Axiom Math formalizes Stacks Project in Lean with agent swarm
This is the strongest public counterexample to the claim that large-scale vibe coding produces only slop: a full mathematical field survived machine verification. Mathematicians and AI researchers can build new proofs on top of verified foundations rather than re-deriving them, with Lean catching any invalid step. It also shows a practical pattern for running agent swams with human-assigned roles on long-horizon tasks.
Axiom Math converted the Stacks Project, a reference text for algebraic geometry, into machine-checked Lean code using a swarm of AI agents. Humans divided the work like an engineering org: some agents handled architecture, others core definitions, others individual proofs. Lean verified every completed proof, and each tagged result links to its original text and dependencies. The result is a free, open-source library where much of modern algebraic geometry exists as computer-checked code. Anyone, human or AI model, can reuse the verified definitions and theorems instead of rebuilding them.
Vibe coding at scale has a reputation for slop, so Axiom Math formalized the Stacks Project to show otherwise.
Mathematicians usually trust a proof because experts read it; Axiom Math turned an entire field’s reference book into Lean code, so a computer can now confirm the logic line by line.
Axiom ran its agent swarm like an engineering org, with humans assigning some agents the architecture, others core definitions and others individual proofs.
Lean checks every completed proof, and each tagged result links to its original text and dependencies, so the pieces fit together like panes of the Louvre’s pyramid.
And nothing entered the library unless the logic held.
All these means that now we have a free, open-source library where a big chunk of modern algebraic geometry exists as computer-checked code instead of only as text in a book.
In practice, anyone (a mathematician or an AI model) who wants to prove something new in this field can now reuse these already-verified definitions and theorems instead of rebuilding them, and a computer will flag any step that doesn’t follow.
