  The formulation of a fundamental theoretical description of disordered solids
is a standing challenge in condensed matter physics. So far, the structure and
dynamics of glasses is described in the literature on the basis of
phenomenological models. We develop a theoretical framework for amorphous
materials, relying on the basic principle that the disorder in a glass is
similar to the disorder in a classical fluid, while the latter is
mathematically encoded by noncommutative coordinates in the Lagrange
formulation of fluid mechanics. Under this principle, we construct a model of
the amorphous solids as fuzzy crystals and we establish an analytical theory of
vibrations for glasses, that naturally contains the boson peak as a
manifestation of an extended van Hove singularity.
