"On Life and Math", Chapter 0: Introduction

… and so, despite my intense and undying love for mathematics, I decided to leave academia. It had been quite a journey, at times incredible and at times awful. In any case, I was ready for something new.

What brought me here?

Wanting to be more relaxed.

Wanting to spend time with friends and family and to pursue other passions alongside mathematics, without worrying that I was sabotaging my career. Said differently: wanting to feel free to prioritize love and delight, rather than perpetually deferring them.

Wanting to feel like society at large actually has any idea of what I’m doing, and cares.

Wanting to teach less — a lot less.¹

Wanting to make more money — a lot more.²

Wanting to feel free to decide where in the world I’d live.

Wanting to stop hating myself.

Wanting to be able to change jobs easily, without having to wait until September plus N years for some terrifyingly unknowable N: a nonnegative integer that’d be impossible for me to differentiate from my self-worth.

Wanting to work at least a little less hard.³

Wanting my project timelines to be measured in weeks instead of years.

Wanting to feel like I’m ever fully done with my projects, and can actually take a real break.⁴

But ultimately, at the bottom of it all, it was wanting to shed the inescapable sense that I was giving my entire self away to mathematics, an abstract entity that would never love me back.⁵

Why am I writing this?

The following revelation struck me in a deeply visceral way during my first time at Burning Man back in 2013, and has stayed with me ever since.

My greatest wish in life is to be a light — to others, and to myself.

In the long course of my leaving academia, I received support from many other mathematicians who’d likewise chosen to leave. Hearing their experiences gave me a lot of comfort and clarity, and helped me feel much less alone.

Nevertheless, my experience of leaving academia was at times incredibly sad and lonely. And yet, I knew that while the particulars were unique to my situation, the feelings were generic: uncountably many mathematicians have left (or considered leaving) academia, and surely many of them have felt just as sad and lonely as I did.

The sadness is inevitable. It’s the grief of losing a deep and meaningful relationship.⁶

The loneliness, on the other hand, is not. It’s a result of the fact that we generally don’t talk about the experience in sincere and emotionally resonant terms. We ought to give full respect to the impact of the departure upon a person’s one and only life.⁷

I define community as “a place that you can bring your entire self to”. In this sense, smaller circles — a professor’s research group or a grad student body, say — often provide community for the contemplation of leaving academia. But I’ve found this to be largely nonexistent within the broader math world. I attribute this in part to the incentive to manage one’s image in striving towards the holy grail: tenure.

So, while I don’t think I can make this experience less sad for anyone, by sharing my own story I hope that I can at least make it less lonely. I want to break open the discourse and dissolve the shame.⁸

And also, I’m writing this for myself. I want clarity and closure as I move on from this chapter of my life.

It’s worth noting that I’m definitely not telling you what to do. It’s already hard enough for me to know what’s right for my own life, let alone yours. It’s your journey, after all.

Who is this for?

I’m writing this for my math community: the algebraic topologists, and more specifically the homotopy theorists among them. I feel a desire to be seen, and a desire to be known: by those who have touched my life, and by those whose lives I’ve touched.⁹

More broadly, many of the experiences I describe have the potential to resonate deeply for mathematicians across all subfields.

But even more broadly, this isn’t really a story about math at all. It’s a story about love and inspiration; about accomplishment and failure; about expectations, met and unmet; about belonging, and about self-worth… about making sense of life. Math is just the medium.

Which is to say: If you’re reading it, it’s for you.¹⁰

1. My last academic job came with an extremely light teaching load (just 1-1-0, on the quarter system), and I really couldn’tve asked for stronger students — this was at Caltech. That made me realize that my ideal teaching cadence is more like one single class every 2-3 years. And this is despite the fact that I absolutely love teaching.

2. I’ve mostly heard mathematicians say that they don’t particularly care about money. I thought that was true for me too, but learning how much money math-adjacent skills can garner outside of academia has led me to dream bigger. I dream of regularly bringing my whole extended family on vacation, paying for everything; I want to remove every possible barrier to togetherness. Whereas tenure-track math professor salaries in the US start around $100-150k (which is already quite comfortable), one of my early software engineering jobs (had I stuck with it) would have brought me towards $400k within the first year. That’s not normal, but it’s not totally crazy either. And especially in the era of AI, there are plenty of folks making well over $1 million a year.

3. I applied to the National Science Foundation (NSF) every fall from 2014 through 2020 (7 years in a row!) — earlier for a postdoc fellowship, and later for a standard grant — and every single one of those Octobers was the absolute worst. I’d find myself slaving endlessly over a single document that was supposed to articulate my grand research vision — often sleeping 0-4 hours a night for days on end, consuming stimulants around the clock, all while trying to continue to fulfill my teaching duties, to say nothing of possible job applications — just because an NSF success would be a “nice-to-have” boost for my career.

I finally succeeded in 2020 with a grant proposal entitled Factorization Homology and Low-Dimensional Topology, which I eventually learned succeeded primarily due to a single reviewer’s particularly unbridled enthusiasm. I’m proud and relieved that I made good on at least the core promise of that grant proposal with the joint paper A Braided (∞,2)-Category of Soergel Bimodules.

It’s great that I was able to convince this single reviewer of my research potential, and that was certainly a positive signal of my efficacy as a mathematician. But at the same time, I’m keenly aware of how easily it could’ve ended up that they weren’t one of my reviewers, and for all I know I would’ve failed yet again.

What a terribly stochastic and high-stakes ordeal those NSF applications are.

4. The following comparison illustrates many of the aforementioned wants.

My most joyful and productive math research collaboration — that with David and Nick — began in the summer of 2015. At the time, we naively predicted that our project would take a single summer and result in a single paper of roughly 20 pages. But the project ended up spiraling fantastically out of control, and between the unexpected intrinsic difficulty of the problem and our shared penchant for exploring countless tantalizing avenues of structure and beauty, together we ultimately produced well over 500 pages of original mathematics. However, due to a variety of factors, our first published work didn’t appear in print until 2024 (Stratified Noncommutative Geometry, published as a book in the Memoirs of the American Mathematical Society monograph series). I hope and expect for this to be a reasonably influential work, and I often say that I’d consider it a real success if a few hundred people engage deeply with it during my lifetime.

In stark contrast, in one of my recent software engineering jobs, the first iteration of my work was made available to users after just two weeks of straightforward solo effort, and it was enjoyed by over 15,000 users in the first week alone.

5. I tend to believe that no relationship should be prioritized over the individuals that comprise it. This principle can be particularly clarifying in the context of romantic relationships, and traces back at least to existentialist philosophy — notably that of Jean-Paul Sartre and Simone de Beauvoir. But it applies much more broadly.

6. I’ve seen so much sadness and anxiety and discouragement in academia, much of it centered around the existential question: Will I make it?

Due to how easily it could’ve been my story too, there’s a particular soft spot in my heart for the handful of American mathematicians I’ve met who seem to orbit Europe and Asia, moving friendlessly from one postdoc position to the next, never feeling free to invest in personal relationships. After all, they’re only ever in one location for a few years, and such investment apparently comes at the expense of research productivity: that all-important but largely unquantifiable quantity that dictates whether they will make it or not.

I say “apparently” here because there is a lot of truth to the notion that happier mathematicians produce better mathematics — or rather, that any given mathematician will produce better mathematics if they’re happier. But real friendships take real time and real energy — resources which can feel far too scarce amidst the relentless rhythm of the annual academic job application cycle.

As for “making it”, this means: preferably getting a tenure-track job back home in the US, but really just landing somewhere permanently. But even then, it sounds heartbreakingly lonely to be a stranger in a strange land, permanently.

7. I’ve heard many math folks half-jokingly refer to others as “dead” if they’ve left academia. (“Well, dead to us”, they might admit when pressed.) I hate that joke. It ascribes shame to the mere contemplation of leaving academia — which is insidious, given our deeply programmed desire for belonging.

8. Academia is filled with people who were so good at school that they decided to try and stay forever. Through this lens, leaving academia is the ultimate Fail.

9. Put more darkly, I feel a desire to own the narrative around my departure. This desire is reactive to the way the math community talks about people who’ve left. I feel some shame at how much I care what others think of me, but ultimately I think it’s better to acknowledge this shame up front: to be vulnerable, and to really say it all.

10. I’ve lovingly endowed this memoir with an abundance of endnotes (such as the one you’re reading now), which appear at the end of their respective chapters. I’ve generally used these when I want to include some material that doesn’t fit cleanly into the broader narrative flow. In particular, some of the endnotes contain mathematical asides. Please read these if and only if they interest you; if your eyes glaze over, then they’re not for you! (Said differently, the inverse statement also holds.)