Hans Rohrbach


Hans Rohrbach was a German mathematician. He worked both as an algebraist and a number theorist and later worked as cryptanalyst at Pers Z S, the German Foreign Office cipher bureau, during World War II. He was latterly known as the person who broke the American diplomatic O-2 cypher, a variant of the M-138-A strip cipher during 1943. Rohrbach wrote a report on the breaking of the strip cypher when he was captured by TICOM, the allied effort to roundup and seize captured German intelligence people and material.

Personal life

Hans Rohrbach was a son of journalist Paul Rohrbach and his wife Clara, who were married in Berlin in 1897. There was always confusion around Rohrbachs' name; one source gives his full name as Hans Joachim Albert Rohrbach, while the mathematician Bernhard Neumann believed this full name to be Hans Wolfgang Rohrbach, and was sure his middle initial was a 'W'.
Rohrbach entered the Gymnasium at Berlin-Friedenau in the Autumn of 1909 and studied there until Autumn 1917. He then entered the Fichte Gymnasium in Berlin-Wilmersdorf. After having successfully passed the school leaving exam in 1921, he entered the Friedrich-Wilhelm University in Berlin, where he studied mathematics, physics, and philosophy for two years. In 1923, as a head of the Berlin student organization Mathematisch-Physikalische Arbeitsgemeinschaft, he went with his father to the United States. The visit, which Rohrbach called his propaganda visit, was a tour of American universities to raise money for impoverished Berlin students. Germany's economy, which was undergoing a period of hyperinflation, was making life extremely difficult for students, who had to take employment to supplement their income.
In the autumn of 1924 Rohrbach resumed his studies at the University of Berlin and studied there until 1929. In the late 1920s he started work on his PhD thesis, titled Die Charaktere der binären Kongruenzgruppen mod p2, advised by Issai Schur. He submitted it and was awarded his doctorate on 25 July 1932.
While studying at Berlin University, Rohrbach met fellow student Rose Gadebusch, who studied mathematics starting in 1925. Gadebusch took a major role in the Mathematisch-Physikalische Arbeitsgemeinschaft. After graduation she took a position at the Women's Gymnasium. Rohrbach married her sometime around 1932.
In 1936, Rohrbach was appointed senior assistant at the University of Göttingen. In 1937, he undertook his habilitation there with a paper titled Ein Beitrag zur additiven Zahlentheorie nebst einer Anwendung auf eine Gruppentheoretische Frage.
On 1 April 1938 he was appointed as a senior assistant at the Mathematical Institute of the German University of Prague. In 1941 he was promoted to extraordinary professor and in 1942 he became an ordinary professor. He also served as Director of the Mathematical Institute there.
Rohrbach was a member of the Nazi Party and the Sturmabteilung, but was considered not fully reliable due to his friendship with Jewish colleagues.
After the war ended, Rohrbach was not allowed to teach for a number of reasons. However, he held an appointment as Visiting Professor in the Department of Mathematics in the Faculty of Science at the University of Mainz, 1946–1951. From 1951 to 1957 he was Extraordinary Professor in the Faculty of Science at Mainz, and was later dean of the Faculty of Natural Sciences, 1954–1958. He was then Associate Professor in the Department of Mathematics between 1957 and 1969. While undertaking all these roles, he was appointed Director of the Department of Mathematics at Mainz, a position he held from 1958 until 1970.
Between 24 November 1966 and 1967 he was Rector of the University of Mainz. Between July 1967 – 1977, he was a director of advisory center for student life issues at the University of Mainz. He was also an editor of Crelle's Journal, 1952–1977, assisting Helmut Hasse. He held this chair until he retired as professor emeritus in 1977.

Work

Hans Rohrbachs time was split between work with an academic focus, and work involving the military. During his time of doctorate in the very early 1930s, he published several solutions to mathematical problems that were set by the Jahresbericht of the German Mathematical Society. In 1931, he published a solution to Problem 66, in 1932 a solution followed to Problem 84 and Problem 89 was also solved in 1932.
In 1937, Rohrbach introduced a mathematical puzzle, which was a variation of James Joseph Sylvester's stamp puzzle:
In 1937, he formulated in his paper Ein Beitrag zur additiven Zahlentheorie a related problem, which he considered much more difficult:
Here are some examples from Mactutor, which have been copied verbatim to ensure mathematical accuracy:
Within the paper, Rohrbach find asymptotic bounds for n with h fixed and k large. This is a problem many mathematicians have looked at but have not been solved yet.
It was while Rohrbach was at the Mathematical Institute of the German University of Prague, starting in 1933 as a senior assistant. In 1944, he wrote a report, of which this is an exert:
The work undertaken by Rohrbach was related to the computational problems associated with the manufacture and flight of V-weapons. The research and prototyping experimental work was undertaken at the village of Peenemünde. The scientists detailed in Rohrbach report above were Dr Gerhard Gentzen, Dr Franz Krammer and Dr Paul Armsen.
The other major area that Hans Rohrbach contributed to the German war effort was as working as Cryptanalyst in the Mathematical and Cryptological Section of the special section of unit Z in the Reich Foreign Office .
He was awarded the War Service Cross 2nd Class in September 1944, for his work on the solution of the U.S. Diplomatic Strip System O-2.
Rohrbach had originally broken the cipher in 1943 after working on it for more than a year. The cipher was used by the US state department for diplomatic traffic, and the US Navy from 1940 to 1944. Rohrbach and his team used Hollerith punched card machinery and also built a special decoding machine called Automaton to aid cryptanalysis of the cipher. The Americans who made up the TICOM Team that investigated Pers Z S, ordered Rohrbach to write a report on 6 August 1945, in the form of homework to describe the process. The report was formulated as TICOM document I-89.
This is the introduction to the report:
Here is how Hans Rohrbach split his work between academia and the military:

Missionary concerns

While working at the Mathematical Institute Rohrbach managed to have several mathematicians join his group in Prague, to undertake and assist in war work. Friedrich Bauer wrote about Hans Rohrbach
One of the people that Rohrbach saved was the mathematician :de:Ernst Max Mohr|Ernst Max Mohr from execution. On 12 May 1944 Mohr was arrested by the Gestapo along with his wife, at the Béranek Hotel in Prague. On 24 October 1944, his case was heard before the People's Court, the accusation was to listen to enemy foes, to denigrate Hitler and for expressing defeatism. He is said to have described the war as already lost, the destruction of the Jews as a mistake. His work was important for the war, especially the Luftwaffe. He was nevertheless found guilty and sentenced to death, but intervention by Rohrbach and Alexander Nikuradse resulted in his death sentence being suspended for six months; he was transferred to the Sachsenhausen concentration camp, later on 18 December 1944 to the Plötzensee Prison where he continued to undertake Mathematical calculations for the V-weapon programs. He survived the war.
Rohrbach's assistants Franz Krammer and Paul Armsen were also rescued by Rohrbach. Krammer had been rescued in May 1944 in, he wrote,
Armsen was appointed by Rohrbach first as his assistant, later as a special lecturer.

After the War

Rohrbach and his wife became missionary Christians after the war. Rohrbach became president of the :de:Studentenmission in Deutschland|Studentenmission in Deutschland an organization setup to spread Christian values in schools and universities. He published a number of books which espoused his Christian values. These included: