Sphere packings is one of the most fascinating and challenging subjects
in mathematics. Almost four centuries ago, Kepler studied the densities
of sphere packings and made his famous conjecture. Several decades later,
Gregory and Newton discussed the kissing numbers of spheres and proposed
the Gregory-Newton problem. Since then, these problems and related ones
have attracted the attention of many prominent mathematicians such as
Blichfeldt, Dirichlet, Gauss, Hermite, Korkin, Lagrange, Minkowski, Thue,
Voronoi, Watson, and Zolotarev, as well as many active today....