Exploring Mathematics and Patterns

Hey, I'm Jorge — an applied mathematics student and developer with a focus on ML systems, numerical simulation, and backend tooling.

I build things that sit at the intersection of math and engineering: browser-based neural net controllers, Olympiad problem platforms, AI-powered web tools. My work lives on GitHub and in the Projects section.

I'm also interested in the deeper questions — where mathematical insight comes from, how formal reasoning scales, and what AI exposes about the structure of knowledge. That's what the Blog is for.

Where to start

If you're new here, here's the easiest way to explore:

• Projects — ML tools, math platforms, and client production apps. Built with Python, PyTorch, Next.js, and Rust/WASM.
• Blog — essays on topics from algebra and representation theory to physics and dynamics, plus problem walkthroughs (Putnam, GRE) and anything I find mathematically beautiful or surprising.

Featured post

If you want a post that captures what I've been thinking about lately — contest problems, structure, and what formal proofs reveal — start here:

Putnam 2016 A1: Where Insight Lives (and Why Formal Proofs Expose It)

From problems to systems

I'm fascinated by how reasoning works — not just how to finish a proof once the right idea is known, but how that idea is found in the first place.

That's why I like Putnam-style problems: they force you to notice structure before you can "compute" anything. And it's also why I'm interested in formal proof assistants (like Lean) and math-focused AI: they're excellent at verification, but they expose exactly where the human part of math still lives.

If that kind of thinking resonates, you'll probably enjoy the essays and problem writeups on the Blog.

One theorem on my mind

Currently, one of my favorite theorems is Maschke's Theorem — a fundamental result in representation theory which states:

Every finite-dimensional representation of a finite group over a field of characteristic not dividing the order of the group is completely reducible.

I love it because it's a theorem about decomposition: when symmetry looks complicated, it can often be broken into clean, understandable pieces — the kind of structural clarity I care about in both pure math and modern computational settings.

Thanks for visiting — I hope you find something here that makes you think a little differently about mathematics.