Origin of Classical Singularities
  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. 
M. Heller (Vatican Observatory), W Sasin (Institute of Mathematics,   Warsaw University of Technology)