# Karl Friedrich Wilhelm Rohn

### Born: 28 January 1855 in Schwanheim (near Bensheim), Hesse, Germany

Died: 4 August 1920 in Leipzig, Germany

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**Karl Rohn**attended the Polytechnikum at Darmstadt beginning his studies there in 1872. He had begun by taking engineering courses, with the intention of qualifying as an engineer, but the mathematics he studied as part of his engineering degree became by far the most interesting to him. He studied mathematics and engineering at the University of Leipzig, then mathematics at the University of Munich. He was strongly influenced by Alexander von Brill who taught him mathematics in Munich but the main influence on him at this stage was Felix Klein who acted as his thesis advisor. Rohn was awarded a doctorate in 1878 for his dissertation,

*Betrachtungen über die Kummersche Fläche und ihren Zusammenhang mit den hyperelliptischen Funktionen p = 2*Ⓣ. In this excellent piece of work he studied the relationship of Kummer's surface to hyperelliptic functions. He submitted his Habilitation thesis, again strongly influenced by suggestions made by Klein, to the University of Leipzig in the following year. From 1879 he was a Privatdozent at Leipzig.

In 1884 Rohn was promoted to extraordinary professor at Leipzig, then in 1887 he became a full professor at Technische Hochschule in Dresden where he held the chair of descriptive geometry. Felix Klein lectured during his visit to the United States in Evanston between 28 August and 9 September 1893. During these lectures he spoke about various models of the Kummer surface. He said that Rohn's work on this topic was the most significant. One of Rohn's models for the Kummer surface uses the generating lines on a hyperboloid of one sheet. He then took four lines from each of the two sets of generators, shaded the alternate regions, and then glued a copy of the shaded regions to the original along the boundary. In this way he produced a closed surface without boundary having sixteen real nodal points. He published this construction in 1881 and gave more details in an 1887 paper. Burau writes [1]:-

His love of geometry is also illustrated by his beautiful thread models which were especially produced to excite the curiosity of the uninitiated. Rohn constructed models of surfaces and space curves that he was studying, particularly in the early part of his career. In 1884 the Jablonowski Society proposed as prize problem asking for essays on the general surface of order 4, extending the work of Schläfli, Klein and Zeuthen on cubic surfaces; they awarded the prize to Rohn for his essay in 1886. He made important contributions to the theory of quartic surfaces, in particular of ruled quartics and quartics with a triple point. He also showed that the maximum number of separated ovals possible for a quartic surface is ten. He publishedIn these early writings he demonstrated his ability to work out 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 realP_{2}andP_{3}, where it is possible to overlook the different figures. This concerns forms of algebraic curves and surfaces up to degree four, linear and quadratic congruences, and complexes of lines inP_{3}. Gifted with a strong spatial intuition, Rohn possessed outstanding ability to select geometric facts from algebraic relations.

*Die Flächen vierter Ordnung hinsichtlich ihrer Knotenpunkte und ihrer Gestaltung: Gekrönte Preisschrift*Ⓣ (1886). Rohn was made rector of the Technical University of Dresden during 1900-01. As rector he gave a speech on 23 April 1900 to celebrate the birthday of His Majesty the King. His speech was entitled

*Die Entwickelung der Raumanschauung im Unterricht*Ⓣ and it was published by the Technical University of Dresden in 1900. In Dresden, Rohn gave the course 'Darstellende Geometrie' in the summer of 1904. It was the last session that he lectured at Dresden for in the following year he was appointed to the University of Leipzig. From 1 April 1905 until his death, Rohn held the chair of mathematics at the University of Leipzig.

Let us look briefly at some of the mathematical highlights of Rohn's career, some of which have already been mentioned. In his 16

^{th}problem Hilbert asked about non-singular algebraic curves and surfaces. Rohn published three papers contributing to this problem. We mentioned above his outstanding investigations of fourth degree surfaces having one triple point or having finitely many isolated singular points. In the later part of his career he was involved in deep investigations of Kummer surfaces which possess the greatest number of singular points, namely ten. He also solved the difficult problem of finding the possible positions of the maximum number of ovals, namely eleven, that the real branch of a sixth degree curve can possess. David Hilbert was particularly interested in these results.

The

*American Mathematical Monthly*published this notice of his death which mentions his famous book

*Lehrbuch der darstellenden Geometrie*Ⓣ:-

After Rohn's death, the bookDr K F W Rohn, professor of mathematics at the University of Leipzig since1905, died on4August1920, aged sixty-five years. He is, perhaps, best known to mathematicians through his three volume work(in its third edition,1906)entitledⓉ(1893-1896; fourth edition,1913-16), which he prepared, after the appearance of the first volume, in collaboration with Dr E Papperitz.

*Stereometrie: Ein Handbuch für Studierende und Lehrer*Ⓣ (1922) was published. David Smith writes in a review:-

This work was substantially ready for publication at the time of Professor Rohn's death, in August1922, the necessary completion of the manuscript in minor details having been done by his friend and former pupil Dr Friedrich Wünschmann. Dr Rohn was himself a pupil of Professor Klein, and the latter, in his appreciative introduction, speaks highly of his skill in the field of geometry. The work sets forth in succinct form the essential features of modern projective geometry with respect to solids, thus extending the ordinary treatment of the projective properties of figures in a plane to those of three dimensions. It begins with a review of plane geometry(50pages)and then considers the sphere, cylinder, and cone, proceeding later to the properties of conic sections and other plane figures in space. The work shows a return to the better type of German bookmaking of pre-war days and will be welcomed by students of modern geometry as an aid to their advanced work in this field.

**Article by:** *J J O'Connor* and *E F Robertson*

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