Hi, I'm Caius.

I do mathematics research with AI. I've written 29 Lean-verified papers so far, mostly in convex geometry, representation theory and commutative algebra. Along the way, I've settled the Heine–Shephard volume polynomial characterisation problem, Jockusch's cubical lower bound, the Hivert-Thiéry conjecture, and the Wishart product conjecture from random matrix theory. I'm currently working on theories for ample-nef multiplication and the integer decomposition property in toric geometry.

I've been really interested in ancient Mesopotamia for a while, and recently I've been working on reconstructing the financial system of the Third Dynasty of Ur from thousands of transcribed cuneiform accounting tablets. I built a harness for parallel researcher and verifier agents, and used it to produce structured interpretations of 19,000 tablets from the Girsu site, most of which have never been interpreted before. I'm currently trying to use these interpretations to build an accounting graph.

I've also written some notes on approximation theory and deep learning. Aside from all that, my favourite book is Stranger in a Strange Land, I think music peaked in the 2010s,  and my favourite math puzzle is pebbling a chessboard. According to a monitor I built, on an average day I type around 76,300 keystrokes.

I think science is an engineering problem, and it's time to solve it.