Reflections on Grad School – Ashwin Narayan ’16

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Ashwin Narayan ’16 left Williams with a math and physics degree and found himself in graduate school with little idea of what he was doing. Somehow, he’s muddled his way into his second year of a PhD in applied math at MIT, and he’ll keep going as long as the administration lets him.  Here are his reflections on his first year in graduate school.

The realization that my first year of graduate school had ended only really hit me when I returned from vacation and had to fumble with the keys to my new (and empty) office. The “ziggurat,” a wonderful open-plan maze of cubicles and chalkboards, my home for the last year, was already occupied by the new batch of first-years. The first thought that occured to me was that I’d have to update my Tinder profile: “First year grad student pretending I know things but really subscribing to the ‘fake it til you make it’ doctrine.” As a first-year, impostor syndrome is cute and funny; as a second-year, maybe it’s worrying and sad. With qualifying exams coming up in January, maybe it’s no longer a good idea to answer, “I’m not sure yet …” when someone asks you, “So what type of math do you do?” It’s easy to get overwhelmed by the monumentality of the upcoming challenges, and reflection has always been my way to cope. It’s comforting to look back on what you once thought would be impossible but ended up being completely feasible.

Two years ago, I entered my senior year at Williams with unprecedented levels of self-confidence. The previous semester, I had thrived in Budapest, proving to myself that (a) I could survive in the real world (i.e. without a dining hall) and (b) maybe I was actually decent at math. Then there was a very productive and enjoyable REU experience over the summer which ended with tantalizing whispers of a potential publication. The next steps were obvious: write a thesis that revolutionizes the field, take some more hard classes, go to graduate school next year, draped in flying colors. Then repeat steps one and two. But of course, we remember Of Mice and Men, and this wasn’t even a particularly well-laid plan.

My first indication that I had perhaps over-simplified my future was the GRE subject test in mathematics. After years at Williams, I had forgotten that standardized multiple-choice exams existed, especially in math. I lived for partial credit. And apparently I was pretty terrible at calculus. Getting fewer than half of the questions correct on an exam ostensibly meant to evaluate my competence in the subject I majored in was already demoralizing. But then I stumbled upon this truly awful website where applicants from previous years listed their biodata and the schools they got into. Students who appeared far more qualified than me were getting rejected from schools far less selective than the ones I had set my sights on. Blog posts told me that graduate school was a waste of time unless I was absolutely certain I wanted to go into academia. How could anyone expect a liberal arts student to be absolutely certain about anything? At this point I wasn’t even certain which majors I would be finishing at Williams.

Writing statements of interest compounded the existential dread. Why did I want to go to grad school? Why applied math? What areas of math was I interested in? How was I qualified to attend this program? I couldn’t possibly use the actual answer to those questions. I wanted to go to grad school because I wasn’t ready to go into the real world and couldn’t pay for law or medical school. Applied math because it seemed the most versatile discipline and thus a way to postpone any real decision making. But because I hadn’t actually taken any applied math classes, I had no idea what areas I was actually interested in. And thus I felt in no way qualified for any of the programs I was applying to.

Of course, things worked out in the end, but I wanted to describe the process in such excruciating detail to help you understand my mindset as I started grad school last year. I truly felt that I had no right to be there, and, worse, sooner or later everyone around me was going to come to the same conclusion. I was often lost when the other students would discuss the math they were interested in, citing theorems that everyone clearly knew but I had never heard of or had completely forgotten. To be honest, I still don’t really know what cohomology is or what representation theorists actually study. When professors described their research, I nodded along, but the whole time would be thinking, “Will I ever be this passionate about anything?” At Williams, they always told us that even though the others would know more math than we did, our liberal arts background taught us “how to learn” and that we would have better “depth of understanding.” Now, I have absolutely no regrets about going to Williams and push everyone I know towards small liberal arts schools, but I honestly still have no idea what it means to know “how to learn” and I’m starting to think that maybe I skipped that unit at Williams.

I can’t say that I’ve “overcome” this mentality, but I have found that I can live with it. I now tell myself, Maybe they did make a mistake in admitting me. But I’m here now and it’s too late for them to change their mind. If I can’t convince myself that I deserve to be here, the next best option is to accept that I’m already here regardless. In some sense it’s a meaningless distinction, but we learn in linear algebra that simply rotating our perspective on a problem often makes it far easier to solve. And one thing I did take from Williams is that when push comes to shove, I am willing and able to work as hard as necessary. Hopefully that will be enough.

Thus, despite my many insecurities, I had an extremely productive and enjoyable first year. Once you swallow your pride and accept that almost everyone around you knows more math than you do, you quickly realize how much of an advantage this is. Everyone is so absurdly excited to discuss the things they’re interested in that even innocent bystanders can’t help but get drawn into the enthusiasm. I was relieved that my fellow grad students were more than willing to explain the concepts I didn’t understand, and I learned as much from them as I did from my classes. One of the most striking differences from Williams was the sheer volume of events and seminars and projects and reading groups and classes. Every day the biggest names in various fields are giving talks, research groups are discussing dozens of fascinating projects, classmates are coming up with breakthroughs.

For me this meant that I spent the first semester just trying to figure out what applied math even meant. What was I interested in? In the true liberal arts spirit, I muddled my way into statistics, a field I knew nothing about and never expected to find myself in. Surprisingly, I never felt that this was a problem because the department seemed almost to encourage this experimentation in a way I never expected to be able to in graduate school. For the entire first year, there was absolutely no administrative pressure to decide on an advisor or even a research area. I took classes in quantum computing, (pure) probability, theoretical computer science, machine learning, computational biology, and Bayesian inference. After a year of happily wandering the state space of topics in applied mathematics, I found myself drawn to what I hope will become my research area: developing inference algorithms for analyzing biological data.

Graduate school is starkly different than the undergraduate experience. I needed this to be the case because I don’t think I could have survived another five years of Williams. Graduate school is, for me, an occupation. And even though it’s certainly not a traditional 9-5, this transition has been extremely important. Classes are less important, problem sets are shorter and less frequent, and the focus is on research. There are no dining halls, there’s an apartment to maintain, professional friends to stay in touch with. In other words, there is life outside of school, and it is important. I’m able to emphasize my physical and mental health in a way I never did at Williams. I didn’t realize how much Williams had consumed me until around halfway through last year, when I found myself feeling just healthy, a result of focusing on eating healthily, exercising regularly, and sleeping. This is not everyone’s graduate school experience, but I am utterly thankful that it has been mine.

The existential questions still nag though. As my relatives always ask, What are you going to do with a degree in math? I love working on difficult research problems, but with so many pressing issues in the world, I often wonder if research in mathematics is my long-term calling. For example, the lack of diversity in the math department and in STEM departments across the country is still staggering, and perhaps I should leverage my privilege and go into science policy. We have an administration in place that refuses to treat climate change with the seriousness it requires, so maybe I need to be putting my efforts into fighting global warming. Or maybe I just need to persuade myself that I am good enough at math that I could pursue a worthwhile career in research. The best part of being in a PhD program is that I have four more years to figure it out.

160 thoughts on “Reflections on Grad School – Ashwin Narayan ’16”

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    Ashwin Narayan, a 2016 graduate, reflects on his journey through grad school, emphasizing the intellectual challenges and growth he experienced. He highlights how the rigorous academic environment pushed him to develop critical thinking and research skills. Ashwin also shares the importance of mentorship, collaboration, and staying resilient during tough times. Overall, grad school was a transformative period that shaped his personal and professional path.

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  82. Ashwin, thank you for sharing such an honest and reflective piece about your first year in graduate school. Your candidness about imposter syndrome and the challenges of transitioning from undergrad to grad school is something many of us can relate to, even if we’re not in the same field. It’s refreshing to hear how you’ve navigated the uncertainties and pressures of grad life while still finding joy and purpose in your work.

    I particularly resonated with your point about the value of a liberal arts education and how it prepares you to “learn how to learn.” Even if it feels abstract at times, your ability to adapt and explore diverse fields like quantum computing, machine learning, and computational biology shows how versatile and valuable that foundation truly is. Your journey into applied math and biological data analysis sounds fascinating, and I’m excited to see where your research takes you!

    Your reflections on maintaining a work-life balance and prioritizing mental and physical health are also so important. It’s a great reminder that success in academia (or any field) doesn’t have to come at the expense of well-being.

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  84. This was such an insightful and relatable read! The transition from undergrad to grad school, especially in a demanding field like applied math, comes with so much uncertainty and imposter syndrome. Your honesty about navigating coursework, research, and personal well-being really resonates.

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