# Continuity

I left China at the age of four. My memories of those first four years are scattered impressions: a three-leaf clover I chowed down on while Mom’s back was turned, the smell of a revolting herbal remedy, the time an older girl scratched me on the cheek in daycare.

We went back to visit every several years. The summer before college, I visited my birthplace, Chengdu, to see my grandparents. At some point, we had dinner with a larger group of family friends. Two of the children at that party, as it happened, had been my best friends in day care.

They remembered me. They remembered the daycare we went to, and the street it was on, and the ways our parents were connected. They told me about the group of boys who’d roughly all grown up together: one who excelled in school and was going to Peking University, another who went too deep into League of Legends, another who was currently obsessed with The Three Body Problem. They were so warm, inviting me back home like an old friend who’d always belonged. I was immediately one of the boys - they asked me to translate words they’d heard in American movies, and snickered at the definition of “asshole.” 

To them, I was a thread that had flown off the tapestry of their lives. They picked me right up, dusted me off, and sewed me back in. 

I didn’t remember a damned thing about them – I didn’t even know I had friends in daycare.

—

After arriving in the US, my family toured the M-states: I moved from Missouri to Maryland at six, and then to Massachusetts at ten or eleven.

Missouri is also barely a splash of impressions: climbing chestnut trees, encountering a proto-psychopath on the schoolbus, sitting for hours “helping” my father fish the Ozarks.

In Maryland I have more substantial memories: holding hands with my best friend William before we learned it was not cool, and then finding out why it was not cool. I remember riding my first bike and then having it stolen by the older kids upstairs, and watching my mom sneak out at night to steal it back. I remember the face of the nasty teacher who gave me a C just to put me in my place. 

My memories come alive right around the time William introduced me to Diablo II. Although neither of our parents allowed us to play more than a couple hours a week, we spent many hours theorycrafting and poring over the official strategy guides. For many years after, I’d boot up Diablo just to recapture that time.

—

With the benefit of hindsight and the theory of [spaced repetition](https://en.wikipedia.org/wiki/Spaced_repetition), I understand now why I remember so little of those early years, and why only Diablo remains as fresh as yesterday. After I left China, my daycare chums in Chengdu passed the same streets, met the same elders, played with the same classmates month after month, year after year. Their memories of early childhood were reinforced again and again. They could easily triangulate even my minor, brief role in this world. The brain remembers those patterns that are repeated across time.

I had no such luck. Every few years, the world was switched out by an entirely new stage, with an entirely new cast. There was a surjective function from friends I held dear to days for saying goodbye. For others, life was a single, cohesive drama; for me, it was a series of improv scenes. It is no wonder that my memories are so scattered.

—

Math majors and PhDs often ask me how to decide between academic and industry jobs. Broadly speaking, these conversations have a common dramatic structure: the student lobs a bomb at me in the form of a mad lib:

Compared to academic jobs, industry jobs are 10x easier to find, pay 10x better, demand half the workload and half the red tape, BUT __.

My job in this drama is to defuse the bomb by filling in the blank with a single intangible value or principle - academic freedom, say - so beautiful that it overwhelms all practical considerations and justifies all the tragedy of academic existence. Some students hurl the bomb at me aggressively - in their heart of hearts they are already checked out of the academy and are looking to verify that the ivory tower is full of shit. Others hand me the bomb timidly, because they are romantics and martyrs at heart - with their eyes, they plead with me to half-ass the answer with anything remotely persuasive. They need something sacred to whisper on their lips as they throw themselves onto the cross of the academic job market.

I’ve always disliked this conversation, until now. I finally know how to fill in the blank, at least in a way that would have persuaded my past self:

Compared to academic jobs, industry jobs are 10x easier to find, pay 10x better, demand half the workload and half the red tape, but continuity.

—

I’ve been starved for continuity most of my life. My family moved when I was four, and then six, and then ten. Then, I went to college, did a PhD, did a postdoc, and finally landed a tenure-track professorship, moving seven times in 31 years. Seven times the stage was reset and the cast replaced.

How many more would it be if I go to industry? Everyone is moving, all the time. Startups collapse, or are acquired. Entire organizations are shuffled and reshuffled when new directives are delivered from on high. In many places, the best way to get promoted is to jump ship and be hired at a new level. One day, you’re shooting the wind with the coworker at the next desk over. The next day, the desk is empty.

—

What do I mean by continuity? The great cathedral of Notre Dame began construction in 1163 and was completed in 1345. Continuity is what I imagine being involved in that project was like: your father, and his father, and so on four generations back, all toiling towards a common cause, a single continuous sacred labor, that ties together every aspect of your life.

I completed my PhD in 2021.

My PhD advisor, Jacob Fox, completed his PhD in 2010. Around half of my research projects come from problems Jacob started thinking about more than a decade ago. I see him practically every year at conferences, workshops, or research visits. He is someone I can trust for advice about anything from career development, to research taste, to advising students. 

Jacob’s PhD advisor, Benny Sudakov, completed his PhD in 1999. Benny is a legendary PhD advisor who has trained and continues to train many outstanding mathematicians. This past summer, I raced Benny in the Random Run, a long-standing tradition of the biennial Random Structures and Algorithms conference. On a standard track, the number of laps in the run is determined by the roll of two dice; the second die is only rolled when the front-runner finishes the first set of laps. In the advisor-student pair category, Benny and his student Aleksa edged out my student Ruben and me for the win. In two years, I hope to be in better shape.

Benny’s PhD advisor, Noga Alon, completed his PhD in 1983. I received Erdős number 2 by spending 2021-2024 as a postdoc working with Noga, who is still sharper than any of us. Together with Joel Spencer, Noga wrote the textbook *The Probabilistic Method* which I and many others use to train PhD students. Joel has a fun tradition of publishing photos of young children reading *The Probabilistic Method* on his website. There is a picture of Jacob’s daughter there, as well as one of Noga reading the book to my six-month-old.

This is just one thread of a densely woven tapestry, a community of combinatorialists that traces itself back continuously to the problem-solving circles of Paul Erdős and his university buddies in Budapest. Our story is, I think, not dissimilar to that of the builders of Notre Dame. 

Erdős rolled the dice for the first Random Run in 1983. I pray the dice continue to roll for many years hence.