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Axiom Math formalizes Stacks Project into Lean code using agent swarm
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Axiom Math has formalized the Stacks Project, a major reference work in algebraic geometry, into Lean code so that a computer can verify the logic line by line. The company ran its agent swarm like an engineering organization, with humans assigning some agents to architecture, others to core definitions, and others to individual proofs. Lean checks every completed proof, and each tagged result links to its original text and dependencies. Nothing entered the library unless the logic held. The result is a free, open-source library where a substantial portion of modern algebraic geometry exists as computer-checked code rather than only as text. Mathematicians or AI models seeking to prove something new in the field can reuse the already-verified definitions and theorems instead of rebuilding them, and a computer will flag any step that does not follow.
Source report
Vibe coding at scale has a reputation for producing slop—so Axiom Math formalized the Stacks Project to show otherwise.
Mathematicians usually trust a proof because experts have read it. Axiom Math has instead turned an entire field's reference book into Lean code, so a computer can now confirm the logic line by line.
An Engineering-Org Approach
Axiom ran its agent swarm like an engineering organization, with humans assigning some agents to architecture, others to core definitions, and others to individual proofs.
Verification and Traceability
- Lean checks every completed proof.
- Each tagged result links to its original text and dependencies, so the pieces fit together like panes of the Louvre's pyramid.
- Nothing entered the library unless the logic held.
What This Means
The result is a free, open-source library in which a large chunk of modern algebraic geometry exists as computer-checked code rather than 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.
Source
rohanpaul_aiNeutral / independent
Part of this Story
Axiom formalizes entire Stacks Project in Lean with 16 million lines of code