AI Suggested the Configuration That Broke Maxwell's Conjecture

Arathoon, Ball and Kvalheim broke a 160-year-old bound on electrostatic potentials on July 29, using a configuration GPT-5.6 Sol suggested, per their paper on arXiv.

Maxwell's formula predicted a ceiling of 16 non-degenerate critical points for five point charges, expressed as (n−1)². The three mathematicians found a configuration with at least 24, at least 50% more than the formula allowed. That's the whole story mathematically: a century-plus assumption about how many equilibrium points a charge arrangement can produce no longer holds.

Where it gets interesting is the acknowledgements. The abstract of arXiv 2607.27197 doesn't say anything about AI. Buried further down: "The idea behind this construction was suggested by an LLM (OpenAI's GPT-5.6 Sol)."

The authors didn't hand the proof to the model. They built it themselves, with harmonic-polynomial lemmas and Taylor expansions, applying the implicit function theorem. Mathematica and Maple only checked the answer; they didn't derive it.