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As a contribution to the study of Hartree-Fock theory we prove rigorouslythat the Hartree-Fock approximation to the ground state of the d-dimensionalHubbard model leads to saturated ferromagnetism when the particle density (moreprecisely, the chemical potential mu) is small and the coupling constant U islarge, but finite. This ferromagnetism contradicts the known fact that there isno magnetization at low density, for any U, and thus shows that HF theory iswrong in this case. As in the usual Hartree-Fock theory we restrict attentionto Slater determinants that are eigenvectors of the z-component of the totalspin, {S}_z = sum_x n_{x,\uparrow} - n_{x,\downarrow}, and we find that thechoice 2{S}_z = N = particle number gives the lowest energy at fixed 0 < mu <4d.Comment: v2: Published version. 30 pages latex. Changes in title, abstract,  introductio

FERROMAGNETISM OF THE HUBBARD MODEL AT STRONG COUPLING IN THE HARTREE–FOCK APPROXIMATION