Academics

Now

I’m a sophomore, class of 2028, at Mass Tech. There, I study Course 18-C, or Mathematics with Computer Science. I’m generally interested in finding applied domains to explore using theoretical machinery in mathematics, especially category theory, algebraic topology, and homotopy type theory. I like working on problems where we can formally and rigorously prove things, but also in domains where those proofs genuinely advance our understanding of the world at large. I want to work on the boundary of what’s intellectually tractable and genuinely insightful. This is a theme that motivates most of my current work and research.

Previously

I went to San Ramon Valley High School in Danville, California. I spent most of my time in high school building robots with Team 1280.

Classes

In case you’re not familiar, MIT has a program called OpenCourseWare (OCW) that publishes the course materials for many classes at the Institute online, where they can be accessed for free. In most cases you can genuinely teach yourself the material by working through the course notes and assignments. Where possible, I try to link to the OCW pages for classes I’ve taken, so if you’re interested in any of the topics discussed, you can explore them as deeply as you like.

Courses that start with an “ES.” are equivalent to another standard MIT course, but are taught in the Experimental Study Group (ESG), which is a first-year learning community I joined.

The Independent Activities Period (IAP) is a four-week optional academic program in January that’s a customary interlude between the fall and spring semesters at MIT. You can read more about it here. The gist of it is that you can take both for-credit and non-credit courses (many of which are run by students) along with a smattering of other exciting activities that span the gamut of intellectual distractions.

Fall 2025

• ES.200 ESG Undergraduate Teaching

  • This is the ESG teaching seminar. It’s required of all first-time teaching assistants—this was my first semester as a TA for ES.1802, which I thoroughly enjoyed. Teaching is significantly more difficult than I expected, and there is actually quite a lot of research into pedagogy that I was previously not aware of. The main textbook we used is The Torch or the Firehose, which is a delightfully entertaining guide to teaching a recitation section, written by former MIT mathematics professor Arthur Mattuck. I would highly recommend it to anyone interested in teaching, specifically in a university setting.

• 18.701 Algebra Ⅰ

  • This class is highly nontrivial. Definitely the most challenging class I took this semester. The title is hilariously misleading, though if you add the word “abstract” to the beginning, it’s actually quite accurate. We study the fundamentals of group theory and linear algebra, along with the connections between them. I think the traditional introduction to modern mathematics separates these two topics, but they are fundamentally connected, and studying them in a single course allows you to go back and forth between analogous ideas in the two subjects. I took this class with Prof. Cohn, who is an especially engaging lecturer. He jokingly suggested that rotating pizza (none pizza with left beef, anyone?) using the orientation-preserving symmetries of the plane, , is the greatest application of what we’ve learned, and that’s honestly not far from the truth. The subject matter is mind-bendingly abstract, but it’s also foundational to a whole host of more applied domains, where fundamental universal structures like groups and linear transformations serve as a natural language for describing problems in applied mathematics.

• 18.100B Real Analysis

  • I was lucky enough to take this class with Prof. Guth, whose lecture notes helped elucidate the key ideas behind analysis. We study the great proofs—right and wrong—of the main theorems in calculus, and then develop the tools to understand and apply them. The latter half of the class lies mostly outside the realm of traditional single-variable calculus—we touch on the ideas of completeness and compactness in general metric spaces. It’s an excellent training in pre-topology, if that exists. The last lectures survey a collection of fascinating topics in Fourier analysis, differential equations, and calculus of variations.

• 14.770 Introduction to Political Economy

  • By far one of the most intellectual classes I’ve taken at MIT. The class is divided into an exploration of two distinct focus areas: theory, covered by Prof. Wolitzky, and empirics, covered by Prof. Banerjee. I’m of course partial to theory, but both these concepts complement each other well. We cover the fundamental ideas of political economy, starting with the standard introduction to social choice and ending with a survey of current research into identity politics and political agency (e.g. the effects of protests and revolutions on shaping policy and national outcomes). We of course survey a great many empirical studies which test theoretical predictions, like the median voter theorem, against the reality of local and national politics across the world. I came into the class mostly interested in social choice theory, but I’ve realized there’s so much more to political economy that makes the field such a rich area of study. We also use a fair amount of game theory, the economist’s fundamental mathematical tool, to explain sometimes baffling results.

• 6.1200 Mathematics for Computer Science

  • Essentially your standard introduction to the dark arts of discrete mathematics. This is of course proof-based, but the relevant proofs are not all that complicated. There are a great many tricks you learn for handling common classes of mathematical problems in computer science. A lot of the material, however, is trivialized by more advanced mathematics, like abstract algebra and category theory.

  • All of my problem set submissions, which run the gamut from trivial hacks to complicated algebraic sleight of hand, can be found in this repository.

• 1.044 Applied Category Theory for Engineering Design

  • Most people don’t know what category theory is, and of those who do, the majority can’t even fathom what applied category theory is. This class is perhaps the best introduction at MIT to category theory and applied category theory in particular. Most of the content covered was directly related to my work as a UROP in the Zardini Lab. The fun part is the second half of the course, which is a combination of guest lectures (Petar Veličković’s talk on geometric deep learning was particularly insightful) and a final project.

  • The best part of this class is the final project, where we worked to apply co-design to modeling some real-world challenge (the “applied” in “applied category theory”). I worked with Niclas Scheuer on modeling planetary defense systems with co-design under Project Blue Dome. The results of this technical study, which involved several thunks of Haskell that created a templating metalanguage for MCDP, are publicly available in this repository.

Spring 2025

• ES.S30 Many Interesting Things

  • This was a wonderful seminar run by Christian Cardozo at ESG. It’s a sampling of a random assortment of topics ranging from circuit design to neural networks, though the content changes every year. A significant portion of the class is directed by student interests, as is true for most classes at ESG. As a final project, I gave a talk on the foundations of cryptography; the slides are available on GitHub.

• ES.8022 Physics Ⅱ: Electricity and Magnetism

  • Given my experience with 8.012, I was expecting this class to be unfathomably difficult—I wasn’t completely wrong, but it turned out to be conceptually simpler than 8.012 in many ways. We talk a lot about symmetry and applications of Stokes Theorem and therefore mostly deal with very nice, idealized problems. Think of the spherical cow. The fundamental physical concepts at play here are deceptively simple, and it takes a lot of work to truly understand what’s going on—I’m not even sure I do completely (see my thoughts on 8.223 for more about this point). At the same time, this is the quintessential introduction to “thinking like a physicist” if there ever was one.

  • We used Scott Hughes’s lecture notes as a textbook of sorts for this class, and I found them to be extremely helpful and well-written. They clarify the key concepts, go over common misconceptions, and really try to get to the fundamental principles at work in each example, as opposed to complicating and obscuring the main ideas and further confusing the reader, like most physics texts do (I’m especially disgruntled by Kleppner and Kolenkow’s absolutely incomprehensible An Introduction to Mechanics that I used for 8.012)

  • There were a lot of interactive Jupyter notebooks that we used in this class to visualize certain prototypical examples of fundamental concepts in electricity and magnetism. I attempted to create a working Nix environment to run these notebooks where I could locally test out solutions to different exercises, but it quickly became riddled with Python bloatware and security holes, so I abandoned it at the time. I have not since written out solutions to the exercises or fixed the issues, but I may in the future, in which case I’ll post a link to the source code here.

• ES.7013 Introductory Biology

  • Given my less than passable knowledge of chemistry, it’s surprising my introduction to biology was anything short of disasterous. I somehow survived, but biology seems even more empirical than chemistry and rests on very shaky theoretical foundations. In case you couldn’t already tell, this is a GIR, so I did not have much choice in whether to take it.

  • One of the benefits of taking this in ESG is the ability to do a final project, which for this class is an executive summary of a research paper. I did mine on applications of category theory in developing foundational models in biology, which you can read about on GitHub. It seems there truly is no subject that is immune to the category theory mind virus.

• ES.1803 Differential Equations

  • This class gives you a lot of very powerful tools to tackle entire families of differential equations, but a full understanding of those tools still eludes me, as the class is not proof-based. However, looking back on the material, now with a background in linear algebra and analysis, things begin to make much more sense. Being able to solve differential equations is certainly a powerful skill, but at times I felt as though I was being pushed into engineering territory, which is quite dangerous. All in all, I learned about some interesting mathematical machinery for understanding the language of the universe, though I’m still pondering the relevant theoretical foundations.

• 24.900 Introduction to Linguistics

  • I might be slightly impartial since I had a previous interest in linguistics prioir to taking this class, but I found it an extremely intriguing and thought-provoking introduction to the study of language. Ideas were well-motivated, and even in the short amount of time we spent discussing them, we touched on open research questions in the field, such as causes of wh-movement. Prof. Richards is also a phenomenal lecturer, and his work on reviving the Wampanoag language is very exciting. As part of the class, you conduct a field study of a language other than English, which really highlights the universality of many of the topics we discuss in class.

  • This is also a CI-H subject, which means more essays! There were also problem sets that consisted of some analysis exercises and fieldwork. I chose to study Marathi, and you can find my notes for the class on GitHub.

IAP 2025

• ES.S20 Group Theory Seminar

  • This was a quick introduction to group theory taught as a seminar in ESG, touching on many fundamental concepts that I would later uncover in greater depth when taking 18.701 Algebra Ⅰ. Working through some of the problems in this class showed me that group theory can become quite nontrivial very quickly, and also that there’s a lot of overlap between group theory and number theory—two fields I would not have expected to be related at all. In some ways, this is the beauty of mathematics—abstract structures are fundamentally related to each other, and branches of mathematics do not exist in isolation.

• 8.223 Classical Mechanics Ⅱ

  • Probably the best follow-up class to 8.012. It was still difficult, but noticeably less so compared to 8.012. I think the mathematical elegance of the Lagrangian/Hamiltonian formalism allowed me to tackle significantly more complex problems with equally more powerful machinery. Lagrangians and Hamiltonians are the basic building blocks of modern physics, and applicable well beyond classical mechanics, but this class made me realize that classical mechanics in and of itself is a deeply interesting field of study. Physicists will almost certainly disagree with me, but I stand by this opinion so much so that I feel compelled to take 8.09, or Classical Mechanics Ⅲ, at some point in the future. The final thing I remember from this class is the quote:

    Before I came here, I was confused about this subject. Having listened to your lecture, I am still confused—but on a higher level.

    —Enrico Fermi

    which just about sums up my current understanding of physics.

Fall 2024

• ES.8012 Physics Ⅰ: Classical Mechanics

  • This class was difficult. Most of what I remember from my first semester at MIT is some mix of pondering preposterous physical environments in problem set questions well beyond what I could intuitively understand and exploring the fundamental concepts in classical mechanics in greater depth. Taking this in ESG was certainly a great experience, and, above all, it taught me what physics is really about and the flavor of a “physicist’s approach” to a problem as opposed to a mathematician’s. There’s a beauty in the intuitive yet analytical aspect of physical reasoning that I didn’t quite appreciate until tackling the challenging problems of classical mechanics in 8.012. My experience in 8.223 made me realize I may have suffered for nothing, as classical mechanics is so much easier when treated from a Lagrangian/Hamiltonian perspective. But without a proper grounding in Newtonian mechanics, I don’t think I would have the same appreciation for physics as I do now.

• ES.1802 Multivariable Calculus

  • This is the last class in the required calculus sequence of the GIRs, which I took in ESG. It’s not proof-based, which is disappointing, but luckily Evan Chen happened to be a TA for the class the semester I took it. Turns out this was actually the last semester he taught multivariable calculus! He wrote his own course materials and spent time to answer difficult questions about proofs that went well beyond the scope of the class. I later went on to become a TA for this class in fall 2025. Much of the subject is still a mystery to me, but hopefully differential geometry will shed new light on the more abstract concepts.

  • Classes at ESG don’t have final exams, so in lieu of that, we had a final project that was a presentation on an application of Stokes Theorem. I chose a more theoretical focus and prepared a nonsensical monologue on Generalized Stokes Theorem that’s now available on GitHub.

• 14.73 The Challenge of World Poverty

  • This was a focused exploration of various aspects of poverty and the experience of the extreme poor in developing nations. The standard introduction to economics rarely touches on these topics and instead presents economic principles in a vacuum, without discussion of the impact of different policies on people’s lives. I was lucky enough to be able to take this class with Prof. Duflo, whose insight into the economic studies we discussed was invaluable—you can actually watch most of the lectures in the class OCW page. I am however partial to the more theoretical side of economics and likely will not run any randomized controlled trials. Nevertheless, understanding foundational empirical methods in economics was interesting in its own right.

  • This class is a CI-H subject (that’s code for a communication-intensive humanities class at MIT; i.e. anything that involves a nontrivial amount of essay writing), which means I had to write two essays over the course of the semester. You can find the Typst source for these essays on GitHub.

• 5.112 Principles of Chemical Science

  • This is one of the General Institute Requirements (GIRs) at MIT—i.e. classes that all students are required to take. Technically there are three options for the Chemistry GIR, but I decided to take 5.112 because of the emphasis on physical chemistry, thinking it would be closer to physics than chemistry. I have since learned that I do not like chemistry as a subject, as it’s too experimental and not grounded in theory—this class is, somewhat paradoxically, one of the primary reasons I decided physics was worth studying more deeply.