Anthropic's Claude Fable 5 AI Solves 87-Year-Old Jacobian Conjecture

Anthropic’s large‑language model Claude Fable 5 generated a counter‑example that disproves the Jacobian conjecture, a problem in algebraic geometry that has remained unsolved for 87 years. The breakthrough was announced on X by Levent Alpöge, a mathematician at Anthropic, who asked the model to examine the conjecture and received a one‑line formula providing the counter‑example.

The discovery was made public as the world was still celebrating the FIFA World Cup final, highlighting a parallel excitement within the mathematical community. The result reduces a long‑standing algebraic‑geometry question to a concise expression and marks one of the most striking mathematical advances achieved with a publicly released AI system.