Axiom released the first complete computer-checked proof of the Classification of Finite Simple Groups. The proof spans roughly 15,000 pages across 500 articles by about 100 mathematicians. Axiom used AI agent swarms to produce 43.1 million lines of Lean code over 24 days. The work uncovered 34 noteworthy deviations in the original proof. One substantial deviation involved the Unbalanced Group Theorem. The project also yielded a new result in group theory. The proof covers cyclic groups, alternating groups, Lie-type groups, and 26 sporadic groups. The Monster group is the largest sporadic group in the classification. The formalization builds on both first and second generation proofs of CFSG. Axiom coordinated 108 milestones and 380 tasks across the swarm.
What changed
The Classification of Finite Simple Groups had no complete computer-checked proof.
What it unlocks
A fully machine-verified proof of the Classification of Finite Simple Groups is now available in Lean.
- 15,000 pages across 500 articles
- 100 mathematicians contributed
- 43.1 million lines of Lean code
- 34 noteworthy deviations resolved
What you need to act on it
- Lean proof assistant
- AI agent swarm coordination
Sources