Universal Math Solutions in Dimensions 8 and 24

Now, she and her co-authors have proved something even more remarkable: The configurations that solve the sphere-packing problem in those two dimensions also solve an infinite number of other problems about the best arrangement for points that are trying to avoid each other. Dimension three, meanwhile, is a zoo: Different point configurations are better in different circumstances, and for some problems, mathematicians don’t even have a good guess for what the best configuration is. Then in 2016, Viazovska took the first step by proving that these two lattices are the best possible sphere packings (she was joined, for the Leech lattice proof, by Cohn and the other three authors of the new paper: Abhinav Kumar, Stephen Miller of Rutgers University and Danylo Radchenko of the Max Planck Institute for Mathematics in Bonn, Germany).

Source: www.quantamagazine.org