We report the discovery of a widespread population of collisionally excited methanol J = 4 sub(-1) to 3 sub(0) E sources at 36.2 GHz from the inner 66' x 18' (160 x 43 pc) of the Galactic center. This spectral feature was imaged with a spectral resolution of 16.6 km s super(-1) taken from 41 channels of a Very Large Array continuum survey of the Galactic center region. The revelation of 356 methanol sources, most of which are maser candidates, suggests a large abundance of methanol in the gas phase in the Galactic center region. There is also spatial and kinematic correlation between SiO (2-1) and CH sub(3)OH emission from four Galactic center clouds: the +50 and +20 km s super(-1) clouds and G0.13-0.13 and G0.25 + 0.01. The enhanced abundance of methanol is accounted for in terms of induced photodesorption by cosmic rays as they travel through a molecular core, collide, dissociate, ionize, and excite Lyman Werner transitions of H sub(2). A time-dependent chemical model in which cosmic rays drive the chemistry of the gas predicts CH sub(3)OH abundance of 10 super(-8) to 10 super(-7) on a chemical timescale of 5 x 10 super(4) to 5 x 10 super(5) years. The average methanol abundance produced by the release of methanol from grain surfaces is consistent with the available data.