The Maxwell Conjecture is False
- Published
- Source
- arXiv
- Paper number
- 773
- Field
- Research
- arXiv ID
- 2607.27197
Key points
- It refutes Maxwell's 1873 conjecture that the number of critical points of n point charges is at most (n-1)^2 by giving a counterexample with 5 charges.
- A configuration of an equilateral triangle plus two axial charges produces 21 critical points around the center, for a total of 24 nondegenerate critical points.
- By iterating the construction, 3 plus 2m charges can produce at least 4 plus 20m critical points, which is a ratio of 10 critical points per charge.
- The idea was suggested by GPT-5.6 Sol and then verified in Mathematica and Maple before the authors wrote the mathematical proof.
- The construction improves the previous best ratio of 25/7, or about 3.57, to 10.
Paper links
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