 In 1963 he was awarded the Magnus Schwerd Prize for outstanding achievements in mathematics at school.Vollmer became a member in 1998 of the Leopoldina Academy of Sciences Halle.He is a member of Giordano Bruno Foundation (a society dedicated to a sort of evolutionary humanism, weblink below) and (in 2001) was elected to the learned society, Braunschweig Sciences Society (Braunschweigische Wissenschaftliche Gesellschaft).