The Maxwell Conjecture Is False (GPT 5.6 Sol)
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.
Summary
A new configuration of five point charges challenges Maxwell’s conjecture by demonstrating at least 24 non-degenerate critical points in their electrostatic potential. This finding highlights a significant deviation from the previously accepted limit on critical points for point charge systems.
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