Lean has checked all 43.1 million lines of the finite simple groups classification, and found one gap

What was formalized

The project page describes a Lean formalization of the classification of finite simple groups, following the first-generation proof. Core contributors are Dean Cureton, Vasily Ilin, Bhavik Mehta and Niels Voss, with dozens more credited. It totals 43.1 million lines of Lean, 2.05 million declarations, 100 milestones and 715 papers and books, with every logical step checked by Lean's kernel. The page does not say how long it took.

Along the way the team found an issue in a published argument for the Unbalanced Group Theorem. Their paper, The Unbalanced Group Theorem (arXiv 2610.00575), explains it and gives an alternative route for the simple-group case that builds on Solomon's 1976 theory of maximal 2-components.

Why the thread expected more holes

One commenter wrote:

"I'm surprised they only found one gap."

He had expected multiple fixable gaps given the result was spread over many papers by many people. Another called it a very good use of auto-formalization, since mathematicians have in the past believed they were finished with the classification only to discover a missing sporadic group, and said the original proof was a collaboration of about 100 mathematicians.

A third voice lamented that formalization is now mature but is still done in set-theoretic foundations. The practical lesson for anyone relying on a long, many-author proof is that one gap in 43 million lines is a result.