About

I'm a senior at Princeton University studying mathematics. I recently completed an exchange program at Tsinghua University in Beijing. My current research interests lie in convex geometry, where I'm working on problems related to the isoperimetric inequality.

I'm particularly drawn to finding simple, elegant proofs and explanations for fundamental mathematical concepts—whether it's the fundamental theorem of algebra or geometric inequalities. I believe that the most beautiful mathematics is often the most accessible.

I'm also fascinated by using AI to automate mundane tasks and exploring the edges of what it can do. This website, for instance, was built with Claude! I enjoy experimenting with AI tools to see how they can enhance productivity and creativity.

Beyond academics, I'm passionate about making STEM education accessible to underserved communities. In my free time, I enjoy mountaineering (I've summited Mount Adams, WA at 12,881 ft), baking, and reading the Bible.

Research

Computing the Isotropic Ratio Landscape on Polygons
Joseph Chai • Advised by Professor Ramon Van Handel • Bachelor's Degree Senior Thesis
Mathematicians have conjectured that the simplexes are the polytopes that maximize the isotropic ratio among all convex bodies in \(\mathbb{R}^n\) (the Strong Slicing Conjecture). This has been established only in \(\mathbb{R}^2\), where the triangle is the unique maximizer. In this paper, we use both theoretical and computational approaches to derive explicit formulas for the first and second derivatives of the isotropic ratio of a polytope in \(\mathbb{R}^2\) in terms of its vertices, with the aim of providing a foundation for attacking the conjecture in higher dimensions.
Strict Steiner Symmetrization for Polygons
Joseph Chai • Advised by Professor Alice Chang • Published in the Electronic Proceedings of EPUMD, 2025
In this note, we introduce a method called Strict Steiner Symmetrization that is an altered form of Steiner Symmetrization that fixes the number of vertices. The context of this paper will be to prove the Isoperimetric Inequality in \(\mathbb{R}^2\) via approximation by polygons. Specifically, we aim to establish that among all \(n\)-gon domains in the plane, the regular \(m\)-gon, \(m \geq n\), uniquely minimizes the isoperimetric ratio and that the limit of this regular polygon (that is the circle) achieves equality in the isoperimetric inequality.

Experience

Amazon
Seattle, WA
Incoming Software Development Engineer • SDE Rotation Program
Starting August 2026
Joining Amazon's SDE Rotation Program as a full-time software development engineer.
Amazon
Seattle, WA
Software Engineer Intern
Summers 2023–2025
2025: Led a proof-of-concept financial attribute calculation engine to integrate across 5 services; projected to increase revenue within the org by 3–4% annually.

2024: Built an API Playground website (2,000+ LOC) for Financial Services, reducing onboarding by 6–7 hours/week for engineers and saving clients 3–4 days per integration.

2023: Reduced Elasticsearch query latency from 90–110s to <5s by implementing AWS OpenSearch for an internal financial tool managing 250M+ documents.
Princeton University
Princeton, NJ
Teaching Assistant
2024–Present
TA for COS 126: Computer Science – An Interdisciplinary Approach; supported 100+ students in foundational CS concepts and problem sets.

Projects

多说 Duoshuo — Learn Chinese
Python, AI/ML • duoshuo.up.railway.app
An AI-powered conversational platform to help users practice speaking Chinese. Engage in dialogue with an AI tutor, get real-time pronunciation/grammar feedback, and don't forget to check out the character matching games.
Teach Children STEM
Queens, NY
Founder
2019-2024
Founded nonprofit expanding STEM access to low-income K–12 students; taught 160+ students across the US and Hong Kong through free courses.

Hobbies & Interests

Photography
Back in the day, whenever I traveled somewhere, I would always want to buy something from the gift shops as an artifact of memory. However, I realized that capturing the moments of these experiences was so much more rewarding. Plus, phone cameras right now still can't do as good of a job as digital cameras.
Photography 1 Photography 2 Photography 3 Photography 4
Food
Experimenting in the kitchen is one of my favorite ways to unwind. From trying new recipes to perfecting classic techniques, I love the creative and scientific aspects of cooking. Aside from cooking with others, I love to travel to remote places within other countries and try their local dishes! Whenever I'm traveling, you'll find me taking pictures of the menus of every restaurant I go to.
Cooking 1 Cooking 2 Cooking 3 Cooking 4
Hiking
I've summited Mount Adams, WA (12,881 ft) and enjoy the challenge and serenity of climbing. There's something profoundly rewarding about pushing physical limits while surrounded by nature's grandeur. It's nice to not stare at digital pixels on your screen every so often.
Mountaineering 1 Mountaineering 2 Mountaineering 3 Mountaineering 4