New Proof Shows the Maxwell Conjecture Is False for Point Charges
The Maxwell Conjecture Is False (GPT 5.6 Sol)
We present a specific arrangement of five point charges in Euclidean space that generates at least 24 non-degenerate critical points. This discovery directly contradicts Maxwell's conjecture, which claimed the maximum number of such points for n charges is (n-1)^2. Our findings demonstrate that the established limit for electrostatic potential critical points is incorrect.
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.