For any assumed standard stellar Initial Mass Function, the Sloan Digital Sky Survey (SDSS) gives a precise determination of the abundance of galaxies as a function of their stellar mass over the full stellar mass range 108M⊙ < M∗ < 10 12M⊙. Within the concordance ΛCDM cosmology, the Millennium simulations give precise halo abundances as a function of mass and redshift for all halos within whic...