We map the star formation history across M31 by fitting stellar evolution models to color-magnitude diagrams of each 83"x83" (0.3x1.4kpc, deprojected) region of the Panchromatic Hubble Andromeda Treasury (PHAT) survey outside of the innermost 6'x12' portion. We find that most of the star formation occurred prior to ~8Gyr ago, followed by a relatively quiescent period until ~4Gyr ago, a subsequent star formation episode about 2Gyr ago, and a return to relative quiescence. There appears to be little, if any, structure visible for populations with ages older than 2Gyr, suggesting significant mixing since that epoch. Finally, assuming a Kroupa initial mass function from 0.1 to 100M_{sun}_, we find that the total amount of star formation over the past 14Gyr in the area over which we have fit models is 5x10^10^M_{sun}_. Fitting the radial distribution of this star formation and assuming azimuthal symmetry, (1.5+/-0.2)x10^11^M_{sun}_ of stars has formed in the M31 disk as a whole, (9+/-2)x10^10^M_{sun}_ of which has likely survived to the present after accounting for evolutionary effects. This mass is about one-fifth of the total dynamical mass of M31.