Levent Alpöge Uses Fable 5 to Disprove 87-Year-Old Jacobian Conjecture
Updated
Updated · Mashable · Jul 20
Levent Alpöge Uses Fable 5 to Disprove 87-Year-Old Jacobian Conjecture
3 articles · Updated · Mashable · Jul 20
Summary
Levent Alpöge said on X he used Anthropic’s Fable 5 to find a counterexample that overturns the Jacobian conjecture, a major open problem in algebraic geometry dating to 1939.
A 216-character example with three variables had already been cited in earlier reporting, framing the result as one of the biggest math conjectures AI has helped crack.
Andrew Blumberg of Columbia said the feat does not materially change his view of AI, arguing frontier models are well suited to brute-force searches for concise counterexamples.
Blumberg drew a sharp line between a counterexample and a constructive proof, saying this result may settle the statement without yielding much mathematical insight.
The claim adds to a recent run of AI-assisted math results, after OpenAI said in May an internal model had disproved the Erdős unit distance conjecture in a more informative way.
Is the era of the lone mathematical genius over now AI solves decades-old problems?
An AI found the answer, but can it teach us the intuition humans missed for 87 years?
If AI co-authors a discovery, must its 'thought process' also be published for peer review?
The Disproof of the 87-Year-Old Jacobian Conjecture: How AI-Human Collaboration Reshaped Mathematics in 2026
Overview
On July 19-20, 2026, the long-standing Jacobian Conjecture, first posed in 1939 and unsolved for 87 years, was finally disproved. The breakthrough electrified the mathematical community, with news spreading quickly and experts calling the result remarkable. The disproof was achieved through a unique collaboration between mathematicians Levent Alpöge, Matthew, and the advanced AI Claude Fable 5, who together generated a specific counterexample. This explicit example provided clear evidence against the conjecture, marking a major milestone in algebraic geometry and showcasing the power of human-AI teamwork in solving deep mathematical problems.