One of my {worst, best} personality traits is that whenever someone tells me something is hard or impossible, I have an immediate, almost uncontrollable urge to do that exact thing. That is how I’ve made some of my past choices about college, classes, extracurriculars, projects, and research, which is probably not always a good thing or productive use of time. However, one of my colleagues asked me about how one would encourage this mindset, since he wants his daughter to become more comfortable with being challenged.

So I thought about it, and I think part of the impulse has just been me always being stubborn. But a large part of this impulse also stems from an experience in undergrad that completely broke me. To be clear, I don’t want to advocate for purposefully pushing yourself past the breaking point. But as trite as it is to say, I really do think each overcome challenge makes the next much easier, sometimes in a way that’s hard to fully appreciate until you push yourself almost too far.

I consider the lowest point of my academic career to be the semester I took my first operating systems class. My undergrad required all CS majors to take this class, and it was infamous for having brutally difficult and time-consuming projects. That semester lived up to its reputation: my group and I would spend ≈30 hours in the lab each week struggling to finish these projects (on top of other classes, research, etc.).

The reason I say this experience broke me is because I felt broken: computer science stopped making sense to me, and I no longer wanted to do it anymore. For the first time, I would sit down in front of a problem and have absolutely no idea on how to proceed. That internal sense of direction that used to always know how to navigate a problem had vanished. Devising solutions and coding up answers in that class no longer felt right or satisfying the way they used to.

I had never felt so defeated before, and part of me wondered if this meant I didn’t have what it took to be in computer science. I remember a particularly demoralizing debugging session where I took a break outside and stared vacantly at the 3am sky, wondering if I should switch majors. In the end, I brute-forced my way through the class by working as hard as I could, ultimately performing very well. But even though I was able to derive all of the correct solutions, it was never through that intuitive sense of clarity that had guided me through all of my other classes.

However, I later became a TA for that class. And one day, as I was reviewing one of the project specifications ahead of office hours, I realized that the old feeling I had missed was there: all of the possible solutions to the project just made sense. They were so clear, so obvious—how had I ever been confused by this?

This realization completely changed the way I view intuition, and it made some part of me want to chase after that high of achieving something that had seemed so difficult. It was empowering that a problem that had once seemed so impossible, so inscrutable, was now elementary and trivial to me. I finally understood that intuition was not something I either had or didn’t have, but rather something that could be built. Just as importantly, this experience made me comfortable with that feeling of being broken, of struggling to understand exactly what I was doing, so that I would not give up before things finally clicked.

I later took real analysis in undergrad, intrigued because I had heard so many horror stories about it being some sort of hazing/rite of passage for math majors. It was sort of a similar experience to that operating systems class, where writing proofs was no longer as intuitive and clear as it had once been. I was perfectly fine with epsilon-delta proofs and anything that touched the number line, but the moment things became too abstracted away—well, suddenly it was all just symbols that didn’t mean anything to me, and I had no idea what I was supposed to do with them.

This ended up being the only class I’ve ever had an actual nightmare about, and the only class where I would lie fully awake in bed each night before an exam, unable to sleep from anxiety. But a lot of what got me through that semester was reminding myself that I had once overcome the seemingly impossible in operating systems, so surely I could do it again. I am still not sure if that semester was necessary or worth it, but in the end, I performed well and emerged a much better mathematician.

Though I do not use much direct knowledge from my operating systems or real analysis classes in my research, those experiences have certainly shaped how I go through my PhD. A large part of it is being comfortable with sometimes feeling confused and lost when I work on projects, especially those on initially unfamiliar topics. The other aspect of this is that I am far too eager to jump into hard projects, which may not always turn out to be a good thing.

When one of my advisors was suggesting project topics, he first suggested genome assembly. It was a problem I had always found somewhat interesting, but then my advisor went on to describe it as the hardest problem in our field, saying that this would be the most challenging option by far. That was enough to make me immediately want to work on it—I listened to my advisor’s other suggestions and thought about them as well, but I already knew deep down that I would be picking assembly. Other researchers in my field have similarly described it as an absolute behemoth of a problem to tackle, which only made me more excited to get started.

And, well, who could’ve guessed? They were right; it’s hard. Every step is twenty times more complicated than I had initially expected. Sometimes I open my computer and stare at my deformed assembly graphs and wonder why I was so stubbornly attached to the idea of trying this. I wonder if perhaps I was being too naïve—what if I finally hit the wall? What if I finally flung myself at a problem I can’t overcome?

Since this project is still ongoing, I can’t say whether I will emerge victorious from this project the way I have in the past. Sometimes it really feels like I won’t. But then I think about how much more I know compared to even just a month ago, and how those initial stages of the project already make so much more sense. And I think about those once-impossible operating systems projects, and those once-impossible real analysis proofs, and I think I can maybe emerge okay.