Why a tiny social media post has mathematicians rethinking AI

As millions of people were coming down from the excitement of the FIFA World Cup final at the start of this week, a different kind of excitement was building within the mathematical community. Levent Alpöge, a mathematician who works at the artificial intelligence (AI) company Anthropic, casually announced on X ('hello there the jacobian conjecture is false thanx') that he had found a counterexample to the Jacobian conjecture, a very old and well-known problem in a field of mathematics called algebraic geometry. He had done this using Anthropic's large language model Claude Fable 5, released to the general public only a few weeks ago.