Axiom uses AI agent swarms to fully formalize the Classification of Finite Simple Groups in Lean in 24 days: about 43.1M lines, the first complete computer-checked proof of the longest proof in math history

Background and pain points

The Classification of Finite Simple Groups (CFSG) is one of the great collective results of 20th-century mathematics: every finite simple group is cyclic of prime order, alternating, one of 16 families of Lie type, or one of 26 sporadic groups (the largest being the Monster). The original proof runs about 15,000 pages in 500+ articles by about 100 mathematicians, and no one could fully check it. On Oct 27 AI math company Axiom announced on X a complete Lean formalization of CFSG, alongside an official blog post (dated Oct 26) and the public GitHub repo AxiomMath/CFSG.

Architecture and mechanism

Per the blog, engineers and mathematicians directed swarms of dozens of AI agents for 24 days, rewriting the first-generation proof in Lean with every step checked by Lean's kernel. Because agents produced proofs faster than Lean could recheck them, the team built build caches distributed across workers and parallel checks, and moved expensive finite calculations into separately checkable certificates, which Axiom says sped up verification by orders of magnitude. When progress stalled, agents were assigned to split coarse milestones into precisely stated smaller theorems. The project also reuses about 1.2M lines from Qiuzhen-CFSG and builds on Mathlib.

Benchmarks and verification

This is not a benchmark result, and Axiom has not disclosed which models were used or the compute cost. The project page lists (vendor figures) about 43.1M lines of Lean, 2.05M declarations, 100 milestones and 715 papers and books. Some X posts cite 50M lines; the official figure is 43.1M. The work found 34 noteworthy deviations from the literature, and AxiomProver produced an alternative argument for the Unbalanced Group Theorem, including a new result, Theorem 2.3, in a paper on Hexagon.

Getting started

Browse the interactive proof map at cfsg.axiommath.ai and the Lean code in the GitHub repo; Axiom says the release identifies the final theorem and documents how to check it. Axiom also notes that Lean checks the deductions, but humans must still confirm the formal statement says what the theorem says. For agent builders, it is a real example of large agent swarms with machine-checkable feedback on a very long task, and its task splitting and shared build caching are worth studying.