Maxwell's Conjecture on Point-Charge Equilibria
Do point charges whose electrostatic potential has only non-degenerate critical points always have at most of them? A configuration of five charges - three at the vertices of an equilateral triangle plus two small central charges pulled apart into a shallow bipyramid - has at least non-degenerate critical points, so the conjecture is false.
- Result
- Disproved
- Status
- Resolved
- AI contribution
- AI co-developed
- Method
- Construction
- Field
- Classical electrostatics
- Posed by
- James Clerk Maxwell
- Year posed
- 2004
- Years open
- 22y
- Solved
- 2026-07-29
- Model
- GPT-5.6 Sol
- Vendor
- OpenAI
- Collaborators
- Philip Arathoon, Gavin Ball, Matthew D. Kvalheim
- Verification
- Unreviewed
- Publication
- Preprint
- Significance
- 30 / 100
- Disclosed cost
- —
- Wikipedia
- No dedicated article
What the AI did
The idea behind the counterexample construction was suggested by the model; the authors verified all mathematical details and wrote the note.
Verification
Short arXiv note with an explicit five-charge configuration and non-degeneracy verification; not yet peer-reviewed.