Mathematician Levent Alpöge uses Anthropic's Fable 5 AI to refute Jacobian conjecture

Harvard-affiliated mathematician Levent Alpöge announced that he employed Anthropic’s large‑language model Fable 5 to produce a counterexample that disproves the Jacobian conjecture, a nearly 90‑year‑old open problem in algebraic geometry listed among Stephen Smale’s famous problems.

Columbia professor Andrew Blumberg noted that while the AI‑generated counterexample demonstrates the technology’s ability to explore vast polynomial spaces, it does not replace a full proof and offers limited new insight into the underlying mathematics. The finding has reignited discussion about the role of artificial intelligence in advancing pure‑mathematical research, following earlier AI‑driven results such as OpenAI’s work on the Erdős unit‑distance problem.