A preprint disproving Maxwell's conjecture discloses that the construction was suggested by GPT-5.6 Sol

Sources: arXiv:2607.27197, discussion
Summary: Philip Arathoon, Gavin Ball, and Matthew D. Kvalheim submitted a short note on 2026-07-29 exhibiting five point charges whose electrostatic potential admits at least 24 non-degenerate critical points, against the bound of (n-1)^2 that Maxwell's conjecture sets as formulated by Gabrielov, Novikov, and Shapiro, which is 16 for five charges. The construction places three unit charges at the vertices of an equilateral triangle and two small charges on the orthogonal axis, and the central equilibrium bifurcates into 21 equilibria while the three edge equilibria persist. The paper carries a section headed "Tool and computational resource disclosure" stating that the idea behind the construction was suggested by an LLM, OpenAI's GPT-5.6 Sol, that the authors verified the mathematical details and wrote the argument in their own words, and that Mathematica and Maple were used to verify computations and produce visualisations.
Why it matters: The paper states at a checkable granularity what the model did and what the humans did, which is the opposite of a vendor claim that a model advanced mathematics.
Follow-up: The preprint is not peer reviewed and no independent verification of the result was found in this run, so track whether the construction is confirmed.