Stable Forking Conjecture in Model Theory Refuted via ChatGPT-Assisted Proof
The paper reports a counterexample to the stable forking conjecture, a long-standing open question in model theory posed by Hart, Kim, and Pillay in 1996, which asked whether forking independence in simple theories could always be reduced to stable formulas. The authors state they found the counterexample with the help of ChatGPT 5.6, constructing a new algebraic structure that exhibits unstable forking within a simple theory. Twitter commentary highlights that model theorists considered this one of the field's major open problems, with some excitement framed around the fact that AI assistance played a role in cracking it, and admiration for the novel mathematical object produced as the counterexample.
Discussion: 2 tweets from 2 authors · @RadishHarmers, @jimfreitag