Mathematically Ethical

or: escaping the mines of mathbrain

Last month, Caroline Ellison was sentenced to two years in prison for her role in the FTX/Alameda collapse in 2022—the latest sentencing in a legal saga that is still ongoing. Ellison’s crimes at Alameda have often been attributed to her EA sensibilities (and, according to her defense, manipulation by her boss and former partner)—but maybe there’s more to the story. In this essay, Amy Fan unpacks the culture of competitive math where she and Ellison found a love of math at a young age, and cautions us all against its potential downstream dangers.

— Shira Abramovich, Reboot Editorial Board

Mathematically Ethical

By Amy Fan

The Card Players, Theo van Doesburg. Public Domain.

In eighth grade, I qualified for the final round of a citywide math competition: a public buzzer contest where contestants faced down one-on-one until a final champion was crowned. My heart pounded. My competition came from the backgrounds that I had feared—the wealthy suburban schools, the private schools, the schools with the dedicated preparation programs, even the one with a nationally recognized coach. I felt like an imposter, completely unprepared.

What the audience might have noticed was that I was the only girl. I realized I was the underdog of the group. If I won, the additional preparation and resources my peers had had wouldn’t matter. Being a girl certainly wouldn’t matter. I could prove myself worthy, beating the guys on their own terms. I could be the exception to the rule.

Instead, I stepped onstage, hyperventilated, and was eliminated almost immediately.

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Last month, I found myself remembering my competitive math years when Caroline Ellison was sentenced to 24 months in prison for her role in the FTX collapse. In an interview for the FTX podcast, Caroline is asked about her own participation in middle school math competitions while explaining how she ended up working in quantitative finance. Later, she talks about how competition style problems were a part of the interview process at Jane Street, the firm where Caroline interned twice, met Sam Bankman-Fried, and landed her first trading role before being recruited to Alameda Research. At Jane Street, with its culture of risk-taking, games, and constant betting on small things, she was one of three, and then the only, woman in her intern class.

At the sentencing, Caroline said that "not a day goes by that I don't think about all of the people I hurt" and brought up the relief that came with finally being open and honest with what happened at Alameda Research. But the question of how she ended up there still stands. Earlier, Caroline's lawyer filed dozens of letters, from family members, family friends (mostly academic economists, including the Nobel Prize winner Esther Duflo), former classmates and friends, all testifying to Caroline's character. Many tried to unpack what may have led Caroline to commit her crimes. The most common culprit that people point to is effective altruism (EA), with one letter writing about Caroline’s conversion “from Catholicism to Effective Altruism” as a belief system.

Caroline's lawyer has noted that after the scandal, Caroline "has been totally cut off from the EA movement."¹ But like any ideology, effective altruism has many variants. To understand the mathy, probabilistic strain that Caroline and the other FTX and Alameda executives were drawn to, I thought back to the mathematical environments in which we’d both grown up, influenced by competitive and corporate math interests, and how we had both strayed from the norms in different ways. 

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Pure mathematicians often like to talk about the field’s beauty. My college professor liked to quote the poem “Geometry” by US Poet Laureate Rita Dove: "I prove a theorem and the house expands.” To them, math is a poetic medium, closer to art or philosophy than the other STEM fields with which it is often grouped.

Unlike tinkering with computers, or being fascinated with animals and nature, math is abstract enough that it usually takes a unique upbringing to get excited about it as a child. Caroline received that early exposure from her parents, both academic economists who had studied math in undergrad. They introduced Caroline and her younger sisters to empirical, evidence-based research and economic styles of reasoning early on. Math was the foundation by which they built their models to explain the world. 

Caroline learned about Bayesian statistics before middle school and once presented her dad with a study of stuffed animal prices at Toys 'R' Us in lieu of writing a birthday card. In middle school, she begged to be enrolled in after-school math enrichment classes. Even though her parents resisted at first, they obliged after a year. Her father coached her math team, which Caroline captained, and later developed his lessons into math enrichment textbooks for other advanced students to use.

Like Caroline, I was also brought up with math as part of my childhood, but my exposure came from having a specific kind of immigrant parents, who moved to the US after receiving funding for their master's degrees. To them, math was universal, the one academic subject that held constant across linguistic and national boundaries, that didn’t require translation or additional cultural context to understand. It's a proud family story that when my uncle immigrated to Houston a few years later as a high school student, he excelled in his math classes even as he was still learning English.

For immigrants like my parents, math and the sciences also laid the foundation of their belonging in the US: their educational degrees, the jobs that secured their work visas and then their greencards. Growing up, many of my peers had parents who understood firsthand the grueling nature of studying for exams and working in labs, but still believed that science was the only reliable way to do good in a world full of political decisions out of their control. Even if they hoped for more comfortable careers in tech and business for their children, they believed a solid science foundation was crucial.

Perhaps with that goal in mind, my mother left puzzle books around the house and encouraged me to read them. As I got older, the puzzle books progressed to actual textbooks. When I found the exercises fun, my parents didn't stop me from working on them. As the problems got harder, my dad would even work through a problem with me, sometimes spending hours before showing me his solution. 

Both Caroline and my interests in math developed against the cosmopolitan backdrop that academia afforded, and our upbringings came with an implicit affirmation: certain kinds of knowledge—science and math—were universal, and scientific ways of knowing, even with their limitations, were the best ways of understanding the world and leading a good life.

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In high school, Caroline’s mathematical entanglements continued to grow: she did research with a professor at MIT, spent a summer at a residential summer program that her father had also attended, qualified and competed in a national math competition for girls three times, and again captained her math team.

Meanwhile, when I was in high school, I was starting to become part of a very different community. After joining a group of students who wanted to push for youth voices in local educational decision-making, I was going to school board meetings and organizing house meetings of students at schools across my district, trying to forge a collective student identity. At first, what surprised me were the sheer resource inequities within my district: while I envied the mathematical resources of private schools and affluent suburban school districts, my peers shared stories about shortages of teachers, fundamental supplies, course offerings, mental health support. To them, I went to the school that provided me with everything I needed and more, politically shielded from the worst of the district.

Eventually I just became frustrated: what good was an education that never acknowledged the blatant inequalities so close to home? And how removed from the world was I to be interested in something like math, abstract and distant from the real, urgent conflicts in my district?

My mathematical world was mostly limited to my high school math club, a group of six to twelve students in our school of over 3000. Like Caroline and me, the other club members were all kids of immigrants, college professors, or both. Trying to explain my organizing work to them or the other peers and adults I had grown up around typically led to resistance: Inequality wasn't an issue as long as some people from poorer backgrounds worked hard, went to good colleges and got high paying jobs, precisely by excelling at something like math. Politics was only something that people who weren't good enough to do science did. The world would be a better place if scientists and economists ran it. But it was all useless to think about anyways, since political decisions weren’t something we could influence. While I too had been raised with similar beliefs, I was starting to question some of the implicit underlying assumptions.

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Caroline was also interested in social questions in high school but underwent a different intellectual transformation. While her peers focused on their social lives or worried about college admissions, Caroline’s preoccupations were much more abstract. She had been raised in the Catholic Church, but according to her friend and classmate Michael Dinsmore, she was looking "for a comprehensive moral and metaphysical worldview like the church offered, but [...] more intellectually coherent." She learned about effective altruism through rationalist communities online, and had shown up to some EA meetings by the end of high school.

One of Caroline’s sisters wrote that Caroline may have been drawn to effective altruism because "[t]he philosophy placed a large emphasis on helping all people instead of just those similar to you [...] and on the practical results of interventions." Plus, the community had "people who were able to argue convincingly for what they believed in, using the same sorts of economic research we had heard about so often growing up."

This made sense to me: in college, a friend of mine pointed out that the structure of these effective altruist arguments also mimicked math proofs, starting with principles ("all lives are created equal") and then using them to derive logical conclusions ("it's cheaper and therefore more efficient and ethical to donate to save lives abroad than in the United States").

That might have appealed to me had I not realized that math was too abstract to offer me answers to many of the problems I was concerned about. Instead, I treated math as an escape from the complexity of the world that I was still struggling to understand. Regardless of any existential crises and anxiety over my life after college, I could walk out of the library at night reassured that I had typed up a problem set with statements that were True.

Caroline reached the opposite conclusion: that EA’s rigorous and utilitarian style of thinking offered the best lens into how to make the world better. In her first term at Stanford, one of her classmates invited her to an EA group that was just starting. Caroline was the fifth member to join—and eventually became the group’s vice president. She used common EA rationales (namely, earning to give, a path many EA organizations now only recommend for “a small proportion of people” ) to justify taking her internships and then job at Jane Street, where she donated a substantial amount of her income and met Sam Bankman-Fried. 

Jane Street was also where Caroline learned to structure her thinking around the concept of “EV,” short for expected value. She was previously familiar with the concept—expected value comes from probability theory and shows up routinely in statistics, economics, and EA ethics—but it was especially central to Jane Street’s risk-taking culture. Jane Street taught her to focus on maximizing the “EV” of trading strategies and pay less attention to the potential losses, according to her lawyer.² That framework bled into other aspects of its traders’ lives as well: later, when Sam Bankman-Fried tried to recruit Caroline to Alameda Research, he argued that it would be “high EV” for her, and for the world—because she could potentially make more money to donate to charity working at Alameda. She accepted the job offer. 

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The rest of Caroline's story is well known from here: the meteoric rise of FTX and Alameda, the fraud behind the scenes, the crash, the scandal. And as I learned more about the FTX collapse, I started to wonder whether concerns I had kept private for years suddenly had broader relevance. 

After high school, I worried about what felt like a rift growing between my mathematical world and the new world organizing had opened up for me. Mostly, my concerns were self-interested: I simply wanted to know where I fit in as I accumulated personal, professional, and academic experiences that kept pushing me further away from math and complicating my worldview. 

At the beginning of the pandemic, I encountered the concept of a theory of change while part of a youth civics collective in Houston. An epidemiologist doing program evaluation work had helped us create a flowchart that articulated how we thought our collective advanced our mission. Looking back, that flowchart – our theory of change – was a mess: dozens of color-coded boxes, criss-crossed lines all over the screen, interconnected goals across programs, multiple paths between a program, its goals, and its link to our mission. 

To the math kids I had grown up around, it also must have looked like a minefield of untested theories waiting to be falsified. But from the collective’s perspective, the evaluation was useful mostly to help articulate to funders why our work was important. The theory of change we had put down would always be an oversimplification, constantly evolving according to the needs of the community that we were working with. 

That experience left me thinking about the distance between the complex and dynamic theory of change informed by organizing, and the analytical, often statistical, rigor behind the static theories that my academic training had taught me to respect. My fears about this disconnect seemed to have materialized in the FTX and Alameda executives: absent life experiences or perspectives that could have led to a more robust, complex theory of change, the group went all-in on mathematical logics. While their style of thinking is often attributed to effective altruism, the question they were always seeking to answer also could have been lifted from an introductory probability class: what's the best way to maximize expected value?

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In 2015, the philosopher Amia Srinivasan wrote, "Effective altruism doesn’t try to understand how power works, except to better align itself with it." Nearly a decade later, I look at the fields I felt like I might have entered with my math degree – technology, finance, fintech, machine learning, AI – and see how neatly they align themselves with power, or often are the powerful institutions themselves. After all, wasn’t that the whole point of studying math, the reason it carried so much prestige?

But while it’s clear that being good at math can be lucrative and profitable, I’ve never been sure why being good at math offers any authority into how to make the world a better place. As I watch these applications of mathematical thinking bleed into social realms, I worry about all the power exclusively granted to people with a specific kind of quantitative training, even if they’re not Caroline Ellison, even if they’re not in cryptocurrency, even if they don’t believe in effective altruism, even if they aren’t the kind of person who would find themselves committing fraud. 

As FTX collapsed and the trial unfolded, I watched as the internet turned on Caroline, for her actions and their consequences, but also for her appearance, for the people she dated, for the ideas she expressed online. While media reports on Caroline testifying against Sam Bankman-Fried focused on how her ex-boyfriend was truly the worst, comment sections pointed out how that framing denied her agency. Before her sentencing, federal prosecutors wrote to the judge that "The Government cannot think of another cooperating witness in recent history who has received a greater level of attention and harassment [than Caroline]." 

At the end of the day, she still pleaded guilty to seven federal charges. The judge still sentenced her to two years in prison, remarking that he could not give her a "get out of jail free" card in a fraud case this massive. FTX customers may finally be repaid soon, nearly two years after FTX and Alameda filed for bankruptcy. 

Meanwhile, Caroline has been volunteering as a math tutor, helping low income residents prepare tax returns, working on a statistics and data science textbook with her parents and another professor, writing a novel, all non-effective altruist ways of doing good, some of them related to math. 

Michael Dinsmore writes “It is no exaggeration to say that Caroline has reassessed the entire period of her life consumed by Alameda Research.” Her sister notes that "[Caroline] has always only wanted to be helpful, and that has not changed, but I do think she puts less stock in slick arguments now and more in conventional wisdom." 

I wonder what Caroline’s theory of change is now.

Amy Fan is a data journalist based in Washington, DC. While working on this piece for Reboot, she saw Charli XCX, found out a project she worked on won an Emmy, and was laid off from her job.

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🌀 microdoses

• Need more FTX/Alameda ephemera?

  • If you’re interested in reading more about Ellison’s sentencing and her role in the FTX/SBF trials, this piece by Molly White of Citation Needed explained the defense and sentencing.

  • Post-FTX, crypto’s changed—but how? For one opinion, check out this K4 piece by

    Tony
    on the FTX collapse’s implications for crypto ecosystem.

  • Though FTX may be long gone, crypto money is still very much in politics—and its candidates have been winning.

• It’s internship application season—if you’re looking, here’s a very Reboot-coded position at IBM research!

• Is poetry dead?

💝 closing note

If this piece resonated with you, sending a letter to the editor is a very high-EV activity ;) We are also open for pitches and love hearing from our readers. Finally, we’ve got a lot of great pieces coming up in the next few weeks—it’s a great time to subscribe to get them fresh in your inbox!

— Shira & Reboot team

1. He did not respond to a request for comment.

2. Jane Street did not respond to a request for comment.