We present the key scientific questions that can be addressed by GMOX, a Multi-Object Spectrograph selected for feasibility study as a 4th generation instrument for the Gemini telescopes. Using commercial digital micro-mirror devices (DMDs) as slit selection mechanisms, GMOX can observe hundreds of sources at R~5000 between the U and K band simultaneously. Exploiting the narrow PSF delivered by the Gemini South GeMS MCAO module, GMOX can synthesize slits as small as 40mas reaching extremely faint magnitude limits, and thus enabling a plethora of applications and innovative science. Our main scientific driver in developing GMOX has been Resolving galaxies through cosmic time: GMOX 40mas slit (at GeMS) corresponds to 300 pc at z ~ 1:5, where the angular diameter distance reaches its maximum, and therefore to even smaller linear scales at any other redshift. This means that GMOX can take spectra of regions smaller than 300 pc in the whole observable Universe, allowing to probe the growth and evolution of galaxies with unprecedented detail. GMOXs multi-object capability and high angular resolution enable efficient studies of crowded fields, such as globular clusters, the Milky Way bulge, the Magellanic Clouds, Local Group galaxies and galaxy clusters. The wide-band simultaneous coverage and the very fast slit configuration mechanisms also make GMOX ideal for follow-up of LSST transients.