“We exhibit a configuration of five point charges in Euclidean space whose electrostatic potential admits at least 24 critical points all of which are non-degenerate. Maxwell’s conjecture that the field of n point charges has at most (n-1)² critical points which are all non-degenerate is therefore false.”
Five charges, 24 critical points, and the 1870s bound of 16 is dead. GPT-5.6 Sol suggested the construction. Three humans then did the actual work of proving it holds, which is the part the OpenAI executives quote-tweeting this leave out. A model that generates a promising guess is useful. It is not the same thing as a model that settles a conjecture, and the gap between those two claims is where all the hype lives.