GPT-5.6 helps disprove the Maxwell conjecture — but not the one everyone thought

On July 29, a short note titled 'The Maxwell Conjecture is False' appeared on arXiv. The next morning, co-author Philip Aratun wrote on social media that the conjecture was false and that AI had found the counterexample, with mathematicians merely relaying it. Greg Brockman, president of OpenAI, reposted this, and the news spread. However, many misunderstood the meaning, thinking it involved Maxwell's equations, leading to questions about electromagnetism. The actual conjecture, formulated by Gabrielov, Novikov, and Shapiro in 2007, concerns the maximum number of non-degenerate equilibrium points for n point charges, proposed to be at most (n−1)². The counterexample involves three unit charges at the vertices of an equilateral triangle (giving four equilibrium points) and adding two tiny charges along a perpendicular axis, splitting the central equilibrium into 21 new ones, totaling at least 24. The magnitude of added charges must scale as ε³ with a uniquely determined coefficient. The preprint credits the language model GPT-5.6 Sol with suggesting the construction idea, while the authors verified the math, with Mathematica and Maple used for checks. The significance has been debated: some call it niche, but it serves as a test for AI, and it leaves the true order of growth unknown, with previous bounds being super-exponential. The result lacks peer review and formalization in Lean, but it is elementary and reproducible, and no one has publicly objected within five days.