AI Models Are Demolishing Longstanding Math Conjectures. The Jacobian Conjecture Is Latest to Fall

AI Toppled Three Math Conjectures in Just Eight Weeks

The Jacobian Conjecture, an open problem in algebraic geometry dating to 1939, has a counterexample. Claude Fable, Anthropic's model, produced it, and the account @__alpoge__ announced the result July 20 on X, crediting Akhil Mathew, a professor of mathematics at UChicago, for raising the question and Fable for doing the work during the World Cup final 1. The counterexample is a polynomial map from three-dimensional complex space to itself with a constant Jacobian determinant of negative two that sends three distinct points to the same image, violating the injectivity the conjecture would require 1.

It is the third landmark conjecture in pure mathematics to fall to AI in eight weeks. The connection between the three is the story: AI is not just finding individual results. It is building the formal verification infrastructure that makes those results trustworthy, at a pace that dwarfs a decade of human effort.

The three falls

ChatGPT disproved the Erdős Unit Distance conjecture in discrete geometry on May 20, 2026, using a deep theorem from 1960s number theory to construct its counterexample 2.

In early July, at a formalization workshop organized by Kevin Buzzard at Imperial College London, Akhil Mathew raised a question of Grothendieck's: whether every finite free group scheme of order n was killed by n. The day after the workshop ended, July 11, Mathew messaged Buzzard that OpenAI's model Sol had found a counterexample. Four hours later, Fable had autoformalized the entire proof into 1,076 lines of Lean code that compiled in under five minutes 2.

Then the Jacobian Conjecture fell on July 19.

The hidden infrastructure story

The individual conjectures are striking. The pace of formalization is what should matter to anyone building or investing in AI.

The Erdős counterexample relied on a theorem whose proof spans over 100 pages of class field theory. Formalizing that body of mathematics was, as Buzzard wrote on the Xena Project blog, "a fantasy" as recently as 2025 2. Then Boris Alexeev, who works at OpenAI, used Sol to autoformalize the entire counterexample from the axioms of mathematics upward. Sol generated 1.2 million lines of Lean code in three weeks 2.

For scale: Lean's mathematics library, mathlib, contains 2.3 million lines accumulated over nine years by a global community of contributors 2. One model produced half that volume in three weeks.

Buzzard, a mathlib maintainer, put it plainly: "large AI-generated developments of mathematics are inevitable" 2.

Two labs, one workshop

The Imperial College workshop became an accidental proving ground for competing AI systems. Buzzard purchased Claude Max subscriptions for attendees so they could use Fable. When OpenAI learned of this, they offered the same attendees free ChatGPT Pro access to use Sol 2.

The division of labor between the two models is the competitive signal. Sol found the Grothendieck counterexample. Fable formalized it in four hours. For the Jacobian Conjecture, Fable appears to have produced the counterexample itself. Buzzard ran all AI-generated Lean code in a sandbox on his own laptop because Lean is a programming language and malicious code can execute arbitrary commands. Verification is not a passive check; the code runs as an executable program 2.

The so-what

Theorem-proving has graduated from academic curiosity to measurable AI benchmark. The Erdős result took roughly five weeks from disproof to complete machine verification. The Grothendieck counterexample went from discovery to verified Lean code in hours. The Jacobian result landed in a weekend social media post.

For researchers, the bottleneck is migrating from finding proofs to vetting AI-generated code at scale. For builders, the push by Anthropic and OpenAI into formalization tooling signals a capability with a market. Buzzard paid retail for Claude access. OpenAI gave theirs away for free. Both labs wanted their models in the hands of formalization mathematicians because theorem-proving is becoming a scoreboard.

Buzzard adopted Lean nine years ago because he no longer trusted many human mathematicians on technical details. The models he now runs in a sandbox are producing verified mathematics faster than the community that built the field.