First things first, don't take this post too seriously. At the end of the day I'm just messing around, and sharing… to reddit. Oh god.

I thought it would be fun to make AI try to "solve" a hard problem, and I choose 3×3 matrix multiplication. I have no idea what it's doing. I am not a mathematician. I am watching it go brrrr

Quick note: I use use many AI across many instances and architectures, and I am the human in the loop orchestrator, but I will refer to this as "the AI" since LLMs are doing the heavy lifting, and I'm just going along for the ride like a messenger boy.

This is the best I can articulate what it is (or what it thinks it is) doing:

• I started by getting it to build the ADE (algebra discovery engine), designed to generate novel algebras.
• It ran that and looked for known algebras to pop out as benchmarks. Things like the Cayley-Dickson tower were apparently produced unprompted, and many quaternion and octonions-like things.
• After that we scanned the algebra space using gradient descent methods with random seeds.
• Every result is logged to a database, and "isomorphisms" are checked to make sure they aren't the same algebra in disguise.
• Then it seeded algebra multiplication, the M(3, R). One interesting algebra M(3, R) has an associator defect of 1.0, which I am told is weird.
• At this point it's doing alot test of the most novel algebras. Mostly null results, but some new leads. About 10 hours of computation on a Ryzen 9 5900X yields about 700 "novel" algebra, and about 30 M(3, R) flavour ones.
• We also have a system where novel results are backfed as seeds for the next round of exploration

So yeah, that's what I've been up to this week. I don't really know what it's doing, I wanted to share the pretty data, and it's fun as hell 😈