The Maxwell Conjecture Is False (GPT 5.6 Sol)
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- The Maxwell conjecture claims that the electrostatic potential of n point charges has at most (n-1)^2 non-degenerate critical points.
- The authors exhibit a configuration of five point charges whose potential has at least 24 critical points, all non-degenerate.
- Since 24 > 16 = (5-1)^2, this counterexample proves the Maxwell conjecture is false.