Hans Rohrbach (27 February 1903 – 19 December 1993) 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.
Hans Rohrbach was a son of journalist Paul Rohrbach and his wife Clara (née Müller), 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 (school) 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 (Mathematics and Physics Working Group), 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 (The characters of the binary congruence groups 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 (born 1905), 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 thesis paper titled Ein Beitrag zur additiven Zahlentheorie nebst einer Anwendung auf eine Gruppentheoretische Frage (A contribution to additive number theory together with an application on a group theoretical question).
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 (the party's original paramilitary wing, later superseded by the SS), 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.
Hans Rohrbachs time was split between work with an academic focus, and work involving the military. During his doctoratal studies, in the very early 1930s, he published several solutions to mathematical problems that were set by the Jahresbericht (Annual Report) 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:
I have a large number of stamps to the value of 5d and 17d only. What is the largest denomination which I cannot make up with a combination of these two different values.
In 1937, he formulated in his paper Ein Beitrag zur additiven Zahlentheorie (A contribution to the additive number theory) a related problem, which he considered much more difficult:
An envelope may carry no more than h stamps, and one has available k integer-valued stamp denominations. Given h and k, find the maximal integer n = n(h, k) such that all integer postage values from 1 to n can be made up. In addition, find all sets of k stamp denominations satisfying this condition. The problem statement is usually modified by augmenting the solution sets with a stamp of value zero, and requiring that a letter carry exactly h stamps.
Here are some examples from Mactutor, which have been copied verbatim to ensure mathematical accuracy:
n(2, 3) = 8 with the unique solution set {0, 1, 3, 4}.
n(2, 6) = 20 with five solution sets {0, 1, 2, 5, 8, 9, 10}, {0, 1, 3, 4, 8, 9, 11}, {0, 1, 3, 4, 9, 11, 16}, {0, 1, 3, 5, 6, 13, 14}, and {0, 1, 3, 5, 7, 9, 10}.