While most media outlets report on disasters, at Tangente we prefer to celebrate successes! Maryna Viazovska recently solved the problem of the optimal packing of identical spheres in dimensions 8 and 24. Why is this so extraordinary? To see why, let's look at dimensions familiar to us. In dimension 2, the “spheres” are circles. It has long been known that placing circles at the vertices of a hexagonal lattice produces the greatest density. Yet a complete proof was not given until the 1940s by Lászlò Fejes Tòth (1915–2005).
The densest packing of circles in the plane. The six circles (in blue) tangent to a given circle (in red) form a hexagonal lattice.
