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arXiv · 2607.27197

The Maxwell Conjecture is False

Philip Arathoon·Gavin Ball·Matthew D. Kvalheim
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Abstract

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.

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Philip Arathoon, Gavin Ball, Matthew D. Kvalheim. 2026-07-29. The Maxwell Conjecture is False. https://arxiv.org/abs/2607.27197

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