15,000 pages of maths in 24 days: AI agents computer-check the "Enormous Theorem"
Start-up Axiom says it has fully formalised the proof of the classification of finite simple groups in the Lean proof assistant – using swarms of AI agents. It has not yet been independently rebuilt.
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The classification of finite simple groups is considered the longest proof in mathematics: around 15,000 pages in more than 500 papers by about 100 mathematicians over decades. Start-up Axiom Math now says it has translated the entire proof into the language of the Lean proof assistant, in which the computer checks every logical step. Dozens of AI agents worked in swarms for 24 days, producing about 43.1 million lines of Lean code.
Along the way the agents found 34 noteworthy deviations from the published literature, Axiom says; human mathematicians investigated the consequential ones. Axiom consulted group theorists Richard Lyons and Ronald Solomon, and humans also checked that the formal statements really express the intended theorem. The term "Enormous Theorem" was coined by mathematician Daniel Gorenstein.
That this is the first complete computer-checked proof is so far Axiom's own claim. Asked whether anyone outside the company had already rebuilt and checked the proof, CEO Carina Hong told RuntimeWire: "Not yet." Axiom is publishing the build artifacts to encourage outside groups to do so.