ROHN, KARL

(b. Schwanheim, near Bensheim, Hesse, Germany, 28 January 1855; d. Leipzig, Germany, 4 August 1920)

mathematics.

Rohn entered the Polytechnikum at Darmstadt in 1872, studying engineering and then mathematics. He continued his work in the latter at the universities of Leipzig and Munich, receiving his doctorate at Munich in 1878 and qualifying as lecturer at Leipzig a year later. In 1884 he became an assistant professor at Leipzig, and in 1887 full professor of descriptive geometry at the Technische Hochschule in Dresden. From 1904 until his death he was full professor at the University of Leipzig.

In his dissertation and in his Habilitationsschrift Rohn, Stimulated by F. Klein, examined the relationship of Kummer’s surface to hyperelliptic functions. In these early writings he demonstrated his ability to work out the connections between geometric and algebraic-analytic relations. In the following years Rohn further developed these capacities and became an acknowledged master in all questions concerning the algebraic geometry of the real P₂ and P₃, where it is possible to overlook the different figures. This concerns forms of algebraic curves and surfaces up to degree 4, linear and quadratic congruences, and complexes of lines in P₃. Gifted with a strong spatial intuition, Rohn possessed outstanding ability to select geometric facts from algebraic equations.

In several instances no decisive advance has been made on the results that Rohn obtained. This is especially true of his investigations on fourth-degree surfaces having one triple point or having finitely many isolated singular points. Most later studies concerning fourth-degree surfaces with only isolated singularities have been devoted to Kummer surfaces, which possess the greatest number of singular points (sixteen). Early in his career Rohn also constructed spatial models of the surfaces and space-curves he was studying. Rohn was the first to solve the difficult problem concerning the possible positions of the eleven ovals that the real branch of a sixth-degree plane curve can maximally possess. These problems were of great interest to Hilbert, but he did not succeed in resolving them.

BIBLIOGRAPHY

I. Original Works. Rohn’s writings include “Über Flächen 4. Ordnung mit dreifachem Punkte,” in Mathematische Annalen, 24 (1884), 55–151; “Über Flächen 4. Ordnung mit 8–16 Knotenpunkten,” in Bericlite über die Verhandlungen der Sächsischen Akademie der Wissenschaften zu Leipzig, 36 (1884), 52–60; Lehrbuch der darstellenden Geometrie, 2 vols. (Leipzig, 1893–1896), written with E. Papperitz; and “Die ebene Kurve 6. Ordnung mit 11 Ovalen,” in Berichte über die Verhandlungen der Sächsischen Akademie der Wissenschaften zu Leipzig, 63 (1911), 540–555.

II. Secondary Literature. See O. Hölder, “Nekrolog für K. Rohn,” in Leipziger Berichte, 72 (1920), 107–127; and F. Schur, “Karl Rohn,” in Jahresbericht der Deutschen Mathematiker-vereinigung, 32 (1923), 201–211.

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