Sphere Packing Solved in Higher Dimensions | Quanta Magazine

In a pair of papers, a Ukrainian mathematician has solved two high-dimensional versions of the centuries-old “sphere packing” problem. In dimensions eight and 24, Maryna Viazovska has proved that two highly symmetrical arrangements, the E8 lattice and the Leech lattice, pack spheres together in the densest possible way, using the theory of modular forms to construct a special function that provides the exact answer.