From the intro to the paper:

> In J. C. Maxwell’s 1873 treatise on electricity and magnetism he discusses the number of equilibria of the electric field generated by n point charges [5, §113]. Apparently unaware of this, M. Morse and S. S. Cairns in 1969 posed the problem of finding an upper bound for the number of equilibria [6, p. 293]. The first general bounds were supplied by A. Gabrielov, D. Novikov, and B. Shapiro in [3] who, based on their reading of [5, §113], formulated the ‘Maxwell conjecture’ which states that if the critical points of the electrostatic potential generated by n point charges are all non-degenerate then their number cannot exceed (n − 1)^2. These bounds were later improved by V. Zolotov in 2023 [8] and further improved by H. Edelsbrunner, C. Fillmore, and G. Oliveira in 2026 [2]. Maxwell’s bound is trivially achieved for n = 2 but it is not known even for n = 3 if 4 is the maximum number, except in the case of equal charges [7]. Further related problems in classical electrostatics are discussed in [1].

And reference 3:

> [3] A. Gabrielov, D. Novikov, and B. Shapiro, Mystery of point charges, Proc. Lond. Math. Soc. (3), 95 (2007), pp. 443–472.

This is pretty niche and the conjecture was only proposed about 20 years ago. It was actually not conjectured by Maxwell himself.