The Maxwell Conjecture is False
2026/07/29 by Philip Arathoon, Gavin Ball, Matthew D. Kvalheim · 5 voices
Mathematics · Physics and Astronomy · #math-ph #math.MP #physics.class-ph
paper · pdf
arxiv created 2026/07/29 · arxiv updated 2026/07/30
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.
Discussions
- The Maxwell Conjecture Is False (GPT 5.6 Sol) [hn, 155 points, 139 comments]
- We're seeing some theoretical physics already at least on the border between math and physics. See for example arxiv.org/abs/2607.27197 . [bsky, 2 points, 1 comments]
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- The Maxwell Conjecture Is False (GPT 5.6 Sol) https:// arxiv.org/abs/2607.27197 # arxiv [mastodon, 0 points, 0 comments]
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