A strong-coupling expansion for the phase boundary of the (incompressible) Mott insulator is presented for the Bose-Hubbard model. Both the pure case and the disordered case are examined. Extrapolations of the series expansions provide results that are as accurate as the Monte Carlo simulations and agree with the exact solutions. The shape difference between Kosterlitz-Thouless critical behavior in one-dimension and power-law singularities in higher dimensions arises naturally in this strong-coupling expansion. Bounded disorder distributions produce a ''first-order'' kink to the Mott phase boundary in the thermodynamic limit because of the presence of Lifshitz's rare regions.