  Weyl was particularly well positioned to handle some of the  mathematical and foundational problems of the new theory of quantum  mechanics. Almost every aspect of his mathematical expertise, in  particular, his recent work on group theory and his very early work  on the theory of singular differential-integral equations  (1908–1911), provided him with the precise tools for solving  many of the concrete problems posed by the new theory: the theory of  Hilbert space, singular differential equations, eigenfunction  expansions, the symmetric group, and unitary representations of Lie  groups. 