A member of the Nazi Party (NSDAP) and Sturmabteilung (SA), the military wing of the NSDAP, from 1931, Teichmüller agitated against his Jewish professors Richard Courant and Edmund Landau in 1933. He was drafted into the Wehrmacht in July 1939 and took part in the invasion of Norway in 1940 before being recalled to Berlin to undertake cryptographic work with the Cipher Department of the High Command of the Wehrmacht. In 1942, he was released from his military duties and returned to teach at the University of Berlin. After the German defeat at Stalingrad in February 1943, he gave up his position in Berlin to volunteer for combat on the Eastern Front. He was killed in action in September 1943.