  The kissing number problem asks for the maximal number k(n) of equal size
nonoverlapping spheres in n-dimensional space that can touch another sphere of
the same size. This problem in dimension three was the subject of a famous
discussion between Isaac Newton and David Gregory in 1694. In three dimensions
the problem was finally solved only in 1953 by Sch\"utte and van der Waerden.
In this paper we present a solution of a long-standing problem about the
kissing number in four dimensions. Namely, the equality k(4)=24 is proved. The
proof is based on a modification of Delsarte's method.
