Zoll's surfaces are a special kind of surfaces generalizing the spheres, in that all of their geodesics are closed and of the same length.

I've tried to gather some biographical details on Otto Zoll but apart from the mention that he was David Hilbert's student I couldn't find any.

Does anyone in here can help me with some references?


1 Answer 1


The Ph.D. was conferred on Otto Zoll by the Georg August University of Göttingen in 1901. The title of his dissertation, which functioned as a prize essay at the same time, was: Ueber Flächen mit Scharen von geschlossenen geodätischen Linien (On surfaces possessing families of closed geodetic lines). The Ph.D. thesis was accepted on June 5, 1901, and the Ph.D. defense took place on July 29, 1901. The faculty awarded the full prize, as the thesis addressed the prize problem in the most satisfying manner ("in befriedigendster Weise"). It also lauds the clear and easy to read writing. A scan of the dissertation can be found at Google. Otto Zoll's Ph.D. advisor was David Hilbert.

There is a brief CV at the end of the dissertation, according to which Zoll's full name was Carl Otto Zoll. He was born April 2, 1878 in Hückeswagen, a small town some 30 miles from Cologne, as the son of Fritz Zoll, the managing director of a factory. The German Wikipedia has a page on this factory from which I learned that this was a yarn spinning and textile mill belonging to Arnold Hueck, and that in 1921, after the death of Hueck, Fritz Zoll became a co-owner jointly with Hueck's widow. There is also a picture of the remaining main building, painted entirely in red.

The CV further states that Zoll attended schools in Hückeswagen and Wipperfürth followed by high school in Düren, from which he gradudated Easter 1897. Thereafter he studied mathematics: From Easter 1897 to Michaelmas 1897 in Munich, from Michaelmas 1897 to Easter 1899 in Berlin, since Easter 1899 in Göttingen.

Zoll's Ph.D. thesis served as the basis of his only publication in a scientific journal, available as a scan at the Göttingen Digitization Center:

Otto Zoll, "Ueber Flächen mit Scharen geschlossener geodätischer Linien." Mathematische Annalen, Vol. 57, 1903, pp. 108-133.

The Center also has a picture of Otto Zoll dating to about 1920 to 1922, part of a photo album with portrait shots of mathematicians presented to David Hilbert on January 23, 1922.

I found further information on Otto Zoll in a research report: Manfred Goebel and Christian Schlensag, Hans Brandes (1883 – 1965) Promotion in Halle – Lehrer in Braunschweig, Reports on History of Mathematics, Report No. 08, Martin Luther University Halle-Wittenberg, Mathematical Institute, 2008. The following paragraphs are largely based on this report.

From 1905 through 1947 (his retirement) Zoll was employed as a senior teacher at a high school in Düsseldorf, from 1916 with the rank of professor. He died January 20, 1952 in that city. From 1931 to 1943 he served as co-author and editor of a multi-volume textbook of mathematics for secondary schools, Mathematisches Arbeits- und Lehrbuch, published by Vieweg in Braunschweig.

The organization and content of the book as well as the name appear to have been adjusted multiple times to track changes in the school system. Based on offerings by used book sellers, it appears that after the school reforms of 1937/1938 there were three volumes for use by students: One for grades 5 and 6 ("Unterstufe"), one for grades 7 through 9 ("Mittelstufe"), and one for grades 10 through 12 ("Oberstufe). These were augmented by a volume with additional exercises and a volume for use by teachers. The textbook appears to have had a special emphasis on exercises based on various real-life scenarios. The research report finds that especially with the revisions of 1937 and 1939 numerous exercises directly related to Nazi ideology or with a military context (some even provided by the German Navy) were included in the book.

Needless to say this caused problems with the Allied military administration in Germany after WW2. The publisher apparently tried to rework the textbook in conjunction with authors and editors to remove all objectionable matter. In a letter to Vieweg dated October 2, 1945, Zoll himself raised the issue whether it was even possible for him to remain as an editor, given that he had been a "Parteigenosse", that is, a member of the Nazi party. After objections from the Education Branch of the British Military Government in Germany the publisher ultimately replaced Zoll as editor in fall of 1947.


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