I am a graduate student in mathematics who refuses to pretend physics is a different field. This is the notebook where I shall write about that; about structures, symmetries, the unreasonable effectiveness of one for the other, and the small joys of working at the seam which joins mathematics with nature.

The name A Feral Mathematician has a few things going on. The most obvious is a small literary debt: I read Neal Stephenson's Anathem in my early 20s when it was first published. Part 7 of that novel is titled "Feral." Feral refers to an avout who has left, been cast out, or maybe never was a part of this monastic order of academics, yet persists in the pursuit of knowledge. More broadly, a feral is someone who lives outside the ivory tower yet has devoted their life to understanding nature and mathematics. Less obviously, "A Feral" is an anagram of my middle name, Rafael. I won't pretend the layering wasn't intentional.

A bit of context: I'm an MS student at the University of South Alabama, currently working on reconstructing \(\mathfrak{sl}_2(\mathbb{C})\) as a diagrammatic algebra under the direction of Dr. Aparna Upadhyay. I teach the calculus sequence as a graduate TA; I'm preparing for a PhD next. Long-term I want to focus on Hilbert's sixth problem and what it means to axiomatize physics. I take a modern view that if axiomatization is the goal, then categorification is the method. Ultimately, I believe that this is a viable way to achieve unification of GR with QFT. I am also greatly interested in string theory, TQFT, and many other aspects of mathematical physics. Some people will tell you mathematics and physics are disparate fields and the gulf between them widens every day; I am already familiar with that view; they are kindly mistaken.

What lives here:

• Blog — long-form expositions on things I'm thinking about. Diagrammatic algebra, category theory, TQFTs, geometry.
• Fragments — shorter pieces. Conjectures, half-thoughts, references to remember. They share the tag pool with the long-form posts, so a fragment and a post on the same idea end up under the same tag.
• Research — pointers to active and finished work as it appears.

The Scriptorium is the year-grouped archive of everything published here, filterable by kind (all, posts only, fragments only). The Tags page lays out every label as a word cloud sized and colored by usage; each tag has its own page that mixes posts and fragments together.

The technical writing uses MathJax for inline and display math; code blocks get syntax highlighting in both themes (the toggle previews the destination, so you can see where you're headed). The thematic breaks on the About page are stylized analemmas, the figure-eight curve traced by the sun's noon position over a year, computed here from the equation of time and solar declination. The shape fits Anathem's tone of patient sky-watching, and astronomy is one of the older loves that brought me to mathematics. Atom feeds live at /feed/ for long-form posts and /fragments/feed/ for notes. No analytics, no trackers, no comment section. If you'd like to get in touch, email me at andy@andygarcia.me.