The Maxwell Conjecture is False

View PDF HTML (experimental) 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.

Subjects: Classical Physics (physics.class-ph); Mathematical Physics (math-ph) Cite as: arXiv:2607.27197 [physics.class-ph]   (or arXiv:2607.27197v1 [physics.class-ph] for this version)   https://doi.org/10.48550/arXiv.2607.27197 arXiv-issued DOI via DataCite (pending registration) Submission history From: Philip Arathoon [view email] [v1] Wed, 29 Jul 2026 17:58:42 UTC (341 KB)