Failing on its own terms

Mathematics is unreasonably effective. In several ways. And that’s dangerous.

I am always surprised by the elegance of the Power Rule from Calculus. Humans worked very hard to make sense of instantaneous rates of change, but it surprises me that the slopes of tangent lines are computable, it surprises me that we can globalize these computations into a coherent new function that encodes these slopes at each point, and it shocks me that we can express these derivatives across the family of power functions in such a simple and elegant way: For any number n, (xn)’ = nxn-1.

I am also awed by how flexibly humans have applied mathematics to model systems and phenomena in order to understand ourselves and make predictions about the world, from the stars to microbes to the ways we behave in large groups.

But this elegance and flexibility is seductive. There are stronger metaphors, but one that should be uncontroversial is that with a hammer this powerful, all the world seems to be nails. If you are faculty, I am absolutely confident that you’ve had the frustrating experience of being at a department meeting with other professional mathematicians attempting to deduce a solution to a question for which deduction is absolutely not an appropriate approach, whether it’s about awarding your departmental undergraduate award or strategizing about the future of the program.

I think that lots of mathematics learning spaces select for people who approach tasks in this manner. I don’t remember this, but my mother says that she once told me to “get in the bath” as a euphemism for taking a bath that I didn’t want to take, so I went up and stood in the dry tub for a few seconds and went on with my day. This obnoxious and legalistic approach to language was useful and rewarded in math classes. And it’s clear that I was further trained to use these kinds of tools to prove theorems.

But this selection and training, paired with the elegance and flexibility, seems to convince lots of people that this approach is the only valid approach, that doing anything other than hammering nails is not only inferior but somehow also harming the hammer. In many ways, my work is focused on the fact that mathematics has a disciplinary worldview, an element of which is often the avowed belief that mathematics doesn’t have a disciplinary worldview. This element of (this version of) the disciplinary worldview is exclusionary and harmful, and I believe that other versions of a disciplinary worldview can exist that support the positive elements of mathematics while allowing us to redress the exclusion and harm. But this will take work, and and this work is subtle because of this pressure not to see pieces of the powerful worldview. Here are some ways this subtlety plays out.

People have said nasty, hateful things about mathematics education to me and in my presence. My personal hypothesis is that training that focuses us so much on deduction has made many of us impervious to data as evidence and dismissive of other ways of supporting claims, leading to people deciding in advance that education research cannot possibly have solid results. Unlike biologists, who can think about their students as biological creatures, psychologists who can think about students’ psychology, and historians who can use their historical tools to understand their classrooms in context (and essentially every other discipline) lots of mathematicians seem to believe that there is no possible overlap between our disciplinary research and our work as educators. This is false, but I’ll leave discussion of that for a longer, future essay. But I will point out that these other disciplines have explicit discussions of their methods and theoretical frameworks, which I think leads to stronger results than those possible without the conscious attention to worldview.

But this dismissive perspective on mathematics education also rests on an unsound vision of mathematics as a discipline. For example, I would challenge readers to define “proof”. I expect that almost none of us could give a definition of proof that is operationalizable in the way we demand of mathematical definitions. The few who can are likely really doing metamathematics, and these definitions don’t really match with the ways proof is used in the discipline. An education research colleague did some excellent work a few years ago to find multiple facets of a potential definition of proof, from an artifact itself to the argument to which that artifact refers to the conviction or communication it is supposed to support between humans, but found that accepted proofs regularly failed to have multiple of the supposedly definitional facets in different contexts. So the central object of our disciplinary methods does not meet our overt disciplinary standards. [I’m not trying to erase forms of applied mathematics that are not focused on proofs, but I am much better equipped to talk about this piece.]

This perspective leads many to use mathematics as the prototype for “objectivity”. There has been a lot of very angry yelling that “2+2=4” recently. First, this statement is not true without context, in much the same way that that (ex)’ is not equal to xex-1 with the familiar interpretation of the symbols. Sure, in context one could deduce the sum of two and two, but that context is a model, not a truth, and others are possible. For example, if fencing requires a support post every yard and two people each have the posts they need to support two yards of fencing, how much can they support together: five yards. Furthermore, 2 does not exist in the universe; it requires a conscious observer to collapse the stuff of the universe into objects that have some abstract property represented as 2. And moreover (running out of my favorite words here), work like that of Kurt Goedel shows that our attempts to formalize something as foundational as numbers will still include non-standard models! Beyond the mathematical analysis of this point, there’s the historical fact that trying to use “2+2=4” to invalidate anothers’ experiences comes from a particular, racist tradition of anthropologists using poorly formed linguistic questions to “decide” if Indigenous peoples were “civilized”. This tradition continues in the ways we treat mathematics tests as unproblematic measurements of something innate.

Some people are committed to maintaining this vision of a “pure” mathematics that rejects discussion of other aspects of our discipline. Setting aside the choice to use a word from eugenics and using it in the same way, this is still impossible. Lots of mathematicians seem to be Platonists, asserting that mathematics somehow exists a priori. I disagree, but even if we accept this point, it functions as an unsupported axiom, not a conclusion like this perspective tries to frame it (commonly known as assuming the conclusion). And even if this version of math were to “exist”, our discipline would be about the human work of connecting to the knowable pieces. Organizations devoted to mathematical research at the exclusion of dimensions of human identity are literally social clubs about not wanting clubs to be social, at least if taken at face value. And seen in context of the ways that power continues to work in our society, they seem more likely to be safe spaces for people who don’t want to be asked to feel responsible for making places safe.

As a final example, we mathematicians have a tendency to model the world as a zero-sum game. Content coverage vs active learning, rigor vs compassion, productivity vs inclusion, and many others. Mathematics is regularly used as a bogeyman that requires us to run classrooms that rush through ideas from an expert’s perspective but can’t allow for much learning, to treat students in ways that pretend to have high standards but block them from meeting them, and that organize our community around validating the current work of a select group while blocking the growth that could be. We are being used to claim that high school curricula that are not focused on selecting privileged students and concentrating resources on only them is destroying this country. Let me be clear about two points. First, these are not zero-sum situations. Active learning supports students in learning and in learning about learning all while we are able to focus on multiple ideas in parallel, and in my experience this means that my students get to explore more than would have been possible if my classrooms were focused on passive transmission; the research certainly makes it clear that we can set aside the fears about “what if they haven’t seen this thing for the next course”, though there is plenty of room to improve other aspects of these systems. Compassion supports students in excelling, and in my experience it is the compassion that supports the multidimensional excellence. And inclusion supports productivity, whether seen as more progress in the previous, narrow/extractive vision of productivity or as progress on the broader goals of a more diverse community. So if the conjecture is that it’s not possible to have both coverage and active learning, rigor and compassion, productivity and inclusion, then I am happy to provide a proof by counter-example to answer the conjecture firmly in the negative. But second, embedded in the first point, it’s clear to me that it’s the belief in the zero-sum that causes the undesirable outcomes, or somewhat conversely it’s specifically the focus on BOTH AND that leads to growth on either.

Stepping back from the examples above, here’s what I’m saying: mathematics as a discipline (the hammer) is regularly invoked in ways that fail to meet its own standards and in ways that fail to apply those standards in context, being distracted by the elegance and flexibility respectively of hammering nails. It’s failing on its own stated terms. This challenge is part of what happens when a group of humans share a disciplinary worldview, and we need to talk about it.

I’m disappointed with the AMS’s decision to terminate the space provided by these blogs because I think it blocks this conversation from spaces bound by a shared identity as doers of mathematics. The future of this particular blog is uncertain. Perhaps we will end up at the MAA. I certainly feel more at home in MAA spaces, but for me these are spaces bound by a shared identity as mathematics educators, where these kinds of conversations are already part of the fabric.

For those of you interested in resisting the erasure of our disciplinary worldview and the consequent harm, I would like to suggest a useful starting axiom: I have things to learn from other people about mathematics and mathematical spaces, especially from Black, Indigenous, and Latinx folks, and when I encounter something I don’t understand I should start from the assumption that I and those around me will be better served by working to understand it rather than working to explain it away.

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This Post will Self-Destruct

I’ve been working on part two of my last post, but it’s been slow going and painful.

I’ve been trying to understand things that have happened to me, understand how to situate current struggles within the longer narrative of my life, all this with the hope of finding a way to learn something worth sharing. It’s exhausting, but I believe it is worth doing.

Well, I found out that AMS will not be publishing my part two.

We’ve been given two weeks notice that they are “winding down” their blogs.

screenshot from AMS website "Free Resources" section which describes The Living Proof blog and the inclusion/exclusion blog. Screenshot has been edited to cross out the blogs.

Took the liberty of updating their website for them.

I suppose two weeks is enough time for me to finish the post I’ve been working on (though maybe not the last two weeks of December), but why should I? Why should I give anything more to AMS?

Here are some words that have been sitting in an unfinished draft:

I will let you in on a little secret. People don’t actually listen to me or care what I think or care if I’m hurt. Maybe you do (thank you!) but not the people I work with; not people with power. The very few instances where someone attempted to take a risk for me, they found themselves immediately discredited as biased. Go figure. The point is that nothing I do is mattering in the short-run for people at approximately the same power level as I am.

Senior mathematicians who read my writings will still moderate racist and frankly cowardly conversations in the guise of “reaching people where they are.” You must know you are not leading them by example if you have to step on me in order to reach them. This phenomenon is especially troubling when the event is advertised as being anti-racist. The way I have to keep reminding people that I’m not just a collection of social justice opinions. The way the powerful will shut me down so as to reach more people. It is hard to keep showing up. Honestly AMS owes me money.

I keep talking because I know that these conversations we have, the endless panels, I know we are forming a community. I know we are gaining strength in fighting for (undergraduate) students and protecting them from the status quo. But I’m honestly running out of energy for it, because we ourselves are still lost. We are still under attack, and I have to say, I do not see that ending.

I naively thought that I had accumulated some kind of credibility here. The fact that my writing has been shared so much, and the fact that people keep telling me my words have helped them. The invitations. I thought it meant something. I thought it meant I would be listened to. That we would be listened to.

Instead all I see is garbage.

I regularly tag the AMS (you know, the host of this blog) on Twitter asking what they are playing at when day after day brings a new exercise in exclusion. I’m so tired of it. Sometimes I just stare off into space (the blank wall opposite me when I work from home in my basement of boxes and a chair) and I wonder is the AMS salvageable? It pretty clearly isn’t. For every Nice Statement you get out of an AMS president, are perhaps countless instances of racism, homophobia, and just a blatant disregard for the mathematicians I care about.

I looked around at AMS’s website for my tweet storm and realized that of course it is inherently racist, sexist, transphobic, etc. I’m not an expert on capitalism, but it shouldn’t take an expert analysis to understand that systems invented by white men need to be dismantled and anything short of that is racism and gaslighting. I hope some day I am free and unbothered enough to get a good hearty laugh at people who honestly think that structures created by white men to benefit white men could become acceptable to all simply by making small changes in admission. I cannot wait to be able to joyously revel in the absolute clownery of thinking the AMS is actually trying to not be racist.

For now, though, I can’t laugh, because it hurts too much.

I know I am just one person, not deserving of anything more than anyone else, so when I am hurt that an institution or organization doesn’t care about me, it’s not because I want them to care about me more than they care about anyone else. It’s that I know that I am more representative of people excluded from math than I am representative of people included in math, even with my academic privileges. I know that when I am excluded it is representative of too many people’s experiences, and I also know how hard it is to stay safe in these situations.

I think that’s what kills me in all of this, between AMS’s sloppiness and the toxic political rigidity of those who cling desperately to the academic traditions they were able to exploit, there is just no understanding of humanity. They refuse to believe we are hurting, or if they concede that, they have an elaborate fictional backstory about how we deserve it, how it doesn’t matter, or how it would be morally wrong to make it their problem. They hold our resilience against us; weaponize it. They host and/or reject debates on whether we require or deserve special treatment whilst they are the ones who can only feel safe atop a system of exploitation. They are the ones who need the rest of us to not matter. They are the ones who crumble at any hint that their power is not wholly and legitimately earned through merit and effort.

Shot of young Queen Elizabeth II from The Crown; top text says "The Crown must win", bottom text says "must always win"

Mathematical societies steeling themselves for the difficult task of doing nothing in the face of racism.

I am a mathematician.

I am a person.

I have worth.

I am no more deserving than anyone else.

I am no less deserving than anyone else.

If you do not care to support my research, you do not support mathematical research. If you choose concepts over humans, you are working against community, against sustainability, and against human flourishing.

If you choose institutions or money over people, you are following in the violent footsteps of those whose statues we are tearing down.

I improve any space I’m in, not because of my credentials, my connections, or my academic pursuits, but because I am unwaveringly committed to justice, to seeing worth in everyone, to ending abuse, and to dismantling causes of suffering.

When people hate me, it’s not because I don’t respect them; it’s because I respect myself.

When people write me off as not good enough, that tells you who they are, not who I am.

Over and over again AMS has chosen itself, while offering sympathies, and collecting fees.

Friends. Fam. Oomfies. Is this your mathematical society?


AMS Task Force Report

AMS welcomes NSA

AMS apologizes for getting a citation wrong

AMS regrets their naming mishap

Who will celebrate you? by Noelle Sawyer

I’m breaking up with my oppressive professional society by Chad M. Topaz

Black woman powerfully walking away from car that is on fire (from Waiting to Exhale)



Will Smith looking at empty living room from series finale of Fresh Prince of Bel-Air


Posted in racism, social justice, social media | 1 Comment

Testimonios: Dr. Erika Tatiana Camacho

Testimonios is a publication by MAA/AMS edited by Pamela E. Harris, Alicia Prieto-Langarica, Vanessa Rivera Quiñones, Luis Sordo Vieira, Rosaura Uscanga, and Andrés R. Vindas Meléndez and illustrated by Ana Valle. It brings together first-person narratives from the vibrant, diverse, and complex Latinx and Hispanic mathematical community. Starting with childhood and family, the authors recount their own particular stories, highlighting their upbringing, education, and career paths. Testimonios seeks to inspire the next generation of Latinx and Hispanic mathematicians by featuring the stories of people like them, holding a mirror up to our own community.

The entire collection of 27 testimonios is available for purchase at the AMS Bookstore.  MAA and AMS members can access this e-book for free through their respective member libraries (MAA | AMS). Thanks to the MAA and AMS, we reproduce one chapter per month on inclusion/exclusion to better understand and celebrate the diversity of our mathematical community with folks who are not MAA/AMS members. [The AMS has recently decided to end its blogs, so the future of this effort is unclear.]


From Mexico to Los Angeles

Dr. Erika Tatiana Camacho, Illustration created by Ana Valle.

My dad died when I was three months old leaving my mother to care for me and my three older siblings, ages four, three, and two. This was in Guadalajara, Mexico, where a lack of money meant lack of opportunity. After struggling to raise us by herself for a few years, my mother took up the offer of my grandma (my dad’s mom) to take the four of us in, so that she could focus on working to make ends meet. My grandma lived two hours outside the city and so this also meant that my mom was only able to see us on the weekends. Worse was the fact that my grandma was not a caring person. Behind closed doors, she allowed us to be abused often and it seemed like she just considered us free labor. My mom would give her most of her paychecks thinking that the money was going to our clothes and food but this was not the case.

My mami and I celebrating my oldest sister’s birthday in 2020.

We didn’t have any toys to play with and many times would go hungry. She would also have us sell candy on the street and other things that my mom was not aware of. After a few years, my mom finally caught on and took us back to Guadalajara with her.
When I was seven, she met my future stepdad and corresponded with him for a while. He lived in the U.S. and promised an opportunity for a better life. After nearly a year of correspondence dating, he proposed and we soon moved to the U.S. Unfortunately, he had not been honest about his financial situation and we (my stepdad, mom, me, and my three siblings) first moved in with his adult nephew for a year and then into a one-bedroom apartment in South Central Los Angeles. Life was tough as we didn’t speak English and went straight to English-only school. There are many stories of the rough life we endured for the next year in school, walking to and from school, and around the neighborhood. For example, my brother got stabbed within the first week of getting to the U.S. by two 18-year-old guys who followed us when we were walking from school (all I remember is him telling me and my sisters to run as he thought he would hold them back). After two years, we moved to East Los Angeles with my new baby sister to an equally harsh environment but at least we knew the language since most people spoke Spanish. We remained in East L.A. (in the same two-bedroom apartment) until I was already in college.

Giving a speech at Jaime Escalante’s (Kimo’s) memorial.

Shaping my dreams—the teachers who inspired me. It was my time in East L.A. that really formed my academics. I could not speak English that well, in part because the language that was still spoken in my house and community was Spanish. In seventh grade, my overcrowded school mistakenly placed me in Honors English instead of English as a Second Language (ESL) class. When I tried to talk to the school counselor, I was told that I should be happy that I was placed anywhere because at least 100 students still did not have a placement. The Honors English teacher, Mrs. Warnock, who noticed that I was not going to get placed in ESL after multiple times of trying, told me that if I was willing to put in the work during lunch and after school that she would spend the extra hours tutoring me. I accepted, did well, and was placed in Honors English from there on (thus, by chance, ensuring that I would have the required classes to apply to a four-year college).

In high school, I was fortunate to have the late Jaime Escalante of Stand and Deliver fame as my math teacher. He was the one that really showed me the power of math and what it can do with hard work. While I was not featured in the movie (it was based on a class ten years before me), the depiction of a tough-love teacher who had Saturday morning math sessions was very precise. Before meeting Jaime, my dream job was to be a cashier. Jaime, or “Kimo’’ as we called him (for Kimo-sabe, the one who knows it all), often brought alumni into the classroom. One of these alumni was a student who went to MIT and worked at a research lab in California. He talked about what engineers can do with math and about the nice car that he drove and the peaceful neighborhood he lived in. What was an old dream changed: I wanted to be an engineer and go to MIT!

College Years and Beyond

Struggling at Wellesley. My high school student government sponsor, Mrs. Dumas, gave me $500 to apply to colleges when she found out from other students I didn’t have the money and thus was not planning to apply to any college that had an application fee. Being too proud, I told her I couldn’t accept it and I only accepted it after she insisted and put the condition that I would not repay it to her but would instead “pay it forward,’’ which is something I feel I have spent much of my life after college doing with numerous students and individuals with similar struggles. I went to Wellesley College for undergraduate school and wanted to be an engineer and take advantage of the joint Wellesley-MIT dual engineering degree program.

In my first physics class at Wellesley, I struggled, partly because of the language, but mainly because of the racism of both the professor and my lab partner. When I went to office hours to ask for help on a particular topic, he started off by asking where I was from, and then after I answered, proceeded to say that he did not understand why they kept letting people like me in while taking a spot from other more qualified applicants.

Celebrating in college with my friends from high school Becky Marquez and Christina Miranda.

During one of my first physics labs, my partner asked if my accent was French because she had been to France a few times. When I told her my accent was because I was Mexican and I came from East L.A., she said that she could not be my partner because I would hurt her grade and she immediately went to talk with the professor. She was promptly reassigned to a new group—everyone was in pairs except her group of three and my group of one. When I asked the professor if I was going to have another lab partner assigned because it was often hard to do the experiments alone, he repeated the same comment he told me in his office hours and said that he could not blame my lab partner for not wanting to work with me. We had not had a single thing graded up to this point, so I internalized this and began to question if I really belonged there. Either by myself or occasionally with a Spanish major friend helping in the late nights when no one else was in the lab, I struggled through the semester. I was devastated by my C grade and realized that my dreams of being an engineer were gone.

I was always very good at and enjoyed math so I decided to be a math major. I had also taken an economics course and really liked it so I double majored with economics too (and econ was one of the few classes in the sciences where the students were always willing to work with me). Even though I was good at both subjects, I still had to work really hard. There were many times when I was ready to quit. One of the hardest parts was not feeling that I could call my mom because her show of support would be to tell me to come back home, leave college, and that one of my sisters could help me get a job.

When I was in this situation, I would sometimes call Kimo. One of the times I called him, I reminded him that he promised me he would get me to MIT but that I was at Wellesley, and things were rough. He livened the moment immediately by telling me that his estimate is not an exact science. He said he did really good by getting me within 50 miles of MIT since Wellesley is just outside of Boston. He also reminded me of why I needed to stay in school. Key mentors, like Kimo, that supported me in critical moments were what helped get me through undergraduate school.

Towards a PhD in mathematics. One of the things that inspired me to pursue my PhD was being able to participate in a summer Research Experience for Undergraduates (REU). It was after this that I decided I wanted to become a professor, and impact students through research and mentoring.

In grad school, I remember studying analysis with a Latino friend and we were thrilled to be taking the class from the only Latino math professor. We did our homework together and I consistently did better than him. When it came to the exam, he scored higher than I did by a letter grade. On the second exam, I again scored a letter grade lower. I went to the professor’s office to go over a few mistakes I made on the exam. The professor took this opportunity to belittle me and to lecture me on how it was important to do my own work and not to cheat. I asked him what he meant and he said that I was clearly copying from my friend’s problem sets since we had about the same homework score but that he scored higher than me on the exams. I was devastated by the accusation. It was hard to sit through the class for the rest of the semester and the following one too (as I had the same professor). What was most disheartening was that my friend in the class confided to me that he had been given the exams from the previous year and that the questions were almost identical. He did not offer this material and I did not ask him to share it with me nor did I ever tell the professor. I just started to distance myself. A year later he asked why I did not want to work or study with him anymore. I told him about what the professor had told me and he laughed and said it was funny that I was accused of this.

During my third year in graduate school I had my first child. My husband was three years ahead of me, and had just graduated. We tried to move back to Los Angeles as he had a job lined up and I thought I would be able to do my research remotely. After a few months of a lack of productivity for numerous reasons, I realized that if I was going to complete my PhD I would need to move back to Ithaca to do it. It was one of the hardest decisions I had to make. However, seared in my mind was my personal upbringing of my mother, who only had a very limited education, working two to three jobs to support her family because you never know what life will throw at you. I wanted to make sure my son was never in that same position and so I moved back to Ithaca and he stayed in L.A. with his dad (and my mom and family). It was a very difficult two years to finish, but I saw no other way to do it. I was so proud to have earned my PhD, but it came at such a high price.

Early experiences as a professor. In my first permanent job, I was struggling with the lack of respect from students in the service courses I taught. I had a student that, upon receiving a well-deserved C on a test, stood up in the middle of class and proclaimed that his tuition paid my salary and that I needed to curve the exam because he needed a B in the course. I told him that he deserved the grade he got but that he could come to office hours and I would help him. He used profanity and told me I would be sorry I gave him a C and that he would go talk to my Chair, which he did. I was then called to my Chair’s office and lectured that I couldn’t tell the students that they deserved a certain grade and that I needed to schedule more time to work with this student than just office hours because those hours did not work for him. Grudgingly, I obliged, but the student rarely kept appointments we scheduled. From then on, he would use profanity when referring to me in the classroom, which my Chair refused to address but instead reminded me that I could not kick the student out or do anything but continue to be polite and teach.

Not much changed my second year, except for my Chair. One day, she called me into her office and said that I needed to stop wearing skirts and bright colored clothes and this was the root of all behavior problems in my classes. She explicitly told me to start wearing suit coats and pants and to make sure they didn’t fit tight and nothing with bright colors. Her basis was one comment in one student evaluation that said he couldn’t concentrate because I was too cute and young to be a professor. Yet she ignored the multiple comments from students who explicitly wrote “send her back to Mexico,’’ “get a professor that knows how to speak English,’’ “we cannot understand her thick accent,’’ etc. and from others to kick the disrespectful kids out of class. I was devastated but found no other choice than to listen.

There have been many times that I have felt like quitting and multiple times, I was one conversation away from just walking away. In looking back, the striking thing is that it was never about mathematics! It was about the climate and culture at a place, stereotypes that people held, subtle and explicit racism, and microaggressions I endured and to which I am still subjected to this day on a regular basis. I think many people believe that academia is a blind place where your talents will be recognized appropriately and where you will not be judged by your looks or other characteristics. But the reality is that academia is made up of people and those people have their biases just like they do everywhere and is one of the most judgmental, inequitable, and political places. Too many people use “merit’’ to cloak discrimination. While I have had some terrific mentors, both male and female, who were Caucasian, it was hard to go through this process rarely being taught by or working with someone who looked like me.

Research—Applying Mathematics to Understand Vision

I study mathematical physiology, specifically looking at components in the visual system that lead to blindness. I collaborate with experimentalists and together we try to understand what causes blindness in diseases where the photoreceptors degenerate, such as in Retinitis Pigmentosa (RP). I have focused much of my attention on the photoreceptors in the retina, the rods and cones, together with the retinal pigment epithelium (RPE) that works with rods and cones to facilitate vision.

I am the first person to dive into this area from a mathematical perspective. My research and publications on the subject provided the first set of mechanistic models and mathematical equations describing photoreceptor degeneration. I have 28+ publications with 12+ of them pioneering modeling of retinal processes. We developed a series of spatially averaged nonlinear ordinary differential equations models to investigate both the healthy and diseased retinas at the cellular and molecular levels. In my earliest publication in the area, we predicted the existence of something experimentally discovered a year later—the rod-derived cone viability factor (RdCVF) and proposed equations describing the dynamics of rod and cone outer segment (OS) number, and RPE cell number. We extended this model in another publication to account for mutated (phenotype) rods, which were used to describe the diseased state of RP. In another publication, the RP model was further extended to include a control input that represented RdCVF treatment, which was designed using optimal control. The metabolic contribution in RP to photoreceptor death was quantified in collaboration with an experimentalist through a mathematical model. With another experimentalist (the discoverer of RdCVF, Dr. Thierry Léveillard), we showed the role of RdCVF in RP coexistence and mathematically analyzed it.

My recent work extends to multi-scale predictive models that investigate cellular and molecular level dynamics contributing to degenerative process or diseases including Age-related Macular Degeneration (AMD). I want my research to make a difference. Being sought out by some of the top experimentalists in the world for collaboration on how to stop photoreceptor degeneration (and mitigate blindness) has been a huge recognition from my point of view. It was incredibly rewarding when my collaborator Dr. Léveillard said it was because of our models and my discussion with him about their predictions that his team was able to identify previously unknown metabolic pathways that are now under investigation.

Mentoring and Perseverance

I see so many things in academia and outside of it that need to change to make an equal playing field, yet it seems that most people in positions of power are not willing to risk it to make a change. I feel like there are “fights’’ at nearly every step that would lead in the right direction.

Mentoring Roberto Alvarez, Danielle Brager, and students at ASU in 2019.

I am currently in my reflection stage and not sure how to best change academia and the world while not giving up all of me, especially given that there is no guarantee that what I do might make any noticeable difference. It’s tough. What often keeps me going are the many, very personal, and sincere messages I receive from former mentees of how I made a difference in their trajectory. The most touching ones are when they have told me that only after being away for a few years did they really appreciate the mentoring I gave them. Many will ask what they can do to become a mentor like me because they have not found people like me. I explain that I just do what I learned from my mentors who really truly cared about me—those who did not mentor me because they were trying to build an empire or check a box. I have fought many battles for my mentees when they were experiencing bias or unfair treatment by jumping in and changing the situation for them before they were completely broken. I have also fought for many who are not my mentees but who don’t have a voice or seat at the decision table or who are invisible and forgotten, often by making structural changes and creating opportunities. I sacrificed many things to give my mentees and many others equal access and opportunites. I try to do whatever I can to help my mentees realize their full potential and their dreams, in addition to listening and giving advice that I think is best for them irrespective of me. Each one of their successes gives me the motivation to continue. Each one of the mentoring awards I have won is also a validation that what I do actually makes a difference.

Receiving the American Association for the Advancement of Science Mentor Award in 2019.

A lot of mentoring is first learning about the individual because so many factors influence who we are today and why we make certain choices. Then it is a time-intensive endeavor to meet them where they are and to bring them up to their full potential.

As a postdoc, I co-wrote a grant to the National Security Agency (NSA) and the National Science Foundation (NSF) to start my own REU. This led to the launch of the Applied Mathematical Sciences Summer Institute (AMSSI) the summer after my first year in my tenure-track job at Loyola Marymount Univeristy (LMU). The program was joint with Cal Poly Pomona and we split the time between the two universities, moving the students halfway through the program. Over its three years, we had 48 students, and five Teaching Assistants (TAs) participate in the program. All were either from underrepresented backgrounds or schools where research opportunities didn’t exist or were not available to them. Nearly one-third earned their PhDs, with many others earning their master’s. It was a very rewarding program and only stopped because I moved from LMU to Arizona State University (ASU).

I have given motivational talks to groups ranging from elementary school through high school students in addition to college students, professors, and high-level administrators. Each of these talks can get emotional as I’m giving examples from my life to drive home the message. One of the most emotional keynote addresses I gave was in 2009 to the recipients of the Presidential Awards for Excellence in Science Mathematics and Engineering Mentoring (PAESMEM). It was very special to be able to thank each of them on behalf of all their mentees and tell them how their efforts are appreciated even if not all the mentees come back and say thank you. It’s also important to keep in mind that great mentors are not just the ones that have won the big awards, but most important the ones who open the doors for others by creating opportunities and fighting the tough battles to bring about change.

Diversity and Inclusion in Mathematics

I am an applied mathematician and thus I usually see everything as a problem to be solved. I really have come to appreciate what is now known as “team science’’ where multiple people come together from their varied perspectives to try to solve a previously unsolved problem. I think the most challenging problems require this approach.

We need a society that is knowledgeable about STEM or at least appreciative of it! Since math describes and underlies nearly every aspect of STEM, every issue can be helped with the presence of mathematicians. Moreover, we really need to focus on team science where multiple approaches, even beyond STEM, are used to solve the most pressing problems of today.

In higher education, we talk about changing things for marginalized communities, yet we forget to include stakeholders from these communities (we bring high-level administrators or researchers to the table as “representatives’’ who are employed in institutions serving these communities but who have not been raised in these communities or have not lived through the experiences of those they represent).

The mathematics students and faculty need to reflect the U.S. population. I think one of the main barriers is a lack of understanding from the professors about what it means to be a professor. We judge people by their publications and not the impact of all their efforts (scholarly and otherwise). If we want to change academia and agree that we need all professors to be good mentors and to understand the diverse population they are working with, why should people object to requiring a Diversity/Inclusivity Statement and a Mentoring Statement in job applications and promotion documents?

From a different angle, individuals rarely solve the challenging problems of today. If we let those perpetuating the status quo also determine the research agenda, very little will change. We need to bring the richness of multiple backgrounds, including Latinx people, to be at the table and set the research agenda, yet it’s understandably hard for many of those in charge to step aside and let different perspectives weigh in.

In terms of societal/institutional structures, it’s the narrow-mindedness, micro-aggressions, and institutional racism that are the biggest obstacles to learning.

It will take many selfless and courageous people of every race, color, and way of life to eliminate these structures because there are too many vocal people (even if they are in the minority) that want to preserve the status quo or go back to how things used to be and there are too many people who don’t think it’s their problem and will stay silent. We have a generation of Latinx PhD mathematicians that wasn’t present when I started my journey and that really gives me hope that change is on its way. Some are oblivious to the Latinx situation but most are actively doing things to promote our community. Many majority mathematicians show us support too.

We need more Latinxs involved in math because of the need to approach challenging problems from different perspectives and to actually shift the focus of what problems we should be working on.


It’s great to want to change the world. But don’t lose yourself as you try to do it. There will always be detractors and haters, but ignore them as much as possible. Don’t doubt yourself and don’t let others define who you are or your path. Judge people by their actions and not just their words. Finally, while it’s great to have a mentor that looks like you, don’t think that this is a requirement. Some of your very best and long-term mentors may be Caucasian males, and one that may do the most damage to you personally and professionally might be a Latino.

Many times I am speaking to students who have had a rough path yet they have what it takes to overcome the adversity they have experienced. I had, and still have, a rough journey many times. Sometimes they just need to realize that people have done it before, are still struggling to make it in their respective career levels, and they are not alone. The path won’t often be easy, but the rewards, in the end, are worth it.

I have had some terrific and some very hurtful and toxic mentors who are mathematicians. But I have also had great mentors that are not in math and some are not even in STEM, but they are very perceptive, understand things, and can give relevant advice. It’s them needing to realize who I am as a person and what may be best for me. Many people from all walks of life will share and support your goals and dreams. Perhaps there is a correlation between those supporters and people with your characteristics, but by no means should you limit your mentors and advocates to just those with certain characteristics (such as being Latinx). At the same time, believe someone the first time they show you their true colors.

Previous Testimonios:

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Testimonios: Dr. Selenne Bañuelos

Testimonios is a publication by MAA/AMS edited by Pamela E. Harris, Alicia Prieto-Langarica, Vanessa Rivera Quiñones, Luis Sordo Vieira, Rosaura Uscanga, and Andrés R. Vindas Meléndez and illustrated by Ana Valle. It brings together first-person narratives from the vibrant, diverse, and complex Latinx and Hispanic mathematical community. Starting with childhood and family, the authors recount their own particular stories, highlighting their upbringing, education, and career paths. Testimonios seeks to inspire the next generation of Latinx and Hispanic mathematicians by featuring the stories of people like them, holding a mirror up to our own community.

The entire collection of 27 testimonios is available for purchase at the AMS Bookstore.  MAA and AMS members can access this e-book for free through their respective member libraries (MAA | AMS). Thanks to the MAA and AMS, we reproduce one chapter per month on inclusion/exclusion to better understand and celebrate the diversity of our mathematical community with folks who are not MAA/AMS members.


My Parents

Dr. Selenne Bañuelos, Illustration created by Ana Valle.

My parents grew up in very small towns in Jalisco, Mexico. My father was only able to complete the second grade of elementary school, just long enough for him to learn to read and write. He is the oldest in his family and worked with his father to help support his younger siblings. He began working in road construction at the age of fourteen. My father hung around the engineers so much that they started calling him nosey. He took whatever scraps of paper containing calculations that the engineers balled up and threw out. He taught himself geometry through those scraps of paper and still remembers discovering the Pythagorean Theorem in those notes. By the time he was seventeen, he bet an engineer that he could get a section of the road done with his own calculations. He did it beautifully.

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Bending Genre for Modern Needs

Listening to a podcast recently, I heard an advertisement for a “podcast movie” as the first in a new genre. I’m still not certain what this means, but I think it already exists as a radio play. [Aside: I’m loving the audio-book of The Sandman!] This got me thinking about how folks are bending genre and format to meet our modern needs.

Here are three examples that you should read. You should read them because of their content related to mathematics and in/justice, but while reading them, I hope you also appreciate them for the ways they bend genre to achieve their goals. I’ll describe each briefly.


(1) “Everything is Garbage, Now What?”, a live Twitter talk by Piper H

Before starting, Piper estimated that this would have been about a 30 minute talk if it were done live with voices. It turned into more than an hour of tweetstorm fire about how racism is built into our mathematical institutions and the thin stories some of us use to ignore the racism and other forms of systemic oppression.

Tweetstorms and AMAs (ask me anythings) already exist, but conceiving of this as a live talk on Twitter allowed the audience to engage (much like the best feature of Zoom: the chat) while also creating a public record that can be followed in time of the various ways that people are engaging with Piper’s points.

As many others have pointed out: this is required reading.


(2) An open letter “On the value of Math, LGBTQ+ issues, BYU, and the AMS” by Chad Topaz

About a year ago, Chad “broke up” with the AMS in part based on their inaction on issues of the well-being of LGBTQ+ folks in and through mathematics. This year’s AMS Lecture on Education is from a scholar at BYU, a school where students are explicitly not allowed to admit being LGBTQ+. Chad’s point is that this choice is part of a pattern of choices that communicates that it’s OK to uplift math contexts in which queer folks (and others!) are not safe.

My own experiences with discussions about education hosted by the AMS are alienating for other reasons as well. Education is a discipline of its own, with at least as much expertise and research work required as other forms of mathematics. But in these AMS spaces, people (who are loud and get centered) regularly tell me that anyone with education training cannot be trusted, that evidence-based practices are not only trivial fads but are mysteriously harmful to students, and broadly that caring about teaching will cause a faculty member to be a worse scholar. As a result, even in the more overtly reasonable conversations, in my experience, the AMS lifts up people who are trained in proving or modeling when talking about teaching to the exclusion of people who are trained in education, sometimes lifting them up for having reinvented an idea that is a well-known, evidence-based practice in other communities (and as a result often giving white men credit for “discovering” ideas they really learned from others). I’m proud to know lots of people who are trained in proofs and models who are doing the work to learn about all dimensions of teaching, but it will likely be years before I can expect this to be the norm in some spaces.

I like that Chad’s open letter is more dynamic than many other open letters because of the nature of Twitter, allowing more direct engagement with the recipient, which happened here. I hope the speaker takes up Chad’s ideas about how to use the invitation to address some of these issues.


(3) A historical analysis of “SOHCAHTOA” by Michael Barany

As many readers will likely know, a video of a high school math teacher mocking Native American cultures in an attempt to “teach” the trigonometric mnemonic SOHCAHTOA recently came to light. In this thread, Michael Barany gives a historical analysis of this racist trope in math classrooms and curricula in the context of the political economy of mathematics education.

Historical analysis of primary sources has existed for far longer than social media, but I appreciated two aspects of this being formatted as a thread. First, the format allowed me to engage more directly and easily with the primary sources that were supporting the analysis. And second, as with the other threads in this post, this format allowed for more engagement from readers, such as another scholar pushing Barany to attend more directly to the racial dimensions of this phenomenon.


Homework: Read these threads, use what you learn to make math spaces better, and bend some genres along the way if it helps.


[I adapted the featured image from the Twitter logo, giving it a cute purple sweater vest and jaunty top hat.]

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Testimonios: Dr. Federico Ardila Mantilla

Testimonios is a publication by MAA/AMS edited by Pamela E. Harris, Alicia Prieto-Langarica, Vanessa Rivera Quiñones, Luis Sordo Vieira, Rosaura Uscanga, and Andrés R. Vindas Meléndez and illustrated by Ana Valle. It brings together first-person narratives from the vibrant, diverse, and complex Latinx and Hispanic mathematical community. Starting with childhood and family, the authors recount their own particular stories, highlighting their upbringing, education, and career paths. Testimonios seeks to inspire the next generation of Latinx and Hispanic mathematicians by featuring the stories of people like them, holding a mirror up to our own community.

The entire collection of 27 testimonios is available for purchase at the AMS Bookstore.  MAA and AMS members can access this e-book for free through their respective member libraries (MAA | AMS). Thanks to the MAA and AMS, we reproduce one chapter per month on inclusion/exclusion to better understand and celebrate the diversity of our mathematical community with folks who are not MAA/AMS members.

De Donde Vengo Yo

Dr. Federico Ardila, Illustration created by Ana Valle.

My elders come from little pueblitos in the mountains of Santander, in northeast Colombia. My dad’s family would be the ones to call if you wanted a serenade for someone in Zapatoca. My great-grandma would host the afterparty and challenge the young ones to trash-talking battles in rhyme. Meanwhile my great-grandpa slept on a hard wooden block, in contrition for his sins. My dad, Jorge, loved math and science as a kid in Bucaramanga and wanted to study engineering. Fortunately, his dad won the Totogol—a sort of lottery where you had to guess the scores of the national fútbol tournament—winning just enough money to open up the corner store that supported the family for the next few years, and send my dad to college in Bogotá. My father began his career engineering sewage systems. With time, he became really interested in designing systems for groups of different people to work together, en armonía. He will tell you that he always prefers to avoid conflict; but if he has to, he’ll always fight for the weaker side. Continue reading

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Testimonios: Dr. James A. M. Álvarez

Testimonios is a new publication by MAA/AMS edited by Pamela E. Harris, Alicia Prieto-Langarica, Vanessa Rivera Quiñones, Luis Sordo Vieira, Rosaura Uscanga, and Andrés R. Vindas Meléndez and illustrated by Ana Valle. It brings together first-person narratives from the vibrant, diverse, and complex Latinx and Hispanic mathematical community. Starting with childhood and family, the authors recount their own particular stories, highlighting their upbringing, education, and career paths. Testimonios seeks to inspire the next generation of Latinx and Hispanic mathematicians by featuring the stories of people like them, holding a mirror up to our own community.

The entire collection of 27 testimonios is available for purchase at the AMS Bookstore.  MAA and AMS members can access this e-book for free through their respective member libraries (MAA | AMS). Thanks to the MAA and AMS, we reproduce one chapter per month on inclusion/exclusion to better understand and celebrate the diversity of our mathematical community with folks who are not MAA/AMS members.

Early Life

Dr. James A. M. Álvarez, Illustration created by Ana Valle

Olga’s story. My mother, Olga Mendoza, grew up in a small community formed around the turn of the twentieth century as a “company town.’’ The company produced large clay sewer pipes in the town of Saspamco, Texas, which is actually an acronym for San Antonio Sewage Pipe and Manufacturing Company. Before my grandfather, Federico Mendoza, was murdered in 1939, he worked at the company, and so did several of my great uncles and later so did my brothers. This town was (and still is) comprised of more than 95% Hispanic people of different backgrounds. That is, some had been in the area when Texas was part of Spain and Mexico, while others (like my great-grandparents) had come to the area in the 1880s and 1890s, and the remainder were those who had left Mexico during the Mexican revolution in the 1910s.

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On disability and chronic illness in mathematics

Guest post by Allison Miller

This piece comes from my desire to have more conversations about disability, chronic physical and mental illness, and neurodivergence in mathematical spaces. This is not one story but a multitude, shaped not just by diagnoses but by race, class, gender, and more: I hope that by sharing my experience I make a little more space for others to do the same.


Part 1: The personal

When I talk to students about my career path, I almost always tell them about the time that I nearly left grad school. The short version goes something like this.  In my second year, a department culture that “you shouldn’t try to be a mathematician unless it’s the only profession that could make you happy” combined with my own insecurities to predictable effect: I decided that I wasn’t the right fit for graduate school. After months of soul-searching and applying for non-academic jobs, though, I eventually decided that the ways I love math were enough and that I did want to continue towards my doctoral degree.

No part of that story is false, but it is incomplete. At the time, I was also dealing with significant health problems: I had to take breaks on my short walk home, saw my diet transform into whatever food didn’t upset my stomach too much, and was falling asleep all over campus.  Perhaps surprisingly, it took me years to recognize that this mismatch between me and my surroundings might have contributed to my feelings of isolation and inadequacy. In retrospect, of course I struggled to identify with a culture in which rest had to be earned and productivity was identified with personal value!

Today, I’ve found an equilibrium that looks different from that of many people around me.  I need more rest than most, and spend more time and effort caring for my brain and body. I feel guilty about this sometimes, which I suspect stems both from my knowledge that many people who equally need this rest can’t access it, and from internalized ableist narratives equating busyness with moral worth. I work with and around my wonky auditory processing, trying mostly unsuccessfully to balance “assertive enough to be listened to” and “non-confrontational enough to preserve important professional relationships” when asking for accommodations. While I do find this challenging, as a white woman I have significant privilege here: this line is much harder to walk for many others, especially BIPOC women (see Aparna R.’s piece, linked below).

While writing this piece, I sometimes worried about being perceived as that “ cultural bogeyman…the attention-seeking, trouble-making, fraudulent scrounger” [Limburg] who asks for undeserved special treatment. After all, I have been successful according to mainstream standards: who am I to make a fuss? There are many possible negative reactions, ranging from “you’ve done well, so what do you have to complain about?” to “you haven’t done well, so maybe you’re just not that good at math”. Both ends of this spectrum serve to silence critique and preserve the status quo: if both success and failure are delegitimizing, which disabled people are worth listening to?


Part 2: The political

The lens of disability can offer a powerful perspective on how to make academic mathematics more equitable, just, and humane. One key framework is the social model of disability, which argues that “for many people with disabilities, the main [sic] disadvantage they experience does not stem directly from their bodies, but rather from their unwelcome reception in the world, in terms of how physical structures, institutional norms, and social attitudes exclude and/or denigrate them” [Goerig]. As a personal illustration, I often have difficulty understanding all of people’s speech, especially when I can’t see their faces. The medical model of disability would locate any disadvantage from, for example, not being able to access a podcast as coming from a flaw of my body; the social model would emphasize that the podcast producers did not include a transcript. Both the medical and social models of disability have value in certain contexts, but I believe the latter gives us as mathematicians– people who design courses, advise students, and shape research environments– more to work with.

Writer and advocate Rebekah Taussig defines ableism as in part “the process of favoring, fetishizing, and building the world around a mostly imagined, idealized body.”  This process of “building the world” takes place in mathematics classrooms, research groups, and institutions as much as anywhere else. For example, see the decision to hold the 2022 JMM exclusively in person, during an ongoing pandemic that continues to have brutally disparate impacts (and despite nearly eighteen months of proof that virtual meetings can succeed while broadening access across many dimensions!). Even limiting myself to personally relevant examples, I could list off accessibility failures in our community ad infinitum: the assumption that all conference participants will enjoy a nice vigorous hike at high altitudes; the lack of even automated closed captioning at the majority of virtual talks; conversations on mental health in math that don’t acknowledge the existence of mental illness except as coming from the pressures and stresses of academia (see Mental Health in the Mathematics Community, linked below, for a notable exception).

However, such a list would be inevitably incomplete, and might also give the impression that there is such a thing as a perfectly accessible space. One conference attendee’s bright-enough-to-read-by is another’s migraine trigger; one student experiences a highly flexible course as invaluable in letting them work around pain flare-ups, while another finds it overwhelms their available executive function. Thirty years after the passage of the ADA, the legal requirement to provide reasonable accommodation for documented disabilities is both frequently unfulfilled and simply not enough. We must move beyond doing the bare minimum and towards a philosophy of “how can we best meet the needs of everyone who is– or should be– in the room?”

We need to acknowledge the fact that ableism in mathematical spaces is unsurprising given the broader societal context, then pay attention to the ways in which our subculture’s norms and structures shape this ambient cultural noise. As a part of this, we can recognize that academic mathematics can offer accessibility advantages. Flexibility in when, where, and how work happens can be invaluable to the professional success of someone with a chronic illness.  While we may take such flexibility for granted in research math, in many other careers one would struggle to receive this even as a formal accommodation. But there are also deeply embedded structural aspects of academia (and mathematics in particular) that disadvantage disabled people. For example, the early career expectation to move every few years from grad school to postdoc and onwards disproportionately harms those who rely upon stable support networks and ongoing relationships with healthcare providers.

Success in mathematics should not depend on whether someone’s needs happen to mesh sufficiently well with institutional structures and spaces that have been designed to serve only certain kinds of minds and bodies. Moreover, it is not enough to take a piecemeal approach of making individual accommodations within the current system. We need an understanding that math happens not in disembodied brains but in and between people with particular strengths, needs, and limitations, and this must be accompanied by a commitment to honor needs and respect limitations as much as we celebrate and even fetishize strengths. (That said, there are excellent checklists for websites, meetings, events, and course materials that, while not systemic change, can make an immediate difference in making mathematical spaces more accessible– I encourage you to take a look.)

Many of the questions at the heart of disability justice, from ‘Whose needs are normalized and whose pathologized?’ to ‘Who is treated as an authority on their own experience?’, are deeply entwined with race, class, and gender. As a cis white woman without visible disabilities, I have been protected by privilege as well as harmed by discrimination: real progress will require hearing many voices and focusing on the most marginalized. I would be grateful to any readers who would like to take this space to talk about their own experiences, even and especially as they differ profoundly from mine. That said, if you don’t want to or feel safe in sharing, please know that you don’t owe disclosure to anyone. Even coming from a place of relative privilege and security, I have chosen to omit many details from this piece. Whether, when, and how to share intensely personal information is a set of questions without right answers, just trade-offs that each of us deserves to navigate in our own way.


Part 3: Acknowledgements and references

*Thanks to Miriam Kuzbary for much needed encouragement throughout the months-long process of writing this, to Siddhi Krishna for very thoughtful comments on every version of this piece, and to the editors of inclusion/exclusion for their helpful suggestions.

*Am I disabled?, by Joanne Limburg, for eloquently articulating the implications of answering this sometimes challenging question.

*Rethinking disability: the social model of disability and chronic disease, by Sara Goering, for the above quote about the social model of disability.

*Sitting Pretty: The View from My Ordinary Resilient Disabled Body by Rebekah Taussig, for the definition of ableism excerpted above and more.

*Mental Health in the Mathematics Community, by Mikael Vejdemo-Johansson, Justin Curry, and Julie Corrigan, from the August 2019 AMS Notices.

*The Disability Visibility Project led by Alice Wong, a large collection of “original essays, reports, and blog posts about ableism, intersectionality, culture, media, and politics from the perspective of disabled people.” The pieces “The burden and consequences of self-advocacy for disabled BIPOC” by Aparna R.; “Academic Ableism: Fighting for Accommodations and Access in Higher Education” by Krys Méndez; and podcast Episode 64: Disabled Teachers with Travis Chi Wing Lau and Dayniah Manderson are especially relevant.

*Indigenous Mathematicians, Lathisms, Mathematically Gifted & Black, and Spectra, for inspiring me to think more about the importance of individual and collective stories in mathematics.

Posted in ableism, equity, graduate school, intersectionality, mental health, universal design, victim-blaming | 1 Comment

One year organizing in the mathematics community

Guest post by the Just Mathematics Collective

As we reach the one-year mark of the Black Lives Matter rebellion of Summer 2020, many of us are reflecting on the actions we promised to take last summer and on what we’ve done in the intervening year. Our main objective in writing this post is to let folks in on our experiences organizing in the mathematics community. Tl;dr: we would’ve never thought that something that so often feels like herding cats could also be so joyous and inspiring! We’re also here to give a round-up of our past and current campaigns and to let people know how they can get more involved in our fight for a more just mathematics.

The Just Mathematics Collective (JMC) formed last summer in an effort to try and push our community towards a freer and more just mathematics. One year and several campaign launches later, we write this post in the same reflective spirit mentioned above, and to catalog some of our experiences, victories, and challenges.

We’re overjoyed by the connections, friendships, and solidarity we’ve built with one another! Our collective is now an organizing home to more than 50 mathematicians and scholars of mathematics, including undergraduates; graduate students; post-docs; tenure-track faculty; and tenured and full-time faculty at R1’s, teaching-focused institutions, and liberal arts colleges. We were frankly surprised to find so many mathematicians who are interested in an abolitionist mathematical future!

On the other hand, we’re also frustrated. We’re angry — on behalf of both ourselves and oppressed people all over the world — at the apathy of those who continue to stay on the sidelines. We’re disappointed in senior mathematicians who’ve made names for themselves in the DEI industry but still refuse to take political risks by attaching their names to genuinely radical ideas or pledging to take actions that — by virtue of how true justice is resisted by the status quo — might get them in trouble with colleagues and their home institutions.

In this post, we’ll summarize our year of campaigning and what it’s taught us about risk, seniority, and different forms of power as they relate to organizing within the mathematics community.


“Once I get tenure, I’ll speak my truth”, and other lies we tell ourselves

“It’s just too risky to rock the boat right now — you have to think about your career and your future! Just wait until you have tenure: then you’ll have real power to make change.” JMC members have heard versions of this advice countless times, but most senior mathematicians’ engagement with our work has been to loudly dismiss our campaigns. In light of this enormous gap between promised action and observed inaction, we need to ask: where are all the boat-rocking tenured mathematicians?

In our experience, senior people have played by far the smallest role in the work required for meaningful and lasting change. This lack of engagement is a real shame, since their job security puts them in the best position to take political risks, and because their professional seniority grants them a huge amount of influence in our community. Of course, this is an oversimplification, but we want to highlight four major types of senior mathematicians we’ve encountered in the last year:

  1. The Apathetic Academics
  2. The Militantly Opposed
  3. The DEI Specialists
  4. The Accomplices

We view the Apathetic Academics and the DEI Specialists as the biggest impediments to our organizing efforts.

Complete disengagement is sometimes worse than active opposition. Apathetic Academics do not want to be inconvenienced in any way, and being principled is often very inconvenient! Of course, the Militantly Opposed are not our friends, but unlike the Apathetic Academics, they are at least honest enough to admit that they have political beliefs (regardless of how abhorrent these beliefs actually are!) and are brave enough to express those beliefs in a public forum.

And the eagerness of the Militantly Opposed to share bad and/or misinformed opinions can sometimes be useful to our organizing efforts. For example, consider a hypothetical in which someone announces that they’re so opposed to the idea of ethics informing academics’ choices in where to direct our labor that they would personally recruit for Satan if he were hiring mathematicians. By pointing out how morally bankrupt this position is, we can facilitate a much needed conversation about the relationship between academic freedom and ethical participation in the academy.

Unlike the Apathetic Academics, the DEI Specialists are willing to be inconvenienced. Many of them spend countless hours organizing equity events or conferences tailored to underrepresented and marginalized students. DEI Specialists often portray their work as going completely unnoticed and uncompensated, and they see themselves as rebellious scholar-activists in search of “good trouble”, as evidenced by right-wing extremists targeting their efforts. One problem with this narrative is that right-wing extremists wouldn’t know true equity and justice from a hole in the ground. Moreover, genuine “good trouble” actually requires the possibility of getting in trouble! And since much of the DEI Specialist’s work is institutionally sanctioned, they rarely need to worry about that.

Along these lines, the JMC believes that conventional diversity, equity, and inclusion (DEI) work — much like the neoliberal policies of the Democratic party — simply does not (and fundamentally can not!) address the root causes of injustice in our communities. Toothless DEI work provides cover for our institutions, allowing them to launder their reputations and feign concern without the threat of meaningful, radical change to the oppressive systems they benefit from. It is for precisely this reason that conventional DEI efforts are actually showered with immense amounts of resources and institutional time, and the folks who lead those efforts are often recognized with personal accolades, promotions, and social clout.

Last, and  sadly very much least (in quantity!), we have the Accomplices. Some have become JMC members and contribute immensely to our active campaigns. Frankly, it’s thanks to them that the more junior members of our collective know it’s not impossible to have both tenure and integrity!

Lessons learned: We absolutely can not rely on senior people. The system rewards those willing to uphold the status quo too overwhelmingly for the existence of a strong contingent of senior folks with radical politics. We won’t give up on them as individuals, but we can’t afford to wait for them.


Power: who has it, and who doesn’t? 

Obviously, senior mathematicians with tenure do have power and security, but where do we draw the line between the powerful and the powerless? That there’s no clear-cut way to measure power makes it possible for so many senior academics — including chairpeople — to claim powerlessness when asked to implement even the most minor departmental reforms. Different people have access to different amounts of power, but anyone can feel powerless. And no environment is better at producing spinelessness than professional academia. Researchers are trained to believe that any wrong move could make the difference between a coveted tenure-track position and unemployment; that is, we’re trained to forfeit our power. This is the problem with the “wait until you’re tenured before making waves” advice: by then, this training has already been fully internalized.

Nevertheless, most academics have access to at least a baseline of power: institutional affiliations that can navigate behind paywalls; opportunities to mentor and teach students who themselves may go on to wield power in the future; and spending time in classrooms, offices, and hallways from which most human beings alive today are effectively barred. So instead of asking “Do I have power?”, we think the far more pressing questions are “How do I honor the responsibility to use the power that I do have? How can I be accountable not only to my students and mentees, but to the people I’ll most likely never meet in an academic context?” There’s no single right answer to these questions, but junior members of the JMC believe in our power, and over the last year, we’ve proved that we can exert it to make serious impacts.

Of course, many of us don’t have tenure, and there’s undeniable differences in power and safety from member to member. Collective anonymity is a useful tool for mitigating some of these differences, and acting collectively made us realize that we need to move away from the model of power that sees the individual as its key source. Collective action is where power is built. When those with the authority to make changes are unwilling to do so, either because they’re invested in the oppressive status quo, too cowardly to claim their own power, or more often both, our goal is to organize movements with sufficient energy, volume, and momentum to force hands and shift culture.

Lessons learned: The view of power that ascribes the most to senior people and the least to marginalized folks is reductive and presumes that power originates with the individual and not the collective. In some ways, this view ultimately reinforces the hierarchies we want to dismantle. For example, the more people who sign on to a risky or politically controversial campaign, the more powerful the campaign becomes, and the more the barrier to participation is lowered for the next person. Every time we choose to stand up for our principles, we exercise and claim our power, and when people get together to do this collectively, new power is generated.


Mathematics Beyond Prisons and Policing

About a year ago, an open letter began to circulate calling for an end to collaborations between mathematicians and police. At this time, the JMC was still in the process of formation; some JMC members were coauthors, and many of the people who would become members helped to edit and advertise the letter once it was written. As abolitionists, we envision a future without police and without prisons, and as mathematicians, we have access to the mathematics community. Organizing is most effective when people know each other and have preexisting relationships, so we came together to fight for our principles within our sphere of influence. In a relatively short time, we collected hundreds of signatures. Looking back, we think it was so successful because:

  1. There’s a genuinely strong desire for a police-free mathematics community.
  2. The political energy of the moment placed this issue at the forefront of many peoples’ minds after the police murders of George Floyd, Tony McDade, Ahmaud Arbery, and Breonna Taylor.
  3. We weren’t asking most people to make major changes in the way they did their math — many people already didn’t collaborate with police in their professional work and didn’t plan on doing so in the future.

Of course, Militantly Opposed senior mathematicians acted quickly to express their disagreement with the letter. Several letters to the editor opposing the campaign appeared in the Notices of the AMS. As frustrating as it was to see so much justification for throwing human beings in cages at a time when Black and Brown people were rising up against police violence all over the country, the AMS’ decision to dedicate so much space to folks who thought we should keep working with cops gave us the opportunity to respond on this very blog. We used this moment to introduce an unapologetically abolitionist stance to the practice of professional mathematics and to expand our membership, increasing our labor power and our capacity for deeper and richer organizing work.

Lessons learned: Reading political energy and taking advantage of the right timing is essential to effective organizing. People with little experience claiming their power — such as those in the mathematics community — are often only ready to take small steps, and will therefore be most willing to sign on to campaigns that require little change in their daily habits.


Mathematics Beyond Secrecy and Surveillance 

After laying down a foundation with our Mathematics Beyond Prisons and Policing campaign, we were ready to take on a more demanding organizing project. Security and surveillance organizations play a much larger role in our community than do local police departments, and when it comes down to it, the National Security Agency (NSA), the Central Intelligence Agency (CIA), and their international analogs are policing organizations. They act to uphold the same oppressive hierarchies that local police departments do, and they criminalize liberationist dissent all over the world. As we argued in our campaign document, being a member of an international mathematics community is impossible for so many of the Black, Brown, and Indigenous people of the world in part because of the brutality meted out by these organizations. So we believe that a mathematics event centered around equity, inclusion, or social justice which includes recruitment at the NSA or any related agency, fails on its own terms. There is nothing socially just about training a new generation of Black, Brown, and Indigenous imperialists!

Our ongoing campaign revolves around asking mathematicians of conscience to divest from these agencies. We designed a pledge campaign that allows signatories to pick and choose their commitments, ranging from sharing the document with colleagues and sparking discussion, to refusing to collaborate with the NSA on conference organizing and grant proposals, to refusing to write letters of recommendation for NSA-related programs. This flexibility allows people to sign on only to the parts of the campaign that they felt they could personally support and we’ve noticed that it’s encouraged more participation.

We’re thrilled with the energy the campaign has generated around these issues, and we’re grateful for the number of mathematicians who have already signed on. But in spite of the ease of participation, there are many DEI specialists who have definitely heard about the campaign several times (we’ve made sure of it!), but have yet to engage with it. As far as this campaign is concerned, these folks are far closer to being Apathetic Academics than they’d like to admit.

And if you’re a senior person interested in DEI work and you think we’re referring to you, we probably are. We’d love to have your participation in any of our campaigns and we leave space always for growth — even if you don’t feel like you can support this initiative now, we’re not giving up on you. But in the meantime, we encourage you to engage even in disagreement. You have a point of view; pushing through the fear you may have about airing it publicly is what sparks motion, growth, and dialog. In short: express disagreement with your chest, not your silence.

This isn’t the place for rehashing all of the arguments that cropped up around this campaign: readers can check out the FAQ we wrote for that purpose. We do, however, want to highlight one typical concern:

I’m just one person, struggling to get funded in an environment where money for basic research is harder and harder to come by. If the NSA is giving it out anyway, and my work isn’t really even that related to national security, what’s the big deal?” 

We really do sympathize with this point of view! But we also feel that it misunderstands how agencies like the NSA purchase influence with their grant money. Funding organizations jockey for larger percentages of total awarded dollars so that they can more actively shape the research landscape. A world where surveillance agencies are responsible for a significant portion of available funding is also a world where:

  • research towards a mathematics for the people (e.g., developing open source and freely available technology for people to protect themselves from the police and from governmental surveillance) is much less likely to be funded, and therefore much less likely to be carried out at all;
  • even “pure” or “basic” research conducted by folks who express interest in a mathematics for the people is less likely to happen, since we have no way to hold surveillance agencies accountable, and they have a history of political blacklisting.

Again, we see how an individualist framework misses the forest for the trees. We can only see what “the big deal” is when we zoom out and think about the impact the NSA has on all of us, as a community. And it’s only collectively that we can remove its hold over mathematics, because the sorts of changes required here are big, including: putting pressure on those in power to lobby hard for more basic research funding detached from surveillance agencies, and thinking collectively about more ethical job opportunities for our students so that no one has to choose between leaving mathematics and working with the police state.

Besides asking mathematicians to make individual commitments, this campaign also called on the AMS to explain the nature of its relationship with the NSA, and in particular, to not grant surveillance agencies the space and resources for recruitment at the Joint Mathematics Meetings. Campaign participants were asked to write emails to the AMS, and the AMS responded in an official email from its president, claiming that “the AMS invites any potential employer of mathematicians to engage with our community…” Given the the utility of mathematics and the many organizations with power and money who are also actively white supremacist, queer and transphobic, sexist, etc., we need the AMS to clarify what it means here.

This campaign is active and there are future phases in planning that we can’t say more about yet. For now, you can play a role by taking the pledges, and by joining the email action by sending this updated script in response to the AMS. We also urge all professional societies that claim to care about justice to heed our call and commit to not accepting any funding from the NSA and other surveillance agencies. Spectra has already set the bar by doing so — what will it take for your organization to be next? Please join us!

Lessons learned: Making bigger asks means we need to work harder to achieve the same level of engagement. Integrating flexibility into a campaign allows people to pick and choose how they want to participate. The sort of change we are looking for requires long-term planning and open-ended campaigning. And when we campaign for justice in math, we’re not just standing up for oppressed peoples. We’re also standing up for the healthy — and well-funded — future of our own mathematical community.


Mathematicians for Boycott, Divestment, and Sanctions

On the Day of Action (May 18) in solidarity with the Palestinian uprising, and in light of the recent escalation of Israeli violence towards the entire Palestinian nation, the JMC officially endorsed the Palestinian call for the academic boycott of Israel, and urged individual mathematicians and their societies to follow suit. While this campaign is very similar to our first two in terms of its abolitionist goals, it diverges from them from an organizational perspective in that we didn’t design its guidelines. Our campaign for a liberated Palestine falls within the broader Palestinian-led Boycott, Divestment, and Sanctions (BDS) movement, one that had already been gathering momentum, while also enduring various forms of suppression.

There are already deeply ingrained patterns in how detractors express their opposition to any speech or actions in solidarity with Palestinians, and we’ve seen those patterns play out very predictably in our own campaign. We won’t address all of the opposition here, in part because we think our campaign document already does a good job of that. But, as in the last section, we’ll highlight one or two that have a lot to do with the common theme of this post: power building is collective, and when we stand up for a truly just cause, we stand up for everyone, including ourselves. 

The first common objection we’ll spend some time with revolves around academic freedom:

“I can’t participate because this boycott is a violation of the academic freedom of Israeli mathematicians.”  

We can’t stress enough that the guidelines of the boycott are clear: individual academics are not boycottable. In particular, collaborating with mathematicians from Israeli institutions, inviting them to conferences and seminars, and hosting them at non-Israeli institutions do not constitute violations of the boycott. The “academic freedom” straw man is particularly absurd as an argument against boycott in light of institutional efforts to silence, harass, intimidate, and punish anyone who express sympathy for the Palestinian cause. Not to mention the reality that, as is consistent with the colonial paradigm under which they live and work, Palestinian scholars have little to no academic freedom or mobility.

By endorsing the Palestinian-led call for boycott, we’re at the same time honoring the freedom of Palestinians to determine the best strategies for their own resistance, and honoring our own freedom to express radical political beliefs. So many people have been blacklisted, fired, and shunned for expressing solidarity with Palestine (many of them Black, Brown, Arab, Muslim, and/or Jewish) that civil rights groups refer to the “Palestine exception” to free speech. This is the battleground issue when it comes to the right to express radical and just political points of view, so when you join us, you’re fighting for yourself, too.

The second common objection we’ll highlight focuses on efficacy and impact:

“Academic boycott has low impact. My decision to go to a conference at the Technion has no bearing on the course of the movement.”

In spirit, this response is almost identical to the one we spent time with in the last section: I’m just one person, so what’s the big deal? The whole point of collective power building is that when we join a movement, we get to be more than just ourselves! We’re no longer just a few academics taking a principled stand. We are part of a broad and strong mass of people from many industries — shipping/imports/exports, arts and culture, research and development, agriculture, construction, the list goes on! — who stand together to say NO to apartheid and settler-colonialism. Beyond that, academics, and especially mathematical scientists, play a special role here because academia holds so much power in shaping and shifting culture, and the occupation and apartheid regime rely heavily on the mathematical technologies that we study and teach.

There’s so much we could get into, but we’ll end by emphasizing how much more challenging this campaign has been than either of the others. We were thrilled to find (so far) 65 mathematicians who were ready to sign on with us, but there’s so much more work to be done. Understandably, people are afraid to claim their power. We understand this and we empathize with it, because many of us who have already signed on are also afraid. But we did it anyway because it was necessary to be in line with our own answers to the questions we’ve raised above in the section on power: this is how we use the power we do have to be in solidarity with oppressed people. If you’re on the fence and what you’ve read here resonates with you, ask yourself how you’ll live in alignment with your own answers to those questions. And remember that when you join us, you make participation less risky for everyone.

This campaign is active, and you can join by signing on here.

Lessons learned:  There is a lot of fear in the air around taking this stance. Overcoming that fear requires more targeted organizing strategies: one-on-one conversations, political education, and small group discussions. Progress is slow, but there is ample room for growth and opportunity for impact.

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The First Spectra Conference

Spectra is proud to announce that the first Spectra Conference will be hosted virtually by the Institute for Computation and Experimental Research in Mathematics (ICERM) on August 18th-20th, 2021. The goal of this conference is to create a meeting for LGBTQ+ mathematicians where all branches of the mathematics community (including applied, theoretical, and education) are represented and to create a space for LGBTQ+ mathematicians both to celebrate achievements and to spark conversations of challenges in our community. The conference will feature three plenary speakers as well as contributed sessions of short research talks and lightning talks. Additionally, we plan to have social hours via Gather.Town and a panel to discuss the past, present and future of the LGBTQ+ math community.

1) To attend the virtual conference, please register through ICERM (use the “Apply with Cube” icon):

Registration is FREE!

2) If you would like to also give a contributed talk or lightning talk, please submit your application and abstract using the link below:

The deadline for submission is July 31st 5pm Pacific.

3) If you simply would like to know more about the program of the conference as it becomes available, please go to the conference page:

Titles, abstracts, and schedule for the three plenary speakers, Becca Thomases, Luis Leyva, and Dylan Thurston, are already accessible.


-For the organizing committee:

Rustum Choksi
David Crombecque
Alexander Hoover
Brian Katz
Freda Li
Claire Plunkett
Konstantina Trivisa
Alexander Wiedemann


Allies are welcome to attend as participants as long as they are committed to centering the needs of the LGBTQ+ community in this space.

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