Career
He is a professor emeritus of Ludwig Maximilian University of Munich. As a postdoc at Cornell University, he and David Mermin (and independently of Pierre Hohenberg) proved a "no-go theorem", otherwise known as the Mermin–Wagner theorem. The theorem states that continuous symmetries cannot be spontaneously broken at finite temperature in systems with sufficiently short-range interactions in dimensions.
Wagner is the academic father of a generation of statistical physicists.
Many of his students and junior collaborators now occupy chairs in German universities, including Hans Werner Diehl (Essen), Siegfried Dietrich (Wuppertal, then Max-Planck-Institut für Metallforschung Stuttgart), Gerhard Gompper (Forschungszentrum Jülich), Reinhard Lipowsky (Max Planck Institute of Colloids and Interfaces, Berlin), Hartmut Löwen (Düsseldorf), Klaus Mecke (Erlangen), and Udo Seifert (Stuttgart).