The potential of mean force (PMF) between two methane molecules in water is calculated using molecular dynamics with Ewald boundary conditions for two water models, the WK model (a nonpolarizable model) and the PSRWK model (a polarizable model), for the purpose of understanding what role many-body polarization plays in the hydrophobic interaction. These models of neat water have the same static dielectric constants and similar structural and thermodynamic properties. The methane-water interaction is taken to be exactly the same in both fluids. Nevertheless, the simulated potential of mean force between two dissolved methane molecules is very different for these two models. In the polarizable model, solvent-separated pairing is dominant over contact-pairing, while in the nonpolarizable model the reverse is true.