100-Page Hopf Problem Proof Formalized Into 250k Lines of Lean in Days With Codex
games-and-games · reddit · 2026-08-28
A striking week for mathematics: Levent Alpöge dropped a claimed 100-page proof of the 78-year-old Hopf problem, written with Claude. Just a couple of days later, Boris Alexeev of OpenAI produced a 250,000-line Lean formalization using Codex that appears to check out. As the poster notes, probably no single human fully understands all the details at this point — AI-assisted proving and formal verification now move faster than any individual can digest.
- Original proof thread: x.com/alpoge
- Lean repo: github.com/plby/HopfProblem
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