The Standard Model, besides successfully describing all the relevant interactions, is moreover being crowned as the theory of the origin of particle masses through the Higgs mechanism. There is however one important failure: the prediction of massless neutrinos. The origin of neutrino mass is thus an important window to new physics beyond the SM. I argue that future hadron colliders, and possibly even the LHC, could open that window. I focus on the Left-Right symmetric extension of the SM model, the theory that led originally to neutrino mass and the seesaw mechanism behind its smallness, long before experiment. I show that the minimal LR symmetric model is a self-contained and predictive theory of both the nature and the origin of neutrino mass, in complete analogy with the Weinberg-GIM mechanism for charged fermions.