Programming is fracturing into layers — each with its own model of what 'correct' means. Formal proofs, simulations, probabilistic thinking. The future programmer won't just write code, they'll choose an epistemology.
A new experiment testing whether AI can autonomously solve real research mathematics — and what it reveals about the future of reasoning.
Why coordinates depend on the basis, and why a basis is really a measuring grid.
Coordinates must exist and must be unique. That’s why bases require spanning and linear independence.
A mathematical look at Putnam 2016 A1, focusing on where the real difficulty lies—and what formalization makes explicit.
What PUTNAMBENCH tells us about AI, formal mathematics, and why intelligence keeps shifting as tools improve.
Translating the continuous image of compact sets theorem into Lean 4
Exploring how continuous functions preserve compactness in topological spaces
Dependent type theory sounds abstract, but it's actually the natural way to express mathematical ideas. A hands-on exploration using examples from topology, analysis, and abstract algebra—with Mermaid diagrams to visualize how types depend on values.
What if you could write proofs where a computer checks every step, catches mistakes immediately, and helps you figure out what to do next? Welcome to Lean, the proof assistant that's changing how we think about mathematics.
Why some motions persist forever — energy, phase space, and structure
Stranger Things meets geometry: how three measurements and perpendicular bisectors reveal a circular boundary around the Upside Down.
A personal dialogue on robots, brains, Gödel, and why I still believe in chasing the missing equation—even if we may never write it.
A WASM-powered phase portrait demo.
From traces of representations to character tables for Z₄, S₃, and D₄.
A geometric journey through two-dimensional linear systems — centers, spirals, saddles, and the beauty of phase portraits.
For the third time in human history, astronomers have spotted an object that doesn’t belong to our Solar System. Meet 3I/ATLAS — an icy traveler from beyond the stars.
From small-angle pendulums to Mercury’s orbit, perturbation theory reveals how tiny nonlinearities create measurable cosmic effects.
A clear introduction to perturbation theory — how small parameters help us approximate and understand complex systems.
Pigeonhole Principle explanation
An intuitive guide to understanding one-dimensional dynamical systems through geometric and physical perspectives.
How I created my own custom ChatGPT-powered terminal assistant that understands natural language, runs locally with Ollama + Mistral, and can be launched from anywhere as a global CLI.
We explore how to check whether a finite group is a GVZ-group using GAP, character theory, and code. Includes visual flow and example analysis.
Dr. Harmon’s advice helped me move beyond memorization and learn how to understand the structure of mathematical proofs.
Tech Inequality
A quick guide for learning Astro the practical way, perfect for small business sites, blogs, and component-driven projects.
Interactive demo of how e changes the shape
A behind-the-scenes look at how I combined Framer Motion animations, MathJax rendering, and Astro content to create smooth visual math walkthroughs.
Exploring topological data analysis using persistent homology and the Iris dataset
How the Cantor set and compactness helped reshape my intuition for infinity, structure, and rigor in topology.