In this paper we prove that the second (non-trivial) Neumann eigenvalue of the Laplace operator on smooth domains of RN with prescribed measure m attains its maximum on the union of two disjoint balls of measure m/2. As a consequence, the Pólya conjecture for the Neumann eigenvalues holds for the second eigenvalue and for arbitrary domains. We moreover prove that a relaxed form of the same inequality holds in the context of non-smooth domains and densities.