Claude Cracked an 87-Year-Old Conjecture — I Verified the Counterexample in 0.1 Seconds
Last Updated on July 23, 2026 by Editorial Team
Author(s): Chew Loong Nian – AI ENGINEER
Originally published on Towards AI.
Claude Cracked an 87-Year-Old Conjecture — I Verified the Counterexample in 0.1 Seconds
On Sunday evening, while most of the world was watching the World Cup final, a mathematician at Anthropic posted three polynomials on X and quietly ended an 87-year-old open problem. The Jacobian conjecture — unsolved since 1939, survivor of multiple famous false proofs, one of the problems on Steve Smale’s list for the 21st century — is false. Claude’s Fable 5 found the counterexample.
After the lead, the article explains that the disproof is strikingly compact: the author verifies with a short SymPy script that the Jacobian determinant of the provided polynomial map is identically −2 (a constant everywhere), yet the map is not injective because three distinct input points collapse to the same output—so no inverse exists. It then walks through how to reproduce the check quickly (including sample code), describes the early expert analysis in the following 48 hours (homogeneity structure, finite-field point counting, and a geometric origin for the example), and notes that mathematicians and proof assistants moved to formalize the result (e.g., Lean/DeepMind formal conjectures). The piece places this in context as a broader trend—an AI-produced counterexample pattern that has resolved multiple famous open questions—arguing that counterexamples are “easy to verify” compared to the difficulty of finding them, especially when paired with deterministic checking tools. Finally, it lists caveats (the two-variable case remains open; provenance details are partly opaque; formal peer review hasn’t happened yet) and concludes with what the result suggests for building with LLMs: emphasize generate-then-verify workflows, use mechanical verifiers, and recognize that expert-guided problem selection is a key bottleneck.
Read the full blog for free on Medium.
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