**Berlin postdoc Maryna Viazovska proves the lore in dimensions 8 and (with pals) 24**

Erica Klarreich brought the readers of the Quanta Magazine some wonderful summary of three mathematical preprints on the arXiv:

Sphere Packing Solved in Higher DimensionsThe question is sort of obvious even to little kids. You have equally large \(n\)-dimensional spheres (the sphere is a set of points with a fixed Pythagorean distance \(R\) from the center). How do you arrange these non-overlapping objects in a big box so that the number of balls in the box is maximized?

You may fill the 1-dimensional space, a line, with 1-spheres, i.e. line intervals, completely. That was easy! ;-)

For 2-spheres, i.e. circles (or disks), the hexagonal packing is almost obviously the densest packing (the filled fraction is \(\pi/\sqrt{12}\approx 90.69\%\)) even though this result was only rigorously proved by Fejes Tóth in 1940. But what about other dimensions?