Axiom Math verifies Stacks Project, enhances 7,654-page library with Lean code

Axiom Math announced on Wednesday that it has formally verified the Stacks Project, one of the most extensive collections of modern mathematics ever compiled by human researchers. The verification, performed by the startup’s fleet of AI agents, translates the 7,654‑page online library into roughly 16 million lines of Lean code that a proof‑assistant checks line by line. The effort marks the first time the entire Stacks Project has been rendered into a machine‑checked formal proof, a milestone for the $1.6 billion AI‑driven venture founded by former Stanford PhD student Carina Hong.

The move comes amid a flood of AI‑generated mathematics that has raised concerns about quality and reproducibility. In the past month alone, OpenAI released 719 manuscripts claiming breakthroughs on some of the field’s toughest problems, many of which later required human scrutiny to confirm. Formal verification offers a way to guard against such “AI slop” by ensuring that every theorem rests on a sound logical foundation, similar to how engineers verify chip designs or how French researchers have used the technique to catch bugs in social‑benefit software. By anchoring AI‑driven research in a rigorously checked base, Axiom hopes to keep the rapid pace of discovery from devolving into a sea of unverified claims.

Axiom’s AI agents were tasked with converting the Stacks Project’s interconnected web of definitions, lemmas, and theorems into Lean, a programming language designed for formal mathematics. Maintaining the intricate dependencies across the 16 million lines of code proved challenging; the team had to ensure that each definition remained consistent and that no paradoxes slipped in. “Things that are big and delicate in life just don’t go together,” CEO Carina Hong told TechCrunch. “You want theorems to be consistent and not paradoxical, and the definitions not to fight with each other.” The company raised a $200 million Series A round led by Menlo Ventures in March, funding the ambitious effort that began shortly after its March 2025 launch.

If successful, the verified Stacks Project could become a trusted foundation for future AI agents that write software, prove new theorems, or even conduct scientific research. Mathematicians such as Columbia’s Peter Woit have long praised the Stacks Project as comparable to the historic Bourbaki volumes, and its formalization may set a new standard for how the discipline embraces automation. Axiom plans to extend its verification pipeline to other major mathematical libraries, aiming to create a growing corpus of machine‑checked knowledge that AI can safely draw upon without risking logical errors.