Axiom Math's AI Agents Build World's Largest Computer-Verified Math Library With 16 Million Lines

Axiom Math Achieves Formal Verification of Stacks Project

Axiom Math announced Wednesday that its AI agents have formally verified the Stacks Project, converting approximately 7,654 pages of advanced mathematics into 16 million lines of computer-checked code1

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. The $1.6 billion startup, founded by 25-year-old Stanford dropout Carina Hong in March 2025, now claims to have built the world's largest computer-verified math library. Columbia mathematician Peter Woit described the Stacks Project as having "nothing else really comparable," drawing parallels to the famous Bourbaki books that rebuilt mathematics from its foundations in the 20th century1

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AI Agents Working in Parallel to Preserve Mathematical Integrity

The formal verification of Stacks Project addresses a critical challenge facing mathematics today. Last month alone, OpenAI released 719 manuscripts claiming solutions to some of the field's hardest problems, raising concerns about AI-generated errors infiltrating mathematical research1

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. Axiom Math's approach uses AI-driven verification through the Lean programming language, where a proof assistant checks code line by line to ensure logical consistency. The interconnectedness of theorems and definitions in the Stacks Project made the task particularly delicate. "Things that are big and things that are delicate in life just don't go together," Carina Hong explained, noting that maintaining consistency across 16 million lines while preserving every connection posed significant uncertainty1

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To accomplish this AI-driven breakthrough, Axiom's technical team gave its agents a loose hierarchical structure and allowed them to work in parallel. "The agents were finding tasks for themselves and identified things that they could work on in parallel," said Ashvin Swaminathan, a member of Axiom's technical staff1

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. The company also trained its own models specifically for mathematical reasoning, an approach Hong said distinguishes Axiom from other verification startups. Initially, the team relied on in-house Lean experts to teach the agents human-like judgment, but over time, the AI systems developed this capability independently1

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Filling the Gap in Algebraic Geometry

The Stacks Project, launched in 2005 by Columbia mathematician Johan de Jong as an open-source reference, covers results from college-level algebra through the field's most advanced ideas across algebra, geometry, and number theory1

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. Before Axiom's work, researchers wanting to check new work in algebraic geometry with Lean had minimal foundation to build upon. "When you look at what has been formalized in mathematics, there's this huge black hole. And that black hole covers algebraic geometry," Swaminathan explained1

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. The verification process also uncovered problems in some original mathematical statements, including missing conditions and claims that were not always true, with AI systems identifying counterexamples and proposing corrections2

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From Mathematics to Software Development

Axiom Math's ambitions extend beyond pure mathematics into software development and scientific research. The company argues that each verified result becomes a building block, allowing future proofs to rely on checked mathematics rather than starting from scratch. Fields Medal winner Terence Tao has articulated this principle simply: "The more formalized proofs you have, the more formalized proofs you can make"1

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. As AI systems generate increasing amounts of code, developers face growing challenges guaranteeing their software remains free of bugs and security vulnerabilities. "We believe that mathematics is the domain where you start building these things, and that it's a transferable skill," Swaminathan said. "Agents can read our code, understand it, and build new infrastructure on top of it"1

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Hong, who holds bachelor's degrees in mathematics and physics from MIT and a master's in computational neuroscience from Oxford as a Rhodes Scholar, has attracted prominent researchers from Meta and Google to Axiom2

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. The company initially raised $64 million in 2025 at a $300 million valuation, then secured another $200 million led by Menlo Ventures in March 2026, pushing its valuation above $1.6 billion2

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. In January, Axiom reported that its AI system solved all 12 problems from the prestigious Putnam competition for university students, though only eight were completed within the official time limit2

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. The resulting collection has been made publicly available for mathematicians to examine and use, positioning Axiom's verified foundation as the substrate upon which future AI agents can build reliable systems.