April 3, 2026
Proofs, pull requests, and popcorn
Automatic Textbook Formalization
AI study group formalizes a math textbook — cheers, side‑eye, and data drama
TLDR: A team of AI agents auto‑formalized a graduate math textbook in the Lean proof checker, showing AI can help write and verify serious math. Commenters split between excitement over a research breakthrough and suspicion about who gets the training data, with extra debate over which systems and foundations should win.
Bots just did a grad‑level reading group — and passed. RepoProver, a squad of AI “agents,” just auto‑translated, proved, and reviewed chunks of a real math textbook inside a shared code repo, then merged it like a normal software project. The prize? A formalized version of Darij Grinberg’s Algebraic Combinatorics — proof‑checked by Lean, a strict math verifier.
Cue the comment fireworks. The hype camp is loud: one user called it a “big step” toward AI doing actual math. The skeptics aren’t quiet either. The spiciest take claims this is secretly a data pipeline for future chatbots — complete with the jab that “Facebook paid” for training data — a claim very much framed as speculation, but enough to spark a mini‑conspiracy thread about who benefits from all these machine‑made proofs.
Others questioned the basics: Which chatbot models are even doing the work? No clear answer yet, though a helpful commenter dropped more details. Meanwhile, the “foundations war” broke out: one student said learning set‑theory‑based math in class while coding in Lean’s different logic felt like living in two universes. Translation for non‑nerds: folks are arguing whether the math language these bots use matches how humans traditionally write it.
Jokes flew too: “grad students replaced by a merge queue,” and “proof assistants becoming proof interns.” Love it or hate it, everyone agrees on one thing: if AI can crank through textbooks with human‑style reviews and clean merges, the math library of the future might build itself — and the comment section will be there with popcorn.
Key Points
- •RepoProver is a multi-agent system that automates formalization of mathematics textbooks in Lean using LLM-based agents.
- •Agents are role-specialized: sketchers translate statements, provers attempt proofs, reviewers enforce quality via pull request reviews, with coordination via a filesystem issue tracker and merge queue.
- •The system produced an automatic formalization of Darij Grinberg’s Algebraic Combinatorics textbook.
- •Setup requires a Lean project with Mathlib, organized LaTeX sources, a CONTENTS.md, a manifest.json listing target theorems, and an issues/ directory, with git initialized on main.
- •A coordinator manages agents and progress; distributed runs are supported via a stool launcher that submits SLURM jobs and uses symlinks to avoid heavy copies.