In his famous book “A Treatise on Electricity and Magnetism” first published in 1867 J.C. Maxwell made a surprising claim that any configuration of \(N\) fixed point charges in \(\mathbb{R}^3\) creates no more that \({(N-1)}^2\) points of equilibrium. He provided this claim with an incomplete proof containing many elements of Morse theory to be created 60 years later. We present a modern set-up and generalisations of Maxwell’s conjecture and discuss what is currently known about his original claim which is still open even in case of 3 charges. No preliminary knowledge of the topic is required.