The classification of finite simple groups is one of the great collective achievements of mathematics. Its first-generation proof spans thousands of journal pages, written by about a hundred mathematicians over several decades. It shows that every finite simple group is cyclic of prime order, alternating, of Lie type, or one of 26 sporadic groups.
A team has now presented a complete formalization of this first-generation proof in Lean, with every logical step checked by Lean's kernel. Along the way, the team found an issue in a published argument for the Unbalanced Group Theorem. The accompanying paper explains the issue and the alternative route used in the formalization, and a blog post tells the full story.
The project is substantial in scale, with 43.1M lines of Lean, 2.05M declarations, and 100 milestones reached. It draws on 715 papers and books, and the work is credited to a core group of contributors including Dean Cureton, Vasily Ilin, Bhavik Mehta, and Niels Voss, supported by a wider list of mathematical and engineering contributors.
The Lean code, an agent blueprint, and an interactive proof map are publicly available. The work is also citable as a 2026 misc entry, with the proof map hosted at cfsg.axiommath.ai.
Source: Hacker News · Summarized by HeadlinesBriefing