What happened to the dream?

I finally got to see La La Land with my church community group this week. I appreciated its down-to-earth, intentionally banal depiction of Hollywood as well as the subtle poking fun at LA traffic and lack of seasons (a flash mob dance number during a traffic jam opens the movie, in “WINTER”).

The palm tree is part of the joke.

Everyone in the movie is striving to make it in the entertainment industry somehow. And it’s the depiction of this striving that forms the main tension in the movie and my deepest thoughts after it ended.

Boston has a similar feel, with seemingly everyone striving to achieve academic or entrepreneurial success. Well, that’s not entirely true — I’ve certainly met many, particularly in church, whose efforts also included a healthy dose of family and community. But if you spend enough time on campus and casual social gatherings, the first topic that often comes up is what you work on, or what you’ll be doing after you graduate, and you can come away with the same sort of impression that it’s why everyone came here.

But it wasn’t the cities that the movie made me think about the most, it was myself. What has happened to my dreams?

Because I definitely had them. As we all graduated and parted ways, the class of 2012 wrote out our next steps as well as our hopes for our current life trajectory. Mine was simple and unsurprising: Math Professor. It’s been the first thing everyone my entire life has expected of me.

And yet, as I’ve hinted in my previous posts on grad school life, those dreams have evolved. As my final year in grad school begins this fall, I’ve finally decided to close that door. As Sebastian would ask: Why?

I hope this post can explain. I’ll refrain from my previous habit of instinctively generalizing to others or talking about myself in second person — this is my story, after all. In fact, this post is going to be much more stream of consciousness than my typical post — I haven’t even written out any bullet points or my usual rhetorical flourish of the five-point post (my version of the three-point sermon). In the musical spirit of La La Land, though, I’ll be titling each section with a loosely related song lyric taken from my current favorite band. See how many you can recognize.

What if my dream does not happen? Would I just change what I told my friends?

I can’t remember a time when I wasn’t interested in math. When I first went to school, I was already skipping the regular kindergarten math class for a more advanced math discussion group. I progressed at the fastest pace allowed by my very generous elementary school principal, ultimately taking Calculus as an eighth grader. So when anyone had an occasion to comment on my future, math professor was always the first choice. Oh, I did get “IRS agent” from Myers-Briggs, but that was just because I thought I was an introvert because I didn’t like parties. And Neal Bansal did think I’d fit in well at the NSA…

Anyways, math is in this weird position in school where it’s literally the only class you take your entire education. Well, maybe there’s English as well, but that’s not so clearly tracked. In fact, I was a bit confused when some of my fellow high school graduates decided they’d be majoring in engineering — we didn’t even take that class!

But it wasn’t math classes that ultimately inspired me. They quickly became humdrum, even when they weren’t filled with jocks five years older than me asking if I had picked up any chicks outside class. I might have had what I interpreted as a nightmare when I was young where I wasn’t allowed to take math class, but after I got to high school having exhausted all of the standard curriculum, I hardly missed it.

It’s the few, the proud, and the emotional

That’s because math competitions had taken on that mantle. And it wasn’t just the big moments of making it to National Mathcounts or attending my first Math Olympiad Program the summer after my freshman year. It was becoming the first elementary school in Colorado make States. Cracking under the pressure of the Countdown Round and just missing Mathcounts Nationals my seventh grade year. Then coming back the next year and not just going to Nationals myself, but my teammate joining me and together winning with our coach a trip to Nationals as a team.

Proving my… ability to prove things to one of my coaches between my dismal showing in eighth grade and second place in ninth grade at the Colorado Math Olympiad, and then following that up with the first two perfect papers in the next two years. Avenging two straight failures to make it back to MOP by becoming one of twelve USAMO winners my senior year, and getting perfect scores on the AMC and AIME on the way. Beating legend (and friend) Alex Zhai in our National Mathcounts countdown round and then on the USAMO twice.

I see a whole room of these mutant kids

Yes, I still remember all of those details off the top of my head. And no, I’m not trying to turn back time to the good old days. Instead, my point is how much of this motivation was community-driven. It was the math competition community that I wanted to prove myself to, that I came to find my home. It was my National Mathcounts teammates who first introduced me to the world of actually good board games through Settlers of Catan. And despite Alex and I being the only two out of nine USAMO winner seniors our year not to attend MIT (he went to Harvard), I found myself back among these math competition friends when I got here for grad school.

When I first got to MOP, it was honestly a bit of a fluke. I qualified for the middle of two tiers typically filled with sophomores and juniors, after having not even made it to the AIME the previous year. (If you haven’t picked it up yet, the progression is AMC-AIME-USAMO, and the highest scorers on the USAMO are invited to MOP.)

By the end, I knew it was a fluke. But it was inspiring to me because it opened me up to a fascinating community of passionate math competitors throughout the country and world. Through the experience, I also found the website Art of Problem Solving, a haven for those like me who were bored in math class. I was instantly immersed in that online community; these were my people.

MOP had a few talks by outside speakers, particularly either math professors or speakers from the finance companies that heavily invest in these things. Those became the two dichotomous options, and it was very clear that going to finance was selling my soul. No, it was math that I loved, math that I wanted to do the rest of my life!

Oh dear, I don’t know if we know why we’re here

But what does that actually mean? The fact that everyone takes one math class per year for over a decade is deceptive, because it changes dramatically from the speed computations of Mad Minutes to the days of carrying around a TI-87 Plus Plus (or whatever the latest overpriced graphing calculator goes by), to those dreaded proofs that made Math 1a the most notorious general requirement at Caltech.

I loved all of those stages, and naturally extrapolated. Each new stage was an added challenge, and as I mastered one level, it only opened up another. The challenge of math competitions had sustained my interest through high school, but when I got to college, it was the challenge of taking advanced math classes, as I took what my fellow math majors would label the “suicide sophomore year” set of classes: graduate level algebra, undergrad analysis and topology.

That form of striving was best summed up by what one friend described as his motivation to going to graduate school in number theory: It was, simply put, the hardest subject he could find. There’s a particular status that comes with being able to master material that other people can’t even understand, at least in our own heads.

They think this thing is a highway

I remember early in my grad school years sitting on a panel to discuss grad school applications with some MIT math major undergrads. One of the professors on the panel warned them that they better have straight A’s in their math classes (or close to it) if they want to go to grad school. And, well, I did have straight A’s (or really, A+’s) coming out of undergrad…

So I embraced that path. There’s a certain security with knowing that you have a career option planned out ahead of you. It’s an easy answer to all of the questions from friends and family. It sounds strange, but I remember envying the draft process in major sports, where if you’re good enough, the teams choose you. No need to figure it out on your own; just go where they tell you to.

Unfortunately, the converse of what the professor said isn’t true. Just because A’s are necessary for grad school doesn’t mean that everyone with A’s should go to grad school. And just because I was good at solving competition math problems or problem sets doesn’t mean I’d be good at research.

I’m a pro at imperfections and I’m best friends with my doubt

In the end, my contrarian nature finally caught up to my comfort and ease in following a seemingly pre-ordained path. It wasn’t the first time I rebelled against the most common route; seeing how many math / CS double majors there were at Caltech led me to chart my own path with a math/chemistry double major. When my classmates were taking a utilitarian approach to their classes and majors, I took the approach of passion, describing that double major in chemistry I’d never use as “just for fun.”

The key to my later evolution, though, was that I explicitly questioned my dream. I looked back and realized that a chunk of my motivation was explicitly pride, to show that I was good enough to tackle the next challenge ahead, to study math simply because not everyone was able to do so. I wanted, in the immortal words of my childhood, “to be the best, like no one ever was.”

This wasn’t the only motivation, to be fair. I also love understanding how things work on a deep level, and math offered that in a way that chemistry clearly didn’t. One moment in my summer of chemistry research stands out: My grad student mentor and I were talking about how to get a reaction to work, and we e-mailed the professor. “Use silver” was his reply — the classic professorial curtness combined with an inexplicable suggestion that even if it did work wouldn’t really have taught me anything about why.

But as I wrote about previously, that desire to understand things at the deepest level possible has actually been a liability rather than an asset in grad school. It makes it more difficult to work effectively with others, because if I understand something much deeper than they do, they don’t feel that there is anything to add. It’s also led me to drill down far too deeply into individual problems rather than maintaining broad enough interests to pull different fields together.

Now I’m insecure and I care what people think

The other progression that changed my attitude ultimately came from my faith. Questions like, “Do I really love my math research so much that I’ll deliberately misrepresent my understanding of its applications in order to get funding for it?” forced me to directly resolve conflicts between my morality and my passion. If no one cared about the papers I’d write apart from a very small mathematical community, was it really worth my effort?

This didn’t lead to anxiety or insecurity per se, but it did lead me to consider whether any non-mathematicians would care about my work. And when I ultimately concluded that no, they wouldn’t care, it led me first to procrastinate and drag my feet on my work, and ultimately to migrate to yet another field.

The problem comes when this keeps happening. Finding a good problem is a fantastically difficult exercise; it requires a confluence of at least six generally conflicting attributes: The problem needs to be unsolved yet tractable, general yet useful, important and interesting.

And in the last 4+ years of looking, I have yet to find a good problem that fits all six of those criteria. I still have some hope for my current line of work, but it’s a tenuous hope that sometimes often me turning elsewhere for meaning, from politics to blogging to my church to yes, sadly, online Dominion again.

Heard you say, not today

Scott Alexander articulates a helpful distinction between two types of goals for me:

A pulling goal is when you want to achieve something, so you come up with a plan and a structure. For example, you want to cure cancer, so you become a biologist and set up a lab and do cancer research. Or you want to get rich, so you go to business school and send out your resume.

A pushing goal is when you have a plan and a structure, and you’re trying to figure out what to do with it. For example, you’re studying biology in college, your professor says you need to do a research project to graduate, and so you start looking for research to do. You already know the plan – you’re going to get books, maybe use a lab, do biology-ish things, and end up with a finished report which is twenty pages double-spaced. All you need to figure out is what you’re going to select as the nominal point of the activity. There’s something perversely backwards about this – most people would expect that the point of a research project is to research some topic in particular. But from your perspective the actual subject you’re researching is almost beside the point. The point is to have a twenty page double-spaced report on something.

My entire PhD has been one big long pushing goal. I don’t have a particular end in mind, besides publishing papers that change how people do something in a positive way. I don’t have a feel for the difficulties inherent in industry, and I’m not sure I’d get that without going out into industry first. It’s actually really hard to tiptoe downstream, much easier to communicate from downstream back upstream what the real difficulties are.

This is one reason why I could potentially see myself returning to the ivory tower one day, once I’ve gotten a feel for the lay of the land and where the important problems actually lie. In my ideal world, academia wouldn’t be primarily populated by fresh college grads, but late career professionals and retirees eager to generalize the observations they’ve made in industry.

It’s probably not that likely, though. My current hypothesis is that there aren’t nearly enough generalizable problems for industry to give back to academia at the scale that academia currently exists, at least in the fields I’ve come into contact with. We’ll see, though.

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