Abstract: We briefly review some results concerning the problem of classical singularities in general relativity, obtained with the help of the theory of differential spaces. In this theory one studies a given space in terms of functional algebras defined on it. Then we present a generalization of this method consisting in changing from functional (commutative) algebras to noncommutative algebras. By representing such an algebra as a space of operators on a Hilbert space we study the existence and properties of various kinds of singular space-times. The obtained results suggest that in the noncommutative regime, supposedly reigning in the pre-Planck era, there is no distinction between singular and non-singular states of the universe, and that classical singularities are produced in the transition process from noncommutative geometry to the standard space-time physics.