The Higgs mechanism is a part of the Standard Model of quantum mechanics that allows certain kinds of particles to have nonzero mass. In spite of its great importance, there is no rigorous proof that the Higgs mechanism can indeed generate mass in situations that are relevant for the Standard Model. In technical terms, this corresponds to the “coupling parameter” of the model being small, and the "gauge group” being non-Abelian (the most important cases are SU(2) or SU(3)). I will present the first rigorous proof in this direction, showing that SU(2) lattice Yang-Mills theory coupled to a Higgs field transforming in the fundamental representation of SU(2) has a mass gap at any value of the coupling parameter, provided that the interaction of the Higgs field with the gauge field is strong enough. No background is needed.