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Axiom Math announced that it has completed a formal verification of the Stacks Project, converting this roughly 7,654-page algebraic geometry reference into approximately 16 million lines of Lean code. According to a TechCrunch AI report, the company—founded in March 2025 and which completed a $200 million Series A round led by Menlo Ventures the same year—carried out the translation and proofs through agents working in parallel under a loose hierarchy and claiming tasks on their own, and developed its own math-specialized model, filling the gap left by algebraic geometry's lack of reusable foundations in Lean. Another report states that Axiom's released complete Lean formalization covers about 7,500 pages of the reference, retains the original text's permanent Stacks tags, and allows every Lean declaration to be traced back to the original text, so researchers and AI agents can directly import definitions and theorems; Axiom said that in the process it found dozens of statements in the original text that required additional hypotheses or corrections.
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Nov 6
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Axiom releases Lean formalization library of the Stacks Project
Axiom has released a complete Lean formalization of the Stacks Project, covering approximately 7,500 pages of foundational literature on algebraic geometry, with a codebase of about 16 million lines, which it calls the largest reusable formalized mathematics library to date. The library preserves the original text's permanent Stacks tags, and every Lean declaration can be traced back to the corresponding original text, allowing researchers and AI agents to directly import definitions and theorems. Axiom stated that the translation and proofs were completed through layered multi-agent collaboration, and that during the process dozens of statements in the original text were found to require additional hypotheses or corrections.
TechCrunch AI
Axiom Math Uses AI Agents to Formally Verify the Stacks Project
Axiom Math announced that it has completed formal verification of the Stacks Project, converting this roughly 7,654-page mathematical literature into about 16 million lines of Lean code. The company, valued at $1.6 billion, was founded in March 2025 and completed a $200 million Series A round led by Menlo Ventures in March of the same year. Its agents work in parallel under a loose hierarchy and claim tasks on their own, and the company has also developed its own math-specialized model, filling the gap in reusable foundations for algebraic geometry in Lean.
Nov 5
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Axiom Math Releases a 16-Million-Line Lean Formalization Library of the Stacks Project
Axiom Math has released a complete formalized version of the Stacks Project, totaling 16 million lines of Lean code, preserving its highly interconnected structure while optimizing code quality. The work was carried out by a swarm of agents, with humans responsible for tasks such as allocating architecture, core definitions, and individual proofs; every completed proof was verified by Lean and linked back to the original text and dependencies. This free, open-source library makes much of modern algebraic geometry available as computer-verifiable code, allowing mathematicians and AI models to directly reuse verified definitions and theorems.
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