Welcome to Altered Chain
Hey, I'm Jorge — a student of mathematics with a constant curiosity for the deep structures that connect abstract theory and the physical world.
Altered Chain is my digital lab — a space where I explore how ideas from pure math, physics, and data intertwine, from symmetry in tensor spaces to the hidden patterns behind real-world systems.
Whether you're a fellow math enthusiast, a student navigating science, or someone intrigued by how abstract reasoning explains reality, this blog offers a mix of rigorous analysis, creative inquiry, and reflections on the evolving landscape of mathematical and scientific discovery.
I'm also fascinated by problem-solving itself — how a clever trick or a small shift in perspective can make a tough problem unfold. Here’s one of the problem-solving principles I keep in mind:
problem-solving tactics
Relation between them
Permutations and combinations are connected by $$^nP_k = k!\binom{n}{k}.$$ Choosing first, then arranging.
Join me as I connect ideas across disciplines and contribute to a community passionate about understanding the universe through the lens of mathematics.
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.
It’s a beautifully precise insight into how symmetry can be decomposed — and it reflects the kind of structure and elegance I hope to uncover in both mathematics and physics.