Machine Heart

Jul 20, 2026 · Artificial Intelligence

One Tweet, One Counterexample: Did Claude Fable 5 Disprove the 85‑Year‑Old Jacobian Conjecture?

A tweet by Anthropic researcher Levent Alpoge, aided by the Claude Fable 5 model, presented a simple polynomial map whose constant Jacobian determinant of –2 sends three distinct points to the same image, providing a concrete counterexample that refutes the Jacobian conjecture that has challenged mathematicians for 85 years.