What is the Jacobian conjecture? Now to the Jacobian conjecture. A long history of attempts – and failuresThe two-dimensional version of the Jacobian conjecture was stated by Czech mathematician Ludwig Kraus in 1884. A deceptively simple answerOne of the key reasons the Jacobian conjecture is so intriguing is that, in theory, it should be easy to find a counterexample. At the time of writing, details have not been made public regarding exactly how Alpöge prompted the AI model to produce the Jacobian conjecture counterexample and what its output looked like.