# Hans Rohrbach

### Quick Info

Berlin, Germany

Bischofsheim an der Rhon, Germany

**Hans Rohrbach**was a German mathematician who worked in algebra and number theory. He later worked as cryptanalyst.

### Biography

We should first comment about**Hans Rohrbach**'s name. He himself always used the name Hans Rohrbach but one source gives his full name as Hans Joachim Albert Rohrbach while Bernhard Neumann said that he believed his full name was Hans Wolfgang Rohrbach and he was certain his middle initial was W. Amid this confusion we have decided to simply give his name as Hans Rohrbach. His parents, Paul Rohrbach and his wife Clara Müller, were married in Berlin in 1897. Paul Rohrbach, whose full name was Karl Albert Paul Rohrbach, was born on 29 June 1869. He studied history, geography and theology at Dorpat, Berlin and Strasbourg. He became a Protestant theologian, political publicist, administrator and travel writer. From 1903 to 1906 he served in the colonial service in German South West Africa working as a Commissioner. He returned to Berlin in 1906 and became a lecturer in colonial economy at the School of Economics.

Hans entered the Gymnasium of Berlin-Friedenau in the autumn of 1909 and continued his education there until the autumn of 1917. Germany was involved in World War I from 1914 to 1918 and during this time his father worked in the Foreign Office where he distinguished himself as a spokesman of an anti-Russian policy. He gained more influence for his policies in 1917 when the Russian Revolution broke out. After leaving the Gymnasium of Berlin-Friedenau in the autumn of 1917, Hans entered the Fichte Gymnasium in Berlin-Wilmersdorf. He took the school leaving examination in the autumn of 1921 and, in that year, entered the Friedrich-Wilhelm University of Berlin. There he studied mathematics, physics and philosophy for two years. The first course he took was Georg Feigl's lecture course 'Introduction to Higher Mathematics'. Thirty years later, Rohrbach edited the publication of Feigl's lecture course and wrote an introduction that you can read at THIS LINK.

Later, Rohrbach was taught by some outstanding mathematicians including Erhard Schmidt, Issai Schur, and Ludwig Bieberbach.

In the winter of 1923 Rohrbach went with his father on a visit to the United States. Rohrbach was, at this time, head of the Berlin student organisation Mathematisch-Physikalische Arbeitsgemeinscaft. Germany was suffering the most horrific economic problems with hyperinflation making daily living extremely difficult. Rohrbach called his visit a "propaganda trip" and he travelled round American Universities trying to collect money for Berlin students. At this time "working students" who financed their studies by taking on paid work in parallel to their studies were becoming increasingly common. In the autumn of 1924, Rohrbach took up his studies again at the University of Berlin and was enrolled there until 1929. From autumn 1927 to March 1929 he was an Under-Assistant at the Mathematical Seminar, and from April 1929 he worked there as an Assistant.

During his studies at Berlin, Rohrbach attended lectures, exercise classes and seminars by many leading mathematicians whom he names in his doctoral thesis as: Ludwig Bieberbach, Eugen Blasius, Max Dessoir, Georg Feigl, Heinz Hopf, Wolfgang Köhler, Max von Laue, Karl Löwner, Richard von Mises, Max Planck, Hans Rademacher, Heinrich Rubens, Wilhelm Schlenk, Erhard Schmidt, Issai Schur, Gabor Szegő, Arthur Wehnelt, and Wilhelm Westphal. He writes:-

All my revered teachers, especially Professors Ludwig Bieberbach, Richard von Mises, Erhard Schmidt, and Issai Schur, I would like to thank at this point.Rohrbach undertook research for his thesis advised by Issai Schur and, after submitting his thesis

*Die Charaktere der binären Kongruenz-Gruppen Mod*$p^{2}$ Ⓣ, he was awarded his doctorate on 25 July 1932. Before submitting his thesis, he published the paper

*Bemerkungen zu einem Determinantensatz von Minkowski*Ⓣ in 1931. He also published a number of solutions to problems: his solution to Problem 66 from the

*Jahresbericht*Ⓣ of the German Mathematical Society appeared in 1930, his solution to Problem 84 in 1932, his solution to Problem 89 in 1932 and, shortly after, he published a remark on this Problem 89. The oral examination for his thesis, conducted by Erhard Schmidt and Issai Schur, was held on 12 May 1932.

While studying at the University of Berlin, Rohrbach had met a student Rose Gadebusch (born 1905) who began her studies of mathematics in 1925. Like Rohrbach, Rose Gadebusch took a major role in the Mathematisch-Physikalische Arbeitsgemeinscaft while she was a student. After graduating, Rose became a mathematics teacher at a Women's Gymnasium. Hans Rohrbach married Rose Gadebusch (we have not been able to determine the exact date of their marriage but indirect evidence suggests that it was in 1932).

In 1936 Rohrbach was appointed as a senior assistant at the University of Göttingen. He habilitated at Göttingen in 1937 and he published a number of papers on number theory including a major 30-page paper in 1936 and three further papers in 1937. You can see a list of these and all other mathematical publications by Rohrbach at THIS LINK.

Let us now describe a puzzle that Rohrbach introduced in 1937 that has been the source of much interest and research ever since. The puzzle is a variant on 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.Rohrbach asked a related problem in his paper

*Ein Beitrag zur additiven Zahlentheorie*Ⓣ (1937) but one which is much more difficult to answer [3]:-

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.

- $n(2, 3) = 8$ 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}.
- $n(3, 4) = 24$ with one solution set being {0, 1, 4, 7, 8}.

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 at the German University of Prague. He also served as Director of the Mathematical Institute of the German University of Prague. In that capacity, in October 1944 he wrote a report on the Development of the Mathematical Institute. He wrote:-

I am taking the move of the Mathematical Institute into the recently completed new rooms as an opportunity to give a short report on the development of the Institute in the last year. Up to the end of 1943 no research work was carried out in the Institute. The two established professors had been assigned to war work but, in addition, continued to carry out their teaching duties. The assistant had been drafted into the army, and no additional mathematicians were available. However, since I arrived here, I have made efforts to have the Institute itself to be involved in war related research. To achieve this I required more space and more collaborators. Once my requests to enlarge the Institute were granted in a satisfactory way by the curator, the work of setting up began a year ago.You can read Rohrbach's full report at THIS LINK.

The war work that Rohrbach undertook in the Mathematical Institute was related to computational problems associated with the manufacture of V-weapons at Peenemünde. Peenemünde was a village in north east Germany, at the north west end of Usedom Island where the Peene River flows into the Baltic Sea. It was where Germany undertook research and testing for missiles, called V-weapons, which eventually were fired at England. Rohrbach set up a work group of young girls who were in their final years at a Gymnasium and trained them to carry out mathematical and statistical computations. The girls certainly preferred this type of war work to the hard physical work in a munitions factory. He also managed to have several mathematicians join his group in Prague. Friedrich Bauer writes (see [2]):-

I do not know what Rohrbach's group in Prague calculated. ... In my estimation of Rohrbach's character, the activity of the computing group could have been a [facade] for the rescue of human lives. ... I have treasured Rohrbach's human traits greatly, even if his missionary concerns got on my nerves.We will discuss Rohrbach's "missionary concerns" towards the end of this article. One of the men that Rohrbach "rescued" with his computing group was Ernst Mohr, and later it was Rohrbach's skilful diplomacy that saved Mohr after he had been sentenced to death by the Peoples' Court on 24 October 1944. Rohrbach's assistants Franz Krammer and Paul Armsen were also "rescued" by Rohrbach. Krammer had been rescued in May 1944 in, he wrote, "for me a wonderful action [by Rohrbach]", from the disintegrating eastern front. Armsen was appointed by Rohrbach first as his assistant, later as a special lecturer.

Rohrbach, however, had another role in Germany's war effort, namely working at a cryptologist for the Foreign Office in Berlin. In the October 1944 report from which we quoted above, Rohrbach explains that he cannot give his full attention to the Mathematical Institute of the German University of Prague because of his commitments in Berlin. Here is his own description of how he split his time between these two tasks in the months that followed the report:-

I had concluded my activity there [Prague] for the winter semester 1944-45 [at the end of February] and was in Berlin, where during the war I was busy full time at the Foreign Office. I looked after the work in Prague for only two days in the week during the semester, travelling there at night in a sleeper coach, two night later back in a sleeper coach, thus working four days a week in Berlin, two days in Prague. During the vacations I was busy only in Berlin. I intended to return to Prague for the summer semester 1945 [at the end of April]. I had as always left everything personal behind in the Institute, in particular books, lecture manuscripts, etc. But at the beginning of April 1945 I was already in the store of the Foreign Office in Thuringia.After the war ended, in 1948 Rohrbach published a paper in two parts entitled

*Mathematische und Maschinelle Methoden bei Chiffrieren und Deschiffrieren*Ⓣ. These were translated into English and published as [4] and [5] in 1978. Here is Rohrbach's introduction to the paper:-

In this report we are dealing with a field of applied mathematics which has been foreign to most mathematicians and on which practically nothing has been published up to now. Methods and results have generally been left in secrecy, existing largely in the minds of the people involved. For these reasons we must go into the basic concepts and principles of this field rather thoroughly. Further, we cannot expect this report, as a first approach, to be exhaustive. The written materials needed for a foundation, including in particular the only publication to my knowledge of the character of a scientific journal (Scientific papers of the Dahlem Special Service, published by the Foreign Office, Berlin, 1940-45), either have been destroyed or have been retained by the Allies; the workers concerned are known to me only in small part or cannot be contacted. Accordingly, I can bring only scattered examples to the best of my memory. They come largely from the work of the Foreign Office, the Department of Defense (OKW), and the Department of the Army (OKH). By agreement with those workers that I have been able to contact, I will not give any names - it's a chance selection at best. Naturally much more work in this field has been done in Germany than I am able to take into consideration here, for the reasons already given. It seems to me at least, as will be brought out sufficiently in the material that follows, that mathematical cryptology is a very attractive field of applied mathematics. With good reason have all larger nations selected mathematicians for special use, particularly for use in cryptanalysis.Rohrbach recommended including vulnerability to errors when assessing the security of a method, on the principle that humans err. He developed what is today called Rohrbach's Maxim: In judging the encryption security of a class of methods, cryptographic faults and other infringements of security discipline are to be taken into account.

Friedrich Bauer writes [1]:-

The good cryptologist knows that he cannot rely on anything, not even on the adversary continuing his mistakes. He is particularly critical about his own possible mistakes. Surveillance of one's own encryption habits by a "Devil's advocate" is absolutely necessary, as the experiences of the Germans in the Second World War showed only too clearly.The U.S. cryptologists could not imagine that Rohrbach had broken their M-138-A strip cipher which he did in 1943 after working on it for a year. This cipher was originally used by the U.S. State Department and the U.S. Navy from 1940 to 1944. Rohrbach led a team of mathematicians who used IBM/Hollerith punch card equipment and also built their own special decoding device which they called 'Automaton'. In [2] there are some details of Rohrbach's personal file in the political archives of the Foreign Office:-

From it we learn that since 10 May 1940, thus at a time when he was still senior assistant in Göttingen, he was temporarily employed as a scientific labourer in the Foreign Office and was assigned to the Personnel and Management Department, Project Z, Cyphers and Communication.The file also states that Ernst Mohr was assigned to be Rohrbach's replacement in Prague during his activities in the Foreign Office in Berlin.

After the war ended, Rohrbach was not allowed to teach for a number of years. However, he was appointed as Professor of Mathematics at the University of Mainz in 1951. He continued to hold this chair until he retired in 1977 when he was made professor emeritus. He was rector of the University in session 1966-67. He was also an editor of 'Crelle's Journal' from 1952 to 1977 assisting Helmut Hasse with this publication.

Finally, let us return to Rohrbach's "missionary concerns" which we mentioned above. After the war, Rohrbach and his wife Rose became enthusiastic Christians with a missionary zeal to bring others to the faith. Rohrbach was the first president of

*Studentenmission in Deutschland*, an organisation which aimed to spread Christian values in German schools and universities. He published a number of books relating to his Christian beliefs:

*Naturwissenschaft, Weltbild, Glaube*Ⓣ (1967),

*Mit dem Unsichtbaren leben: Unsichtbare Mächte und die Macht Jesu*Ⓣ (1976);

*Unsichtbare Mächte und die Macht Jesu: Zur Seelsorge an belasteten Menschen*Ⓣ (1985);

*Das anstössige Glaubensbekenntnis: Ein Naturwissenschaftler zum christlichen Glaubensbekenntnis*Ⓣ (1987);

*Die Faszination des Übersinnlichen*Ⓣ (1988);

*Schöpfung - Mythos oder Wahrheit?*Ⓣ (1990); and

*Wunder: Das Ungewöhnliche im Wirken Gottes*Ⓣ (1992). In 1977 Rohrbach and his wife Rose moved to Bischofsheim an der Rhön where they built the Christian Conference Centre 'Christlichen Tagungsstätte Hohe Rhön' Ⓣ. This Centre, on the hill overlooking Bischofsheim an der Rhön, is still run today as a Christian retreat.

### References (show)

- F L Bauer,
*Decrypted Secrets: Methods and Maxims of Cryptology*(Springer Science & Business Media, 2013). - E Menzler-Trott,
*Logic's lost genius: The life of Gerhard Gentzen*(Amer. Math. Soc and London Math. Soc, Providence, RI, 2007). - A Alter and J A Barnett, A postage stamp problem,
*Amer. Math. Monthly***87**(3) (1980), 206-210. - H Rohrbach, Mathematical and mechanical methods in cryptography. I,
*Cryptologia***2**(1) (1978), 101-121. - H Rohrbach, Mathematical and mechanical methods in cryptography. II,
*Cryptologia***2**(2) (1978), 21-37. - W Schwarzm and B Volkmann, Hans Rohrbach zum Gedächtnis: 27.02.1903 - 19.12.1993,
*Jahresbericht der Deutschen Mathematiker-Vereinigung***105**(2003), 89-99.

### Additional Resources (show)

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Written by J J O'Connor and E F Robertson

Last Update April 2016

Last Update April 2016