mathematical-physics / Classical electrostatics
How many nondegenerate equilibrium points can the potential of three positive point charges have? Gabrielov, Novikov and Shapiro had proved at most $12$, and observed that their method would give $6$ if an auxiliary polynomial system had at least four solutions with multiplicity in each open quadrant. That four-solution statement holds, so the bound is $6$, and six is attained for special charge values.
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the sharp bound for three charges; the general Maxwell bound was separately disproved in July 2026
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How many nondegenerate equilibrium points can the potential of three positive point charges have? Gabrielov, Novikov and Shapiro had proved at most $12$, and observed that their method would give $6$ if an auxiliary polynomial system had at least four solutions with multiplicity in each open quadrant. That four-solution statement holds, so the bound is $6$, and six is attained for special charge values.
the sharp bound for three charges; the general Maxwell bound was separately disproved in July 2026
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