Formally verify the Stacks Project in Lean with a fleet of agents

Axiom Math, a startup led by CEO Carina Hong, set its own fleet of AI agents on the Stacks Project, the open-source algebraic geometry reference that Columbia mathematician Johan de Jong started in 2005. The job was to translate every definition and theorem into Lean code that a proof assistant checks line by line, while keeping the dependencies between results intact. The team imposed a loose hierarchy rather than assigning each agent its work: according to Ashvin Swaminathan of Axiom's technical staff, the agents found tasks for themselves and picked out pieces they could work on in parallel. Axiom used models it trained in-house for mathematics, and an internal Lean expert guided the agents early on.

Axiom announced on 4 November 2026 that the whole library, about 7,654 pages, is now formalized as roughly 16 million lines of checked Lean. Hong told TechCrunch the team had not been sure the agents could keep that many interconnected results consistent. Swaminathan says it fills the largest gap in formalized mathematics, since algebraic geometry had little Lean coverage before.

This is a company announcement reported by TechCrunch, not an independent audit; the article gives no cost, run time or count of agents. The agents and the models behind them are Axiom's own and are not available to the public. The result is the formal library, which other researchers and agents can now build on.