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Axiom: AI agents machine-verify 15,000-page Classification of Finite Simple Groups proof in 24 days, find 2,000+ errors
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A swarm of AI agents used the Lean proof assistant to machine-verify the Classification of Finite Simple Groups, a 15,000-page, 500-paper proof written by 100 authors over decades. According to Axiom's count, the 24-day effort produced about 40 million lines of machine-verified proof and uncovered more than 2,000 mistakes in the published papers, most small but one inside the proof of the Unbalanced Group Theorem that had gone unnoticed for decades. The agents found a new proof for that piece, which experts reviewed and verified. Because Lean's small trusted checker validates every line independently, the AI models' potential hallucinations do not undermine the result. The agents claimed tasks, audited each other, and merged work through GitHub with proofs attached, running without a human in the loop. Axiom plans to apply the same machinery to code and chips.
Source report
A Proof Too Long to Read
One hundred authors spent decades writing a mathematical proof so long that nobody has ever read the whole thing: 15,000 pages across 500 papers. It turns out one piece of it had a flaw the entire time—and many of the people who could have caught it are now in their eighties.
The Classification of Finite Simple Groups
The theorem is called the Classification of Finite Simple Groups—essentially the periodic table for symmetry. Physicists rely on it for work on black holes. Mathematicians cite it constantly without anyone having checked all of it, since doing so by hand would consume an entire career.
AI Swarm Completes the Verification
A swarm of AI agents checked every step of the proof in Lean in 24 days. By Axiom's count, that amounted to approximately 40 million lines of machine-verified proof and more than 2,000 mistakes in the published papers—most of them small, and one of them sitting inside the proof of the Unbalanced Group Theorem, where it had gone unnoticed for decades. The agents found a new proof for that piece, experts reviewed it, and it is now verified.
Trust Through Verification, Not Trust in AI
Crucially, nobody has to trust the AI that wrote any of this. Lean has a small, trusted checker that confirms every line on its own, so the model can hallucinate all day and the proof still either compiles or it doesn't.
Human-Free Workflow
That same property is what allowed the swarm to run without a human in the loop. Agents claimed tasks, audited each other, and merged their own work through GitHub, with a proof attached to every hand-off. This stands in contrast to coding agents today, which can write more code than any team can read, making the human reviewer the bottleneck on everything. A checker that never gets tired changes that equation—and Axiom's plan is to point the same machinery at the code and chips the rest of us run on.
The Bottom Line
Decades of papers, 24 days to check them, and a flaw no one alive had spotted is gone.
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aakashgupta
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Axiom AI swarm formalizes 15,000-page Classification proof in 24 days