In his doctoral dissertation held in Koenigsberg in 1885, Minkowski proposed the conjecture that, unlike the quadratic case, nonnegative homogeneous polynomials of higher degree and more than two variables in general cannot be written as a sum of squares of real polynomials. The problem attracted the attention of Hilbert who in 1888 proved nonconstructively the existence of such polynomials. However, the first concrete example of a nonnegative polynomial which is not a sum of squares seems to have been given only in 1967 by T. S. Motzkin [The arithmetic-geometric inequality, Inequalities (Proc. Sympos. Wright-Patterson Air Force Base, Ohio, 1965), pp. 205-224", Academic Press, New York, 1967].