The Algebraic Arcanum
Thoughts, discoveries, and mathematical curiosities.
Inside the Wolfram Student Ambassador Program
A look at how I became a Wolfram Student Ambassador — and why Wolfram Alpha, Mathematica, and Wolfram Player are some of the most underrated tools a math-curious student can have in their toolkit.
The Weight of Error — How Mistakes Shape History More Than Plans
My entry for the John Locke Institute Global Essay Competition — a history essay exploring whether the plans of the powerful or their mistakes leave a bigger mark on the world. Tracing a thread from WWI to Apartheid, I argue that the two are inseparable, history is written by those who know how to turn mistakes into plans.
The Zeta Function: A Gentle Introduction
This past summer at PROMYS, I fell down the rabbit hole of zeta functions — and I haven't looked back since. This article walks through square-free integers, the Euler product, convergence, and how a clever trick with sin(x) leads to one of the most beautiful results in mathematics, ζ(2) = π²/6.
Christiaan Huygens and the Birth of the Pendulum Clock
Before Huygens, clocks lost up to an hour a day. This is the story of the Dutch physicist who changed that — and along the way discovered Titan, advanced the wave theory of light, and stumbled upon the mystery of synchronizing pendulums while sick in bed.
Getting Started with LaTeX: A Beginner's Guide
I've been using LaTeX since 7th grade, and it's one of the best tools I've picked up as a math student. This is the guide I wish I'd had starting out — covering installation, document formatting, essential packages, and a few fun sites that make learning LaTeX actually enjoyable.
My First Research Experience: Dynamical Physics
A behind-the-scenes look at my first independent research project — studying the synchronization of coupled pendulums. From finding a topic on YouTube to building physical pendulums to presenting at science fairs, here's everything I wish I'd known going in.
A USAMTS Year 34 Round 3 & Overall Review
A walkthrough of my experience with Round 3 of the USA Mathematical Talent Search — the hardest round yet. I break down my approach to each problem, where I went wrong, and what I'd do differently, plus some thoughts on why USAMTS is one of the best contests for sharpening your proof skills.
A USAMTS Year 34 Round 2 Review
A problem-by-problem breakdown of my Round 2 experience in the USA Mathematical Talent Search — from a tricky puzzle that almost had me reaching for code, to a problem I nearly solved perfectly but submitted at 9:58. Honest reflections on what worked, what didn't, and what I'd do differently.
A USAMTS Year 34 Round 1 Review
My problem-by-problem breakdown of Round 1 of the USA Mathematical Talent Search — including a puzzle I solved by pure trial and error, a problem I misread until three hours before the deadline, and a game theory problem I almost cracked by playing it with actual cards with my brother.
My Experiences at PROMYS (Program in Mathematics for Young Scientists)
Six weeks of living, breathing, and eating math at Boston University — here's my week-by-week account of PROMYS, from proving the Division Algorithm on day one to winning a frisbee game against MIT's RSI for the first time in 16 years. Equal parts math camp diary and guide for anyone curious about applying.
A Chain of Reasoning in Number Theory (part 2)
The conclusion of the chain — picking up from Bezout's Identity and pushing all the way through to Unique Prime Factorization. This part covers the Fundamental Theorem of Arithmetic, two proofs that every integer has a prime factorization, and why "unique up to units" is a more subtle statement than it first appears.
A Chain of Reasoning in Number Theory
Ever wonder how mathematicians build big results from tiny axioms? This article traces a chain of proofs in Number Theory, starting from a deceptively simple principle and working up to one of the field's most useful identities. It's the first part of a two-part series that ultimately leads to Unique Prime Factorization.