This week, I was separated by small degrees from two separate acts of 
terrorism motivated by hate. (1) Students and faculty/staff on my campus had set up a local version of The Clothesline Project, in which survivors of sexual 
violence and those close to them write affirming messages on t-shirts that are displayed on a clothesline. Someone set part of the clothesline and the shirts on fire. (2) Dr Rochelle Gutiérrez, whose research integrates ideas of access, identity, power, and achievement in mathematics education, has written about how white privilege is perpetuated by the ways we view and practice mathematics. She is being doxxed and threatened by conservative sites on social media. [As you may have guessed, the examples in this post may be intense for some readers.]
Complicit Function Theorem: Acts* of violence, intimidation, and hatred will happen if and only if the agents of these actions can view themselves as part of a larger group that agrees with them and believes that it is on the side of right.
Corollary: In particular, not participating in overt aspects of oppression is not sufficient to stop acts of violence, intimidation, and hatred; the majority must be overtly and actively anti-oppression. A silent majority that simply does not engage in these acts is complicit in the hateful outcomes.
Proof: Sadly, the full proof will not fit in the margins of a blog post, and the people 
who most need to read it have almost certainly already merged back into The Onion’s shrieking white-hot sphere of pure rage. I’ll start with a few comments for people who want to be allies but aren’t sure how to avoid being part of the problem, and then I’ll transition to a brief summary of some recent ideas about how to support scholars under attack that seem particularly salient for mathematics and mathematics education.
The proof of the forward direction relies on this idea: No one thinks they are really the villain in their own story, so the agents of oppression must have assigned themselves other roles. I’m aware of at least two such roles: the avenging victim and the fore-running soldier. The avenging victim has been, in their minds, mistreated and pushed past a breaking point. For example, the narrative around the 2014 shooting in Isla Vista fits this model; the male shooter had posted on YouTube that he was going to take revenge for being rejected by women, who were not giving him what he believed he was owed. Perhaps the avenging victim is part of a group that suffers this mistreatment, but it’s critical that they believe that no reasonable observer would even think to question the umbrage they take at the offense. The fore-running soldier is part of an army that is tasked with work that, they believe, the larger community agrees is necessary but is too squeamish to undertake. For example, the narrative around the torch-carrying mob in Charlottesville fits this model (as do the lynchings by the KKK that their march references); the man who drove his car into anti-hate protesters (and the associated proposed laws to make this action legal) appears to be the kind of action of an advance scout for a larger army. This fore-running soldier might or might not be the first to take matters into their own hands, but it’s critical that they believe they are the active arm of a community, carrying out the will of the larger group. In both archetypal narratives, the hero believes that they are acting with the support of the majority (or at least the generic member of the majority who has the special information to which they are privy). This backing is essentially the assumption of privilege that will protect them from retaliation. In both cases, I claim that the agent can only build this identity embedded in a larger community that at least silently acquiesces to their perspective and interpreted identity. Even the martyr assumes that their fall will teach others their truth, but this assumption too will not function in the presence of active commitments to other worldviews. The proof of the converse relies on the idea that silence means siding with oppressors, and this loud but silent message will certainly radicalize individuals if it is the only force at work.
Turning from the agents to those of us around them, I can see at least two sub-populations. On a spectrum of thought, those closer to the agents agree with their critiques: that it’s sexist to make men who have not committed sexual assault feel uncomfortable about benefiting from rape culture, that bringing identity into discussions of mathematics is ruining an otherwise pure and universal field. They can abhor the violent acts of the agent while viewing themselves as good people who would never act like that, even as they view the survivors and equity scholars as the ones to blame for going too far or forcing the agents of oppression to act. This group can genuinely feel good about supporting a weaponized version of free speech while creating the kind of hostile environment that allows agents to harass and assault others, especially people without their privileges. I view Milo Yiannopoulos’s harlequin as the most extreme version of this sub-population, but I know many more reasonable people who feel they’ve experienced reverse racism or that are interpreting movement towards equality as oppression. Those further away from the agents of oppression can disagree with their actions but still remain silent. People from this group can feel unqualified to address
certain topics, can feel that others can or should do the work, or can simply be unaware. Sadly, I think many mathematicians fall into this category, in part because neither our training nor our evaluation intersects with concepts of justice in most cases. I empathize with the thought that many STEM faculty are not trained to lead discussions about equity, but our silence on these topics tells students that only some faculty care about justice, and our classrooms and buildings are safe places for both students and teachers who are uncomfortable with these conversations, for any reason. Combined, the silence or obtuse support of these two sub-populations is heard by an agent of oppression as a message: a wide swath of our community agrees with (or at least doesn’t disagree with) me, though they may not be brave enough to act. I’ve labeled the people who take overt action in support of oppression as agents, but the point of this piece is that we’re all agents, perhaps sleeper agents rather than field agents, unless we stand against oppression in public.
From this perspective, everyone who is even vaguely willing has a responsibility to be visibly anti-oppression. I do not have a universal standard for what this takes. One of my humanities colleagues, who is a white, cis-gender male, observed that he thinks that the threshold is higher for him than for me. I am openly queer with the surname Katz at a Christian-affiliated school, while he fits essentially all of the categories of privileged identities on campus, at least on the surface, so the default assumption about our stances toward justice might be different. This doesn’t absolve me of responsibility to be overtly anti-oppression, of course. As a mathematician, I think people assume that I can’t and won’t discuss justice with students, so I must work to make my classroom a place where these topics are appropriate, as I’ve written elsewhere. I’ll wrap up the analogy to the Implicit Function Theorem by pointing out that I’ve articulated mild conditions on a community that are sufficient to produce structure — structure that we don’t want in this case.
This post is focused on the way that the majority of people, especially people with privilege, bear a responsibility to make our public spaces healthy, in much the same way that people 
with functional immune systems bear a responsibility to get vaccinated so that as a community we have sufficient herd immunity to diseases so that outbreaks don’t become epidemics. I’m essentially advocating for bystander intervention against bigotry, violence, and hatred. This model seeks to counteract the social distance effect (namely, individuals are less likely to disrupt attack on targets who seem further from their group identities) by making intervention easier and by recommitting to sharing responsibility to do it. A recent essay on how to support scholars under attack posted on Inside Higher Education (IHE) similarly adapts these public health concepts and “conceptualizes the problem as the community’s responsibility”.
The IHE essay lists many excellent strategies at the individual, institutional, and disciplinary levels. I’ll finish by highlighting a few 
that seem to me to be particularly important or appropriate for mathematics.
- #ThankAPublicScholar: Social media attacks can flood the conversation with negativity while obscuring the scholar’s ideas and also making making it harder for other faculty to do public scholarship. One way to resist this effect is to consciously read and share the work of the scholar. This also helps resist false equivalencies between ideas and misreadings of the scholar’s work.
- Challenge those who blame the scholar: As with survivors of rape, survivors of academic harassment can be blamed for causing the reaction of their work. We have a responsibility to challenge this kind of discourse, both by making sure that language gives agents responsibility for their actions and by requiring that people support their claims rather than stopping with specious headlines. We cannot leave these scholars alone to engage in this discourse while being blamed.
- Advocate for statements and petitions that support the scholar: It’s important that these statements actually support the scholar. A statement from an institution that only validates the work of the scholar on the basis of academic freedom, first amendment rights, or a separation between official and unofficial professional communication actually undermines the rigorous scholarship done before publication, and it communicates that the institution agrees with the critiques. [eg: Statement of Support for Gutiérrez from RUME SIGMAA members]
- Demand that your institutions and professional organizations explicitly value community service and public scholarship: Many people hate math as reine vernunft, the pinnacle of the ivory tower, which we must address; but we cannot at the same time allow ourselves to be silenced by shouted claims that math is apolitical and hence we are only allowed to speak about the tower. Education is a public good, and we must expect each other to engage it while supporting that work.
I strongly recommend that you read the whole IHE essay and its many more strategies as well as reading the work of Gutiérrez (search for her professional CV at University of Illinois or start on this blog) and the efforts of The Clothesline Project. And know that 250+ people showed up to the rally to rebuild the burned clothesline on my small campus.
*This statement is an oversimplification, in part because this word “acts” is not defined. I’m referring to overt behaviors related to systems of power and oppression.