondered about the relationship between our work and the tools of war. Bertrand Russell was famously an activist for pacifism; for a fanciful retelling of the connections between political and logic from Russell’s perspective, I highly recommend “Logicomix: An Epic Search for Truth“. I am sorry that I am unable to quote a woman or person of color from the ancient history of our discipline; more recently, Margot Lee Shetterly’s “Hidden Figures” tells the story of three mathematicians who worked at the very heart of a struggle for an American identity. There are, of course, people within our community providing leadership now, around gerrymandering and the March for Science, not to mention the professional development of new faculty through organizations like Project NExT.

Given that math is political, I think we each have a responsibility for navigating our mathematical spaces intentionally around justice, power, and identity. This responsibility has not really been a choice for the many people who do not match the default identities in our community, so I’m really saying that those of us with privilege need to attend to these questions, especially in our teaching. However, talking about race, privilege, power, justice, gender, identity, and many other topics is often completely absent from advanced training in mathematics. As a result, taking up this responsibility is scary for some people in at least two ways. The first is a concern that by talking about issues like race we will inflame the related wounds and thereby perpetuate racism. I’ve argued above that a colorblind approach is not neutral; you can choose to be silent, but this is still a choice, a choice that hurts some people. Racism will fade from discussions when race is not a salient category to individuals, not because institutions are perfectly silent and everyone forgets. This is not to say that racism isn’t a structural problem sustained by cultural institutions, which it clearly is. In the words of Desmond Tutu: “If you are neutral in situations of injustice, you have chosen the side of the oppressor.” We are authority figures in the classroom, and our silence speaks loudly, even if we intend that silence to be neutral somehow. You don’t want to use your authority in the classroom to impose your partisan views on students, but if you approach discussions of power and identity intentionally, I am confident that you can tell the difference between acts of inclusion and oppression. Summarizing this point: you aren’t choosing between participating or not participating in discussions of justice, you are choosing between participating explicitly or implicitly.

The second concern is both much harder to resolve and much easier to start resolving. What should you actually do and say, especially if thinking about justice is not part of your training or experience? Fortunately, local data at my home institution suggest that it matters more to students that you say something than that you know how to say or do exactly the right thing (though I believe this result to be general). As a result, you can start speaking up without waiting for decades of training first. This goes for both local events (like microaggressions in your classroom) and global events (like elections and hate crimes). Of course, you should seek out professional development sessions and readings, such as the piece that sparked this post or Jo Boaler’s work on open and closed mathematics and classroom materials coming out of sources such as PRIMUS, MAA’s Classroom Resource Materials, and the Journal of Humanistic Mathematics. I’m going to close this post by talking about some of the things that are working for me.

My personal approach is to ground these kinds of discussions in the values used to derive the course design decisions. I teach with inquiry, and I emphasize communication, collaboration, multiple perspectives, and learning from each other because of beliefs I hold about learning. Because I’ve been explicit about these values and design choices, I can connect the kinds of discussions of politics in this post to the course, so it feels related. Moreover, because I’ve built this foundation early in the course, these political conversations are part of the continuity of the course, not breaks from the course to do something awkward that closes completely when they’re over. But pausing your course for a few minutes to talk together about the context in which you are all living is absolutely a useful approach too.

Lately, many of my more vulnerable students have gone out of their way to tell me that they appreciate these efforts to make them feel included and supported. I think this speaks to how small gestures are powerful. I also think I get these comments because a couple of small comments is more than these students expected in math or are getting in most educational spaces. I’ve never had these efforts put a chill on a relationship with other students, in part because I think I’m framing the discussion in terms of commonality in the classroom, but I doubt a student would really wander into my office to tell me that they disagree and feel that some students shouldn’t feel welcome in my courses.

Authentic vulnerability is at the core of my approach. I feel a responsibility to be a multi-dimensional, whole person with my students. I ask them to be vulnerable and brave in making their thinking visible in the classroom, so I must reciprocate. I might be the only gay academic they ever meet; if I declare beforehand that this aspect of me is categorically invalid in my discipline, then these students could never know a queer mathematician. I’m trying to shift authority to the students, so I can’t try to be an invisible force with inscrutable decisions, I need to be a person who makes choices for reasons.

I should be clear that I know that my approach uses my privileges. I am white and male, so I get the benefit of the doubt in terms of content expertise and course design authority. Conversely, I think my queer identities open doors by helping students make sense of why I case about justice and attend to their socio-emotional states. In the last 15 years, I have seen students be extremely disrespectful to female colleagues if they are casual with students like I can be safely; I think I must keep reflecting on the structural impacts of the ways that I move through these spaces. In particular, I am not suggesting that you do what I do – I’m suggesting that you find a way to use who you are to acknowledge and integrate the political (justice, power, identity) aspects of mathematics into your classrooms and professional spaces.

Thank you for reading to the end. I’ve asked you to look at a subject you may love for being impersonal as being inseparable from the personal; I’ve asked you to accept responsibility for inequity; and I’ve asked you to be vulnerable and do something new for which you may not have been trained. I’m not asking you to abandon what you love about math; I’m suggesting ways that you can help realize that dream and spread that love.

This entry was posted in cultural pressure in academia, equity, implicit bias, intersectionality, introduction, math education, social justice. Bookmark the permalink.

9 Responses to Supremum/Supremacy

  1. Kimberly Morrow-Leong says:

    Thank you for making the journey to the center, of mathematics and education. Glad to have you.

  2. Julie says:

    this is great. Thank you.

  3. Laura Moss says:

    Circumstances in my situation have pointed me along a similar path. Your comments and references are appreciated. Thank you.

  4. Phil Hart says:

    I will start by saying thank you to Brian for taking the trouble to think about, write about, and post these words.

    As somebody who failed in a very spectacular fashion as an undergraduate student of mathematics in his first year, it is with some hesitation that I write these words, which perhaps illustrates one or two of the points in that post. The best that I can offer by way of reply to Brian is a description of my own perspective.

    I see mathematics as embodying a set of ideas. I am aware this set of ideas exists in a social context. Brian’s post makes explicit many facets of that social context.

    At this point, I am forced to fall back on my own experiences as both a learner and an educator of mathematics.

    As a student of mathematics from kindergarten to high school, the impression given to me by all my teachers was that *all* mathematical problems had known solutions, and it was the task of the students to learn those solutions. It was some years later that I realised that this is not the case – Departments of Mathematics are in the business of research after all – and I found myself delivering mathematics at high school level. While this amounts only to anecdotal evidence, I discussed this issue with one of my students at the end of the course: he was astonished to learn that there are numerous unsolved issues in mathematics, this despite that knowledge informing my own teaching. This is perhaps an area worthy of research.

    I am going to take issue with the notion of ethnomathematics. Even the usage of the word is suggestive of cultural discrimination. While European mathematics perhaps constitutes the bulk of mathematicians and users of mathematics, they are nevertheless an ethnic group. Whenever I work with people who might be termed as ethnic users of mathematics, my perception is that the same underlying ideas are being used in a different social context. By way of example, some parts of the world divide the year into six, not four, seasons. By the same token, Roman numerals could also be considered “ethnic”.

    The factory of model of education works for some learners in some subjects. By way of contrast, I have worked with classes where some learners required one-to-one tuition to overcome their phobia of mathematics. I have yet to find any business or government body prepared to fund such tuition.

    I see innumeracy as a major issue for society. At the personal level there are people who make poor economic choices because they lack simple computational skills. I have also seen examples of teachers of both children and other teachers whose grasp of mathematics is so poor that they teach untruths: “There are six days in the week because Sunday the 8th minus Monday the 2nd is only six days”, and “3^2+4^2=5^2 proves the Pythagorean Theorem”. I see politicians cite irrelevant statistics to push a particular political agenda and much of the electorate is ill-equipped to see through such ruses: “We are the world’s safest airline with NO accidents … but we have never flown anything.”. We have here a cycle of misinformation being used to perpetuate misinformation, and I see it as a very difficult cycle to break.

    Finally, and on a personal note, it always gives me great pleasure to see the joy of learning on somebody’s face regardless of how either they or society chooses to label them.

    • Brian Katz says:

      I agree that “ethnomathematics” is a deeply problematic term; I think I’m hinting in the post at the kinds of critiques you start discussing. In my undergraduate music major, there was a music history sequence and a world music course – that was the/a moment that I realized these kinds of perspectives are built into our systems.

  5. Linda Leckrone says:

    A very interesting read. As a nontraditional graduate student in both math education and mathematics, as well as a teacher of mathematics, I agree that the worlds must be mixed. I’ve also felt for decades that math is not apolitical. If it was, we wouldn’t turn off so many women.

  6. Johan Richter says:

    Is 1+1=2 a political statement? Presumably the author of the article would protest that this is not what he meant, but unfortunately he singularly failed to make clear what he does mean by math being political. Of course math has the occasional political application but that hardly makes mathematics political and neither does any of the other things the author cites.

    As for using this supposed political charge of mathematics as an excuse to bring politics explicitly into the classroom, it seems like an utterly terrible idea. Perhaps the author is assuming that most mathematicians share his political views, or that in the current American campus climate only his fellow social justice warriors will dare use the invitation to speak about politics in the classroom, but if/when the political climate on campuses changes he may regret having dragged politics into mathematics.

    Finally, I want to comment on the following statement:

    “but I doubt a student would really wander into my office to tell me that they disagree and feel that some students shouldn’t feel welcome in my courses. ”

    The author seems to be suggesting that anyone who disagrees with his suggested teaching practices most be doing so because they want students not to feel welcome. With that attitude it is hardly surprising no student has voiced criticism of his teaching practices to his face. And it makes his claims of inclusiveness look rather ironic.

    • Adriana Salerno says:

      It’s nice that some of you have moved on to other posts we’ve written. I don’t think you understand the post, so I invite you to read it again. Better yet, I invite you to read all our posts, because it will give you a better idea of where we stand. Finally, “the author seems to be suggesting” and all your other guesses make me think that you are reading what you want to read (and be angry about) rather than truly engaging with the text, which I thoroughly invite you to do.

      • Phil Hart says:

        I agree with Adriana’s polite and thoughtful reply to Johan. I also see Johan’s comment as being precisely one of the things that Brian was referring to in his post.

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