Brauer studied Mathematics, Physics, and Philosophy at the Free University of Berlin. He received a PhD in Mathematics 1966 from the University of Bonn for a dissertation on the theory of profinite groups.
Wilfried Brauer and his wife Ute were two of the 19 founding members of the German Informatics Society. From 1998 to 2001, he was chairman of the German Informatics Society. From 1994 to 1999, he was vice president of the International Federation of Information Processing.