Lean veterans warn that rushing AI-written math libraries could be worse than none

Quality gate versus volume

The Xena Project post, by Avigad, Buzzard, Commelin and others, is optimistic about AI-assisted formalization but worried about rushed large-scale efforts. Its central line: "A lousy formalization of existing results is worse than no formalization at all." A formalization is only valuable if people use it, the authors say, and they argue the Claude-generated Fermat's Last Theorem formalization (13 million lines) and Math, Inc.'s sphere-packing attempt added little lasting value. OpenAI's Navier-Stokes Lean formalization gave a strong correctness signal but a hard-to-read informal proof and a code dump with retractions and mismatches. They cite OpenAI's unit distance work and Anthropic's zeta-zero density work as positive examples.

The existing ecosystem: Mathlib (65 reviewers, 950 contributors, 2026 Jean-Pierre Demailly Prize), Formal Conjectures, the Annals Challenge, Tau Ceti (an AI-written, AI-reviewed library of about 3 million lines, now larger than Mathlib), Formal Frontier (41 libraries, about 200k lines) and the Palomar registry.

The proposed plan

They predict most of mathematics could be formalized within three years and propose to curate Mathlib, grow Tau Ceti and Formal Frontier tenfold within months, write roadmaps, model scaling costs, keep mathematicians in control of the tools, and set up non-profit or academic hosting. The ten shared values include deferring to Mathlib, public review and linking to the literature.

What working mathematicians say about the volume problem

A commenter who says they are a research mathematician described the same pressure from the other side:

"I drafted eight papers last weekend. This week I advanced on none. AI still gets stuck at the key point on a problem where there isn't already a lot of work done… The arxiv is swamped. A human can't assess the volume of the output."

A user who has Claude Code build interactive explainers offered the counterpoint that it works only when the human stays in the loop: "It is still work! And, I have to struggle to get it to make sense and look nice." Both describe review capacity, not generation, as the bottleneck, which is the Xena post's argument about who audits a library bigger than Mathlib.