If you want to efficiently pack squares in two dimensions, you arrange them like a checkerboard. To squeeze together three-dimensional cubes, you stack them like moving boxes. Mathematicians can easily extend these arrangements, packing cubes in higher-dimensional space to perfectly fill it.

Packing spheres is much harder. Mathematicians know how to pack circles or soccer balls together in a way that minimizes the empty space between them. But in four or more dimensions, the most efficient packing scheme is a complete mystery. (With the exception of dimensions 8 and 24, which were solved in 2016.)