Lean leaders: how to formalize all of mathematics
Confirmed
The takeaway
On Oct 16, 2026 Jeremy Avigad, Kevin Buzzard, Johan Commelin, Rémy Degenne, Kim Morrison, Oliver Nash and Adam Topaz published “How to Formalize All of Mathematics” on the Xena blog, responding to calls from “AI enthusiasts” to auto-formalize the whole literature.
Status
- Claim
Confirmed
- Our reporting
- High confidence
- Importance
- 3 of 5
- Last verified
- 16 October 2026
Your AI and this story
- GPT-6 Astra169 days after its cutoff
- Claude Opus 5.5108 days after its cutoff
- Gemini 4 Argon199 days after its cutoff
- Grok 4.7138 days after its cutoff
None of these four assistants can know about it. The closest, Claude Opus 5.5, stops 108 days before it.
Key facts
- Examples criticised: Math, Inc.’s attempted takeover of the 8-dimensional sphere-packing Lean project (the original team rewrote the AI code); Anthropic’s Fermat’s Last Theorem formalization (13 million lines in 11 days); OpenAI’s Navier–Stokes blow-up with Lean formalization and its large GitHub math release (retractions, informal/formal mismatches, hard-to-read write-ups)
- Examples praised: OpenAI’s unit-distance conjecture work and Anthropic’s Riemann zeta zeros work
- Main argument: a formal artifact has value only if people use it to do more mathematics; poor formalization could waste millions of dollars and set the field back
- Projects described: Mathlib (65 reviewers, 950 contributors; 2026 Jean-Pierre Demailly Prize), DeepMind’s Formal Conjectures, the Annals Challenge (statements of recent Annals theorems), Tau Ceti (AI-written and AI-reviewed, ~3M lines), Formal Frontier (41 libraries, ~200k lines), Palomar registry
- Asks: contribute to Mathlib; scale Tau Ceti and Formal Frontier tenfold within months; expert roadmaps and blueprints; keep autoformalization tools under mathematicians’ control; non-profit or academic hosting
- Tao (Oct 16): questions about formal mathematics mirror those about informal mathematics, a tradeoff between speed, scale and understanding
What happened
The leading maintainers of Lean’s mathematical library wrote a joint position paper on how AI-scale formalization should be done. They do not oppose AI formalization; they want it, and set a three-year horizon. Their objection is to unreviewed, unaudited code released on the promise of later cleanup, and to libraries that duplicate Mathlib instead of building on it.
Why it matters
After Anthropic’s Fermat formalization and OpenAI’s mass release, the Lean community’s leaders set out the standards they expect AI formalization to meet. They also named the projects (Tau Ceti, Formal Frontier) they think should be scaled up.
Sources
2 sources from 2 sites. Numbers match the chips in the text.
2 sources: 1 primary, 1 reaction
Primary
- Xena blog: How to Formalize All of Mathematics (Avigad, Buzzard, Commelin, Degenne, Morrison, Nash, Topaz; Oct 16, 2026)xenaproject.wordpress.com, official
Reactions
- Terence Tao: How to Formalize All of Mathematics (pointer post)terrytao.wordpress.com, discussion
Changes
- Filed (read the Xena post)