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Screenshot of cfsg.axiommath.ai: Classification of Finite Simple Groups Formalized in Lean

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Classification of Finite Simple Groups Formalized in Lean

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Project site presenting a complete Lean formalization of the Classification of Finite Simple Groups, with an interactive proof map, stats, papers, and contributors.

What HN thinks

43.1 million lines later, the Monster is officially real and everyone feels slightly less uneasy.

Welcome confidence in a shaky proof
Many see the formalization as dispelling lingering doubts about a 10,000-page proof spread across hundreds of papers, noting it found and fixed a gap and 34 deviations.
Auto-formalizing everything is harder than it sounds
Replies to the idea of letting models convert all textbooks argue the hard part is choosing compatible formulations and building a coherent, reusable library, much like software API design.
Trusting the formalization itself
Some ask how we know the Lean proof is right; others answer that the small kernel and relatively simple theorem statement make checking far easier than checking the original proof.

Consensus: Most agree this is a major achievement that substantially boosts confidence in the classification, though some question the cost and whether a machine-made 43M-line proof is mathematically illuminating.

Recommended in the comments

Metamath (tool): Cited for research into theorem formulations that compose well as a library.
Cubical Agda library ↗ (library): Offered as evidence that homotopical, constructive foundations are progressing, including constructive real analysis.

Summarised by Claude from the comment thread 1 day ago.

Points: 230
Comments: 71
Best rank: #4
Posted: 2026-10-27 by pfdietz
Category: Science

lean formal-verification group-theory finite-simple-groups theorem-proving mathematics axiom-math

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