Axiom Math Formalizes the Stacks Project in Lean, a Mathematical Foundation for AI Agents
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Axiom Math has translated the whole Stacks Project into Lean with AI agents working in parallel, and the result comes to some 16 million lines. The agents found dozens of statements that called for changes and built counterexamples to show it. Axiom holds those fixes separately, since Johan de Jong does not want AI contributions in the original repository for now.
Axiom Math, a startup building AI for mathematics, released on November 4 a Lean formalization of the whole Stacks Project, the open algebraic geometry reference of roughly 7,500 pages. Lean is a language in which a computer checks every proof, and the result takes up some 16 million lines of code. The company calls it the biggest connected, reusable body of formalized mathematics anyone has put together.
Johan de Jong, a mathematician at Columbia University, started the Stacks Project in 2005, and hundreds of contributors have expanded it since. Each result carries a fixed four-character tag, and Axiom's version keeps it: at stacks.axiommath.ai the original text and the Lean code can be read next to each other, along with the dependency graph. According to Axiom, modern algebraic geometry had hardly any Lean infrastructure, because a single present-day proof can rest on a long chain of earlier theorems.
The work was carried out by a hierarchical system of AI agents designed by the company's mathematicians and engineers. The agents moved through the dependency graph in parallel: they translated statements, looked in Mathlib (the Lean community's mathematics library) for what already existed, built proofs and worked out prerequisites. To check that each formal statement says the same as the original, Axiom combined audits among several agents, automatic comparisons with the text and targeted reviews of the core definitions.
The process turned up dozens of Stacks Project statements that needed adjusting: hypotheses that were missing, edge cases in positive characteristic, and assertions that fail to hold with all the generality given. The agents built counterexamples for those cases and, when a false lemma left a gap in the proof of a larger theorem, found another route to prove it with its original hypotheses.
On October 21, de Jong asked that, for now, AI-generated comments and changes not be sent directly to the Stacks Project repository. Axiom keeps the formalization as a separate open-source project and stores its counterexamples and fixes in a repository of its own. It is the company's second large formalization in a matter of days: on October 27 it released one of the classification of finite simple groups.
According to TechCrunch, Axiom, founded in March 2025 by its CEO, Carina Hong, is a $1.6 billion startup, and in March it closed a Series A round of $200 million with Menlo Ventures at the head. The same outlet puts the Stacks Project at roughly 7,654 pages, while Axiom speaks of about 7,500. The company wants this verified foundation to be a starting point for AI agents, and in TechCrunch Hong and the Axiom team also present it as groundwork for the software those agents write.
Why it matters · analysis and opinion
Mathematical formalization had been moving forward by hand for years, one theorem at a time, and algebraic geometry was one of its big gaps. AI agents covering an entire reference work changes the scale of what is possible, but the most useful part may be what they uncovered: errors in a text that specialists had reviewed for years. The real test will come when mathematicians start relying on this library for their own work and find out whether it is convenient to use, not just correct. It also remains to be seen how it will sit alongside Mathlib and the Stacks Project community, which has asked to keep automated contributions at a distance. For everyone else, the message is a different one: AI that produces results needs something to check them.
Official source: Axiom Math · Written with the help of AI: how we make the news
