Do electrons become ferromagnetic just because of their repulisve Coulomb interaction? Our calculations on the three-dimensional electron gas imply that itinerant ferromagnetim of delocalized electrons without lattice and band structure, the most basic model considered by Stoner, is suppressed due to many-body correlations as speculated already by Wigner, and a possible ferromagnetic transition lowering the density is precluded by the formation of the Wigner crystal.