Kevin Buzzard · 2026-07-20 · notable
Kevin Buzzard — Human mathematicians are being outcounterexampled by AI
Kevin Buzzard's July 20 Xena Project post surveys three long-open conjectures that AI systems have disproved in the last two months — Erdős's unit distance, a Grothendieck question on finite flat group schemes, and the Jacobian conjecture — each with a Lean-verified counterexample.
Xena Project's Kevin Buzzard argues AI + Lean has become a working counterexample factory for mathematics.
What is it?
The Xena Project post 'Human mathematicians are being outcounterexampled' is Kevin Buzzard's July 20 write-up of three recent AI-assisted disproofs of long-open conjectures. Buzzard is professor of pure mathematics at Imperial College London and one of the main voices behind mathlib and the Lean-based formalization of Fermat's Last Theorem.
How does it work?
Buzzard walks through three cases in order. In May, ChatGPT produced a counterexample to Erdős's Unit Distance conjecture using the Golod-Shafarevich theorem, which OpenAI's Sol later formalized in Lean across 1.2M lines. In July, Claude Fable 5 autoformalized a 1,076-line Lean proof disproving a 60-year-old Grothendieck question on finite flat group schemes, and Fable also produced the 3D polynomial counterexample to the 100-year-old Jacobian conjecture that landed in DeepMind's Formal Conjectures repo.
Why does it matter?
Buzzard's angle is that counterexample search — proposing an object and machine-checking it against the statement — is the part of research math where current AI systems are already faster than humans. Formal proof assistants like Lean turn the messy 'is this right?' step into a compile check, so a wrong proposal from an LLM is caught immediately. He argues large AI-generated developments are now inevitable and that formalization has to catch up.
Who is it for?
mathematicians, AI-for-science researchers, and anyone tracking formal proof assistants
Try it
Read: xenaproject.wordpress.com/2026/07/20/human-mathematicians-are-being-outcounterexampled