Weyl sums and atomic energy oscillations

Mathematicians are by nature reductionist and often dream, and also pretend, of being able to deduce rigorously the laws of Science from a small set of first principles. It is a plausible goal having a distinguished history, but very difficult to achieve. And it rarely excites physicists, because what mathematicians can rigorously prove is not usually a hot topic for them.Nevertheless,we can always quote E.Wigner’s comment about the unreasonable effectiveness of mathematics as a fundamental instrument for the formulation and progress of physical theories.