Mathematical puzzle from 1904 takes physical form in gold-studded helium droplets

When identical charges repel each other but are confined to the surface of a sphere, they seek the arrangement with the lowest possible energy. The idea is simple, but the problem gets harder to solve with every charge added. The so-called Thomson problem dates back to the "plum-pudding" model of the atom, which Nobel laureate Joseph J. Thomson proposed in 1904. The atomic model has long been superseded, but the mathematical problem has endured.