The October 2020 issue of the Notices of the American Mathematical Society contained an open letter calling on the mathematics community to boycott collaborations with police and demanding, in particular, that we stop providing law enforcement with the mathematical technology they increasingly rely upon to terrorize Black and brown poor and working class people. The letter mentions the deeply racist feedback loops that predictive policing creates, and points out that predictive algorithms grant the police an unearned veneer of scientific legitimacy.
Alongside the open letter, the AMS published three other letters: one by Ingrid Daubechies, Ezra Miller, and Cynthia Rudin; another by Daniel Krashen, who was also given space to write a separate article expounding on his opinion; and the third by Sol Garfunkel. The arguments in these letters vary, but all oppose the boycott in spirit.
We, the Just Mathematics Collective (JMC), are a collective of mathematicians formed during the 2020 Black Lives Matter rebellion. Our goal is to shift the mathematics community towards justice via anti-racism, anti-militarism, and solidarity with the Global South. We acknowledge the role that mathematics plays in sustaining injustice, and the potential it has for creating a freer world built on mutual care and collaboration.
As such, the JMC wholeheartedly supports the boycott and the purpose of this statement is to respond to these three letters and to Daniel Krashen’s article. [1]
There are JMC members who helped co author the “boycott letter”, but there is no containment in either direction. The boycott letter predates the JMC and the JMC takes specific political stances that are not articulated in the boycott letter, and not necessarily shared by the signatories of the boycott letter. As we will explain, we support the call for a boycott for reasons that go beyond the original letter’s arguments.
While we agree with the claims made in the call for a boycott regarding the racist feedback loops inherent to predictive policing algorithms, our opposition to collaboration with police does not rely on problems with specific algorithms and instead rests on a more fundamental contention:
The role of the police in US society is to protect racial capitalism with coercion and violence. Thus, even if it was possible to create a predictive policing algorithm 100% free of racial bias, providing such an algorithm to the police would constitute an act of oppression.
Therefore, we will not rehash arguments summarized by the authors of the boycott letter about the specific effects of these algorithms.
We emphasise that our position is political, as is any position on the matter of collaboration with police, whether or not that is made explicit. The JMC arrived at our stance not by finding a mathematical error in the literature on predictive policing algorithms. Our position rests in the political tradition of abolition and an understanding of the historical and present role of the police in maintaining unjust and racist structures of political and economic power.
In his article, Krashen claims that “police patrolling will not simply end.” With these few short words, Krashen dismisses decades of political organizing and theorizing by workers, prisoners, and Black feminist thinkers who have dedicated their lives to building a world in which police patrolling will indeed end. No one expects this will happen “simply”, but a major obstruction to its happening at all is an unimaginative collective assumption that it is impossible.
All three of the letters (as well as Krashen’s article) are rife with such assumptions — for instance, that the status quo of throwing people in cages as a means of addressing social problems is a necessary aspect of human society. Crucially, the authors do not explicitly acknowledge that these are deeply political assumptions, and instead obscure their political assumptions with claims to scientific objectivity.
Unlike those advancing these disingenuous arguments, the JMC freely admits our subjectivity — what we state here are our political opinions and we do not pretend otherwise. We see a tendency in the mathematics community to characterise as “rationality” the practice of ignoring lived realities, historical facts, and moral and political questions; unlike some of our colleagues, we will not allude to our “objective analyses” and “logical insights” when making our arguments. Our stance derives from being humans observing actual social and material conditions; from seeing the impacts of prisons and police on our communities, friends, and family; and from engaging in the basic human practice of envisioning a more humane and just world.
To help frame what follows, we list below some historical facts and political opinions that undergird our position.
- Historical fact: The police in the US derive from slave patrols and private strike-breaking forces [2]. There is a direct, well-documented throughline from these origins to the modern day quasi-military forces on our streets [3], and a consistent pattern of collusion with white supremacist vigilantism, fascism, and the far-right [4].
- Political opinion: The true purpose of policing is to preserve “social order”, racial capitalism, and patriarchy [5]. The many connections between the police and explicitly white supremacist groups and movements are no accident, but are in fact an inevitable consequence of the nature of police. Therefore the racism, classism, ableism, sexism, transphobia, homophobia, and general inhumanity that is endemic to modern policing cannot be reformed away. [6]
- Historical fact: Prisons were introduced as a reform, as a means of moving away from gratuitous and unpopular capital/corporal punishment [7]. In the US, prisons have evolved from the paternalism of the early penitentiary and the horrors of the convict leasing system into a massive industrial complex in which prisoners — disproportionately Black and brown people — are treated as raw material [8].
- Political opinion: The US legal system is set up to criminalize non-whiteness and poverty, and to subjugate Black and brown communities through physical violence (via the police, immigration enforcement, and the military), and through the restriction of movement and other basic human rights (via prisons, detention centers, and militarized border zones). In anything resembling its current form, it is incapable of delivering true justice or healing.
- Historical fact: The US legal system has a long history of creating conditions in which sexual and other gender-based violence proliferates. This includes the rampant sexual violence in US prisons [9] and immigration concentration camps [10], as well as the long, ongoing [11] history [12] of forced sterilizations and other eugenics practices [13]. It also includes the system’s tendency to neither investigate [14] nor prosecute [15] intimate partner violence. Gender-based violence disproportionately affects women, children, and LGTBQIA+ people of color.
- Political opinion: White supremacy is deeply intertwined with patriarchy [16]. To those in power, gender-based violence is a desirable feature of the legal system and the misogynistic [17] violence perpetrated in prisons is deeply connected to the misogynistic violence that exists more broadly in society [18]. The fact that all of this overwhelmingly affects communities of color is by design. Abolishing the police and prisons is a fundamentally feminist objective, and patriarchy can not end without achieving it.
- Historical fact: There is little evidence that policing and prisons have reduced social harms, or even that they have much of a reducing effect on the rate at which legally defined crimes are committed [19]. They have, however, sanctioned many physical and social harms and concentrated violence in specific locations from which there is no escape [20].
- Political opinion: Criminalization is a weapon used by the state to buttress its repressive power, and crime — a legal construct [21] controlled by the white supremacist state — should not be confused with harm. Neither policing nor prisons are compatible with an ethos of valuing human life over profits and property, and thus a commitment to humanity requires the abolition of both.
We emphasize that when we make a distinction between “historical fact” and “political opinion”, we are not assigning more worth to one over the other. Many truths are considered opinion and valued less than fact (or erased altogether) by those in power merely because they represent experiences of oppressed people. We will not buy into this devaluation. On the contrary, we often cherish our opinions more dearly than historical fact, since it is ultimately opinion — informed by fact, experience, and feeling — that we use to calibrate our moral compasses and political aspirations. The italicized sentences at the end of each opinion above demonstrate this calibration in action. What we call facts are simply statements represented in the academic historical record for long enough that even the most elitist academics — those who dismiss the lived experiences of marginalized people when they do not appear in the pages of exalted journals — would be forced to admit are true.
Guided by these truths, we now outline some of the assertions mentioned by Daubechies-Miller-Rudin and Krashen and respond point-by-point [22].
“To boycott all interaction between mathematics and police, without any stated demands or termination criteria, fails to recognize the positive potential of mathematics in contributing to whatever concept of law enforcement is envisioned by the movement” (Daubechies-Miller-Rudin)
JMC response: There is no one concerted “movement.” As in any time of political turmoil, there are many voices, expressing many needs and political desires simultaneously. There is, however, a powerful contingency of everyday people, organizers, workers, thinkers, prisoners, and of course those at the intersections of several of these categories, who envision the complete non-existence of police.
We ask the reader to imagine an extinct institution sufficiently heinous such that no engagement with it could possibly have a positive impact. For example, considering the origins of policing in slave patrols, imagine a proposal that scientists of the mid-nineteenth century outfit slave catchers with improved “technology” in an effort to make that practice somehow more humane. We hope the absurdity of this is clear, and we emphasize that such a proposal would have served a political purpose: putting an utterly unearned patina of humanity and legitimacy on the institution of chattel slavery.
“When software developed from mathematical insights for use by law enforcement turns out to promote racist outcomes, it is irresponsible to launch a boycott, cutting short efforts to solve the problem.” (Daubechies-Miller-Rudin)
JMC response: The fundamental problem is not that the software merely happens to promote racist outcomes; the problem is policing itself. The purpose of a boycott is not to disengage from the problem, but to begin finally engaging with it. We support the call for a boycott precisely out of our sense of professional responsibility as mathematicians. We would instead suggest that it is irresponsible to assume certain answers to basic political questions and then restrict our role to technical tinkering within the framework of those (in fact highly contestable) answers.
“Instead of refusing our expertise, why not offer our services with increased fervor…?…Withdrawal is not the solution.” (Daubechies-Miller-Rudin)
JMC response: The only sort of “withdrawal” proposed by the boycott is withdrawal from a position of complicity with a murderous institution. By boycotting, we engage with this issue on our own political terms. And we are committed to fighting for a future in which this quote ages extraordinarily badly.
“…it is critical to realize who our allies are, and to come together in common cause and not pull apart. When we engage in personal attacks and in casting doubt on our colleagues…we risk the destruction of the atmosphere needed to move forward.” (Krashen, Response to the boycott)
JMC response: We are accountable to our friends, our families, our broader extra-mathematical communities, working class people, prisoners, and others deemed disposable by American empire and racial capitalism. The JMC would be honored to be considered allies and accomplices to all such people. So on this point, we agree: it is critical that we realize who our allies are. On the other hand, we have no allegiance to fellow academicians who profit from the brutalization of Black and brown people by selling their expertise to the police.
While the JMC has no issue with criticizing individuals when criticism is warranted, we are confused by this reaction to the call for boycott, as no individuals were explicitly targeted by the boycott letter. We recognize that an effective boycott can cause damage to finances and reputation, and to the mathematicians who are financially and intellectually invested in predictive policing, we say: we are not aware of any clause in the call for boycott that precludes your joining. We believe that everyone is capable of transformation and growth.
“If mathematicians, scientists, and others don’t come together to help formulate algorithms about patrolling, we can do little to influence the potential bias the police can (and likely will) bring.” (Krashen)
JMC response: We reject this claim as false, and also reject it as an insult to decades of organizing and community care that have taken place outside of hallowed academic halls. Mathematicians and scientists can have a tremendous impact on policing by joining the fight for abolition, led courageously by non-scientists and non-mathematicians (at least not in the professional sense). It is in this spirit that the JMC considers participation in the boycott to be a meaningful scientific and political contribution. If mathematicians are intent on designing algorithms related to patrolling, we would call on them to create open access technology for the people, perhaps to help them maintain safety in their communities, including safety from the police.
“This is the time to engage with our colleagues, who have developed and refined their expertise to think deeply about these problems, and who have developed a dialogue with various social institutions” (Krashen)
JMC response: We find offensive the implication that someone who has developed a predictive policing algorithm should be considered an expert on prisons and policing on that basis alone. It is in fact far past time to engage with the real experts on policing and prisons: prisoners and formerly incarcerated people, Black and brown organizers who are leading the fight for abolition, and the working class people whose daily lives are affected in concrete ways by these oppressive systems. Even within the extremely narrow realm of academia, mathematicians who design policing algorithms can not claim the title of expert. This mantle belongs instead to our colleagues in the social sciences and humanities who have spent years thinking about the societal harms caused by policing, prisons, and overcriminalization, as well as the reasons these oppressive systems were created in the first place.
Our sense of morality does not come from having earned an advanced degree or from being deemed expert in a discipline. It comes from being human, from having human experiences, and from learning from the experiences of others. We therefore can not afford to take seriously the proposal that we leave the question of how to engage with the police up to the very people who have the most personally invested in ensuring that the relationship between mathematics and law enforcement remains fundamentally unchanged. We hope the reader can acknowledge the irony of chastising boycott as disengagement, while also suggesting that any mathematician who is not already working with the police should not play an engaged role in deciding whether these collaborations should even exist.
Most of all, we hope our community sees past the shallow arguments made in opposition to the boycott of police collaboration. We look forward to a new culture in the mathematics community, in which issues of ethics and politics are honestly considered at every point of interface between mathematics and the broader community in which it is embedded. Mathematics should be for the people! And so long as we continue to use our training to empower institutions which aim to oppress and brutalize, it can not be. We can collectively build the power to shape our community and move towards a more just and free mathematics. How will you help to claim and exercise that power?
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In the spirit of Krashen’s advice to engage with and learn from those with genuine expertise, we conclude this statement by honoring on-the-ground organizing that has inspired us and that is happening in the cities and states where Daubechies-Miller-Rudin (North Carolina), Krashen (Georgia until recently, and now New Jersey), and the AMS headquarters (Rhode Island) are located. We ask our mathematical community to support these freedom fighters in any way it can:
Black Workers for Justice (North Carolina)
Southerners On New Ground (with chapters in several southern states, including Georgia)
Vietlead (Philadelphia and South Jersey)
Direct Action for Rights and Equality (Providence, Rhode Island)
If these arguments resonated with you and you are interested in becoming involved with the JMC, you can reach out to us here:
justmathematicscollective@autistici.org
Endnotes
- The boycott has been criticised as an inappropriate tactic — Daubechies-Miller-Rudin’s letter cites the lack of “specific demands” or “termination criteria”, but we find a boycott of the type advocated in the original letter to be tactically appropriate. It is true that sometimes boycotts ask people to withdraw their participation in some activity in an explicit way, until explicit conditions are met, at which point participation resumes. For example, customers of a business in a labour dispute with workers may withhold their business by, say, refusing to cross a picket line; in such cases, the boycotters have specific leverage and there are explicit “termination conditions”. However, boycotts can also be used to express — and foment — community disapproval of some state of affairs even in cases where most participants do not have much direct leverage and where the notion of “termination conditions” makes no sense. In such cases, the idea is to build cultural norms against some unacceptable activity. There can’t be termination criteria for the mathematical boycott of police collaboration, because there are no conditions under which it will be acceptable to collaborate with an illegitimate institution. Most of the boycott letter signatories are presumably at no risk of collaborating with police, but by signing, they have publicly expressed disapproval of an intolerable state of affairs and helped to prefigure a culture where oppressive uses of our expertise are less professionally acceptable. To that extent, the boycott is a useful political tactic.
- See e.g. P. Reichel: https://www.ncjrs.gov/App/Publications/abstract.aspx?ID=116023 and A. Vitale: https://www.vice.com/en/article/7kpvnb/end-of-policing-book-extract
- For a thorough account of this history and the current state of affairs, see Alexander, Michelle (2010). The New Jim Crow: Mass Incarceration in the Age of Colorblindness. New York: The New Press. ISBN 978-1-59558-103-7.
- Recent infiltration of American police by white supremacist and far-right groups is well documented in news media; see e.g. https://theintercept.com/2017/01/31/the-fbi-has-quietly-investigated-white-supremacist-infiltration-of-law-enforcement/ or https://www.theguardian.com/us-news/2020/aug/27/white-supremacists-militias-infiltrate-us-police-report. There is also considerable historical documentation of the relationship between formal policing and white supremacist vigilantism, and the process of replacement of racist vigilante violence by racist police violence during the 20th century (see e.g. Silvan Niedermeier’s The Colour of the Third Degree).
- See e.g. R. Wilson Gilmore’s Golden Gulag, or for a shorter and online accessible read, G. Potter’s The History of Policing in the United States
- This article by M. Kaba makes this point in more detail: https://www.nytimes.com/2020/06/12/opinion/sunday/floyd-abolish-defund-police.html
- This is again documented extensively. For example, Chapter 3 of A. Davis’s Are Prisons Obsolete? contains a very useful account of the genesis of prisons.
- See e.g. A. Davis, Masked Racism: Reflections on the Prison-Industrial Complex.
- See https://www.bjs.gov/index.cfm?ty=pbdetail&iid=4881 for a government study on sexual violence in prisons. Almost half of reported sexual assaults in prison are perpetrated by guards, see e.g. https://www.propublica.org/article/guards-may-be-responsible-for-half-of-prison-sexual-assaults. Sexual assaults are uniformly underreported (and it would stand to reason that this underreporting is even more dramatic when the perpetrator holds immense power over the victim, e.g. guards as perpetrators and inmates as victims), so undoubtedly these numbers should be higher.
- For a general discussion on the widespread nature of sexual assaults in DHS concentration camps, see https://theintercept.com/2018/04/11/immigration-detention-sexual-abuse-ice-dhs/ or https://www.nytimes.com/2019/02/27/us/immigrant-children-sexual-abuse.html
- For an account of the current allegations against ICE concentration camps, see https://projectsouth.org/wp-content/uploads/2020/09/OIG-ICDC-Complaint-1.pdf
- For a brief summary of the history of forced sterilization by US law and immigration enforcement, see https://www.ourbodiesourselves.org/book-excerpts/health-article/forced-sterilization/
- For an in-depth discussion about the global history of the eugenics movement and its current successors—and the role that scientists play in defending and facilitating it—see A. Saini’s book Superior: The Return of Race Science.
- Less than 1% of rapes lead to felony convictions. See e.g. https://www.rainn.org/statistics/criminal-justice-system
- There are hundreds of thousands of untested rape kits lying in storage in US police departments, some dating back decades. For a general discussion, see https://www.theatlantic.com/magazine/archive/2019/08/an-epidemic-of-disbelief/592807/
- For an introduction to the notion of intersectionality, see K. Crenshaw’s article Mapping the Margins: Intersectionality, Identity Politics, and Violence Against Women of Color, 43 Stanford Law Review 1241-99 (1991).
- For the notion of misogyny that we have in mind here—the system which serves “to police and enforce” patriarchal norms—see e.g. K. Manne, Down Girl: The Logic of Misogyny.
- See e.g. A. Davis’ article Public Imprisonment and Private Violence: Reflections on the Hidden Punishment of Women in the edited volume Frontline Feminism, ed. M. Waller and J. Rycenga. See also K. Crenshaw’s article From Private Violence to Mass Incarceration: Thinking Intersectionally About Women, Race, and Social Control, 59 UCLA Law Review 1418 (2012).
- See e.g. https://www.scientificamerican.com/article/do-prisons-make-us-safer/ or https://eji.org/news/study-finds-increased-incarceration-does-not-reduce-crime/. Consider also that data on crime rates sometimes ignore crime that takes place within the prison system. Arguments for policing and incarceration as means of ensuring “public safety” therefore sometimes take the implicit position that incarcerated people are not part of the “public”, or not entitled to safety.
- A recent grim summary: https://newrepublic.com/article/153473/everyday-brutality-americas-prisons
- Consider that there are thousands of federal and state criminal statutes — an accurate count is considered prohibitively difficult (https://thehill.com/opinion/criminal-justice/473659-america-has-too-many-criminal-laws). This alone places tremendous and arbitrary power in the hands of the criminal legal system, and gives lie to the claim that police and prisons are primarily a democratic mechanism for maintaining justice or safety.
- While we believe Garfunkel’s short letter was intended to further dismiss the boycott, it is not directly relevant to the boycott since its focus is Andrea Bertozzi’s AWM lecture; the JMC celebrates the decision not to hold this lecture but will not address this here.
The 2021 Joint Meetings of the Mathematical Societies (JMM) will be held virtually January 6-9. Continuing our tradition, this post highlights events at this virtual meeting related to diversity, equity, and justice. In particular, I built the list below be reading the program and noting invited presentations and sessions having either titles indicated that some aspect of diversity/equity/justice would be the focus of the talk or sponsorship by group including NAM, AWM, Spectra & Math Alliance.
An event like this contributes to the visibility of queer people and our accomplices/allies, and a major theme of our conversation was the fact that each of us, by virtue of existing, queered spaces by being in them, from the rugby pitch to mathematics conferences. But for this post, I’d like to reflect on the ways that I saw our queer identities influencing our mathematics.
“Different Differences”. He started by telling us about some of his identities, which developed into an observation that our community treats some identities like race and gender as “standard” differences and often ignores others, like his gay and Caribbean identities. Ron reminded us that the data about representation in the higher education mathematics are sparse (and shameful) for the “standard” differences and often completely absent for the “different” differences. But Ron’s title also applies to the overview he gave of his research. Using calculus-based methods, we describe continuous change using a limit of an average rate of change, and this process can be discretized in multiple ways. Discretizing the most famous definition of a derivative leads to what is often called a forward difference, but those of who have taught calculus will be familiar with versions that could be called backward or center differences, corresponding to various ways to draw secant lines to continuous curves near a point.
Ron’s observation was that these three approaches all implicitly assume that the width of the approximations, h, will approach 0 linearly. In what I saw as the first example of queering
mathematics in the session, Ron demonstrated how we can reject this assumption (i) by replacing the role of h with more interesting functions that still approach zero on the order of h to get “non-standard differences, which he would like to name Mickems differences, after Ron Mickems, and (ii) by taking non-local discretizations, which felt to me like a radical reorganization of an approach to discrete difference modeling.
which she explicitly framed as “queering uniqueness”. Emily’s work is in category theory, a subfield that I see as overtly working to reconsider and rebuild the foundations of mathematics, and this talk showed how we might think of that agenda as a queer one. Emily started from the idea of the first fundamental group of a topological space, which is a group made of all loops at a base point in the space with the (associative) operation of composition (or concatenation). If we loosen the restriction that the paths be loops, allowing them to start and end at different points, we lose the ability to compose an arbitrary pair elements, so Emily’s core question became: when it is possible to compose them, how unique is that composition? Is it unique enough for associativity? She built a tetrahedron representing a homotopy that answers this question affirmatively, but she wanted to step back even further. Uniqueness can be quantified as: there exists an x such that, for all y, x=y. Interpreting this from a categorical perspective, this became the sum over all x of the product of all y of the set of proofs that x=y, where sum and product are adjoints of the pull-back, and uniqueness because the observation that this is a contractible space, which can be proved without referencing the base topological space. I am personally drawn in powerfully by this kind of work in category theory, which reimagines the foundations of what had seemed necessary in mathematics and logic in ways that feel analogous to the work of reimagining the messages of what had seemed necessary in society for gender and sexuality.
Third, Juliette Bruce told us about “Computing Syzygies”. This is a classical subfield that owes a lot to Emmy Noether, but Juliette’s overview showed how there is still so much we don’t know about the relationships between monomials! In light of the themes of queering mathematics above, one particular move by Juliette stood out to me. Her research has made progress in understanding syzygies by bringing tools from applied mathematics for computing with enormous matrices to bear on what had previously been viewed as a classical, abstract problem. While it might be a bit of a stretch from the talk, I see this as Juliette rejecting the false binary of abstract and applied mathematics. I was pulled into algebraic geometry as a graduate student because I like the double vision of seeing objects from both algebraic and geometric perspectives, and I’ve long felt that the most exciting mathematics brings this kind of binary-rejecting double vision to approach problems from new directions. And while we didn’t get to hear about Robin’s work during this event, in a later communication they offered a sketch of a similar interpretation of some of their work in virtual knot theory in which some functions require or break a binary.
Combinatorial: A gay mathematician’s journey”. He told us about his efforts to be an out, proud, mathematician as well as the challenging ways environments have resisted these efforts. In his overview of his work, he described efforts that overlap abstract and applied mathematics, similar to Juliette, in complex network analysis. He studies the hidden geometry behind complex networks, such as social networks, showing how complex social networks often reduce to a small number of characteristics (the dimensions in this hidden geometry). I might be reaching to claim this as queering the mathematics, but this hidden geometry certainly reminds me of Ron’s different differences and my own experiences learning to see implicit social structures that my non-queer peers could safely ignore. Anthony also turned the connection I’m making in reverse, perhaps mathing queerness, stating his axioms for mathematics and diversity/equity/inclusion work that remind me of Federico Ardila’s axioms. In both situations, mathematicians are using the disciplinary concept of an axiom to structure their approach to justice.
This article was written for the Early Career Section of the Notices of the American Mathematical Society. It will appear there in the January 2021 issue. We are sharing the article as a preprint in the hopes that it will be useful for folks this fall as they work to build equitable
online spaces during the ongoing pandemic. Thank you to Angela Gibney for inviting us to write this piece for the Early Career Section and thank you to Brian Katz and the other inclusion/exclusion editors for giving us the chance to share it early via this blog. 
serve the mathematical community. And you want your program to be effective, inclusive, and equitable—and these days, probably online. What should you do?
choosing a need to address, designing the structure of your program, and then carrying out your plans. It is important to bring the same care and judgement to designing your “broader impacts” that you use to craft your research program: we must choose which problems to work on, understand the literature, and find some initial insight on how to tackle the problem—an “edge”.