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The Axiom team used the multi-agent system AxiomProver to formalize the approximately 15,000-page proof of the Classification of Finite Simple Groups (CFSG) theorem into Lean code within 24 days, producing a codebase of 43.1 million lines. During the process, the AI recorded hundreds of anomalies, 34 of which were major logical deviations, including a key closure assertion in John Walter's 1986 paper that does not hold, for which the AI provided the counterexample PSL2(49). The team then contacted group theorists Richard Lyons and Ronald Solomon, and AxiomProver proved a new theorem, Preservation of simple tops, to fill the gap.
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Oct 30
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Axiom's multi-agent system formalizes the classification theorem of finite simple groups in 24 days
The Axiom team used the multi-agent system AxiomProver to formalize the approximately 15,000-page proof of the classification theorem of finite simple groups (CFSG) into Lean code within 24 days, producing a 43.1-million-line codebase. During the process, the AI recorded hundreds of anomalies, 34 of which were major logical deviations, including a key closure assertion in John Walter's 1986 paper that does not hold, for which the AI provided the counterexample PSL₂(49). The team then contacted group theorists Richard Lyons and Ronald Solomon, and AxiomProver proved a new theorem, Preservation of simple tops, to fill the gap.