**Erich Hans Rothe**'s parents were Elise Margarethe and Erich Hans Rothe. His father, Dr Rothe, was a lawyer and the family were Jewish. He attended school in Berlin graduating from the Königliches Wilhelms-Gymnasium with his Abitur (matriculation examination) in October 1913. He was taught mathematics at this school by Dr Dietrich to whom he gave special thanks in a note in his doctoral thesis. Then he began his university studies at the University of Munich where one of his mathematics lecturers was Ferdinand von Lindemann, a philosophy lecturer was Hugo Dingler (1881-1954) and a physics lecturer was Leo Graetz (1856-1941). He had only completed two semesters of study before war broke out in the summer of 1914. Immediately Rothe volunteered to serve in the German Army [4]:-

He joined the artillery and served in the Bayerische Reserve-Feldartillerie-Regimenter No. 10 (Erlangen) and in the Bayerische Feldartillerie-Regiment (Nürnberg). He was at the Battle of Verdun, fought between the German and French armies for almost the whole of the year 1916. The battle, on the hills around Verdun-sur-Meuse in north east France, was extremely costly to both sides with an estimate of almost one million soldiers killed, roughly equal numbers of French and Germans. Rothe survived the battle but he was wounded and eventually discharged from the German Army in December 1918.... although its goals were obviously alien to him.

With the end of World War I in November 1918, Rothe was able to continue his university studies after the four year break caused by the war. He did not return to the University of Munich but instead, in 1919, enrolled at the Technischen Hochschule in Berlin-Charlottenburg where he studied for one semester attending lectures by Rudolf Ernst Rothe (1873-1942). After this one semester, he changed to study at the Friedrich-Wilhelm University of Berlin. There he studied mathematics, physics and philosophy as did his fellow student Maximilian Herzberger who had also returned to university after being released from military service at the end of 1918. The ordinary professors of mathematics at the University were Friedrich Schottky and Erhard Schmidt, while Issai Schur was an extraordinary professor. Rothe took the examinations to become a Gymnasium teacher in 1923 and, from then until 1926, he was a student teacher at the Mommsen-Gymnasium in Berlin-Charlottenburg. At the same time he undertook research for his doctorate on analogies between linear partial differential equations and linear ordinary differential equations. His thesis advisor was Erhard Schmidt. He submitted his thesis, *Über einige Analogien zwischen linearen partiellen und linearen gewöhnlichen Differentialgleichungen, * to the University of Berlin in 1926. An oral examination, conducted by Schmidt and Richard von Mises, was held on 4 March 1926. In a paper with the same title, submitted on 12 July 1926, Rothe thanked Erhard Schmidt for showing him how some of his original proofs could be simplified. The paper was published by *Mathematische Zeitschrift* in December 1928. Rothe was awarded his doctorate on 27 May 1927.

In his thesis Rothe lists all his lecturers at university. Those who taught him mathematics in Berlin include Ludwig Bieberbach, Constantin Carathéodory, Hans Hamburger, Konrad Knopp, Karl Löwner, Richard von Mises, Hans Rademacher, Erhard Schmidt, Issai Schur, and St Jolles (1857-1942); those who taught him physics include Eugen Blasius, Albert Einstein, Max von Laue (1879-1960), and Max Planck; and those who taught him philosophy include Max Dessoir (1867-1947), Alois Riehl (1844-1924), and Eduard Spranger (1882-1963). In addition to his teachers at Berlin and Munich who we have mentioned above, Rothe also lists as his teachers Brentano, Fischer, Fuchs, Grummach, Haarmann, Hammerstein, Henning, Heyn, Hofer, Kükenthal, Külpe, Lagally, H Maier, E Meyer, Reichel, Rieffert, Voss, and Wertheimer. Rothe writes:-

The publication of the paper based on his thesis was not Rothe's first publication. In 1925, in collaboration with Hans Rademacher, he publishedTo all these men, but especially to Prof Dr Bieberbach, Prof Dr von Mises, Prof Dr E Schmidt, Prof Dr I Schur, and my former mathematics teacher Dr Dietrich, I give many thanks.

*Die Differential- und Integralgleichungen der Mechanik und Physik*as Chapter 19 of the first volume of Philipp Frank and Richard von Mises'

*Die Differential- und Integralgleichungen der Mechanik und Physik*. Also in this volume are papers by Constantin Carathéodory, Richard von Mises, Gábor Szegő, Karl Löwner, Ludwig Bieberbach, Hans Rademacher, and Richard Courant.

Now at Berlin, Rothe had met his fellow student of mathematics, physics and philosophy, Hildegard Ille. She had obtained her teaching qualification in 1923 and a doctorate in the following year after studying with Issai Schur. After a year at the Kaiser Wilhelm Institute of Physics, headed by Albert Einstein, she was a student teacher at the Chamisso-School in Berlin-Schöneberg before marrying Rothe in 1928. Rothe had worked at the Institute of Applied Mathematics at the University of Berlin in 1926-27 before being appointed to the Engineering School in Breslau in 1927 and habilitating there in 1928. In addition to his position at the Engineering School, he was appointed as a docent at the University of Breslau in 1931 after a second habilitation there. During his time in these positions in Breslau, Rothe took study leave for a year which he spent at the University of Göttingen. After publishing the paper based on his thesis, Rothe published: *Ein Beitrag zum Cauchysehen Problem* (1928); *Über die Approximation stetiger Funktionen durch Eigenfunktionen elliptischer Differentialgleichungen* (1929); *Zweidimensionale parabolische Randwertaufgaben als Grenzfall eindimensionaler Randwertaufgaben* (1930); *Über die Wärmeleitungsgleichung mit nicht-konstante Koeffizienten im räumlichen Falle* (1931); *Über die Grundlösung bei parabolischen Gleichungen* (1931); *Über lineare elliptische Differentialgleichungen zweiter Ordung, deren zugeordnete Massestimmung von Konstanter Krummung ist* (1931); and *Über eine Verallgemeinerung der Besselschen Funktionen * (1932).

On 15 April 1931, Erich and Hildegard Rothe had a son, Erhard William Rothe, who was born in Breslau. During their years in Breslau both Rothe and his wife reviewed many mathematical papers. We have found around 800 reviews by Rothe and around 170 by his wife.

On 30 January 1933 Adolf Hitler came to power in Germany and on 7 April 1933 clause three of the Civil Service Law provided the means of removing Jewish teachers from the universities, and of course also to remove those of Jewish descent from other roles. All civil servants who were not of Aryan descent (having one grandparent of the Jewish religion made someone non-Aryan) were to be retired, with exemptions for participants in World War I and pre-war officials. Now, as we have seen, Rothe had served in World War I so was exempt but it quickly became clear that the exemption would be ignored. Gábor Szegő was the professor at Königsberg and, like Rothe, was Jewish and had served in World War I. Harald Bohr had persuaded Szegő that he was in great danger, and a position was arranged for him in the United States. While still in Königsberg, Szegő wrote to Richard Brauer who was in Princeton asking him if he could help Rothe emigrate to the United States. Brauer talked to Oswald Veblen who suggested that Rothe might be better trying to emigrate to the Soviet Union. Brauer replied to Szegő in Königsberg [2]:-

Because of his Jewish background, Rothe was dismissed from his positions in 1935. Ignoring the suggestions to go to Russia, he eventually managed to escape with his wife and child and they went to Zurich. Wilfred Kaplan writes [5]:-Veblen judges the possibility of absorbing German mathematicians in America rather pessimistically ... in appointments nationalistic motives play a growing role. Veblen, of course, strongly regrets the latter ... Personally I understand the inhibitions which Rothe has vis-à-vis Russia. But it is difficult about this here. All free-minded people look to Russia with a certain admiration and with much interest. The dangers that may be connected to a life in Russia seem small from a distance.

Later in 1937 Rothe and his family emigrated to the United States. He was appointed as an Instructor in Mathematics at William Penn College, Oskaloosa, Iowa and, as Kaplan writes [5]:-It was in the spring of1937that I first came to know Erich Rothe. I was spending a year in Zurich as a graduate student. I had come to Zurich mainly because of Heinz Hopf, and it was to his friend and former classmate Hopf that Erich Rothe had come as a refugee from Nazi Germany. With him were his wife and child, and all were warmly welcomed by the Hopfs. My first encounter with Rothe was at the Zurcher Kolloquium, where he lectured on his new research on mapping degree and its applications. I was much impressed with the mathematician and the man, for his talent, his warmth, and his modesty.

He worked at William Penn College from 1937 until 1943 but, during these years, tragedy struck when his wife Hildegard Rothe-Ille died from cancer in December 1942. Kaplan recounts how Rothe moved from Iowa to Ann Arbor [5]:-It was a time when academic positions were hard to find, and he considered himself fortunate to have one.

His appointment in 1944 was as an Assistant Professor at the University of Michigan. He was promoted to Associate Professor in 1949, and to Professor in 1955. Details of his contributions to the University of Michigan are given in several sources. We quote first from [6]:-We met again in June of1940at the Topology Conference in Ann Arbor. We became friends, played tennis together, and discussed mathematics and common memories of Switzerland. I knew he was not particularly happy in Iowa and was anxious to move to a rigorous centre of mathematical research. We kept in touch by correspondence; I learned of his tragic loss of his young wife. When an opening appeared at the University of Michigan, where I was then instructor, I told our chairman(Hildebrandt)of him and his interest in such a position. In1944Rothe came to Ann Arbor to begin a long period of brilliant service to the University of Michigan as teacher and scholar.

His colleague at the University of Michigan, Wilfred Kaplan, writes in [5]:-His mathematical talents were versatile and his interests broad. His gift for exposition equalling his power of analysis, he was a persuasive teacher as well as a creative mathematician. Combining a secure grounding in pure mathematics with a highly sophisticated knowledge of applications, he exerted a strong influence on students in both mathematics and mathematical physics. As chairman of the departmental doctoral committee, he contributed significantly to the formal organization of advanced mathematical study. Among his peers, he was respected for his many tangible accomplishments and for an elegance and style of mind that helped to set the intellectual tone of the Department.

In 1964, having reached the age of 69, Rothe retired from his professorship at the University of Michigan. However, he taught in 1967-68 at the Western Michigan University in Kalamazoo. Retirement certainly did not mean that Rothe stopped undertaking research into mathematics.Rothe brought something very special to mathematical life in Ann Arbor. His unusual depth of understanding of topology, its applications to analysis, and of mathematical physics(he was a contributor to the second edition of the famous text of Frank and von Mises)gave a new breadth to the atmosphere in courses and seminars. He was called on for advice and leadership in fields across the whole spectrum of pure mathematics and in physics. He helped to guide many brilliant students to the Ph.D., His contributions to mathematical research reflect his great breadth: differential and integral equations, linear and nonlinear functional analysis, topology, calculus of variations. If one seeks a guiding thread through his many papers, it is perhaps the extension to general spaces of the ideas of elementary calculus, in order to answer basic questions arising in partial differential equations and integral equations. Through his papers, his lectures, and his work with graduate students he has made a profound impression in the areas of his work.

Rothe continued to publish research papers; we have seen at least 14 papers published after his retirement. In 1978 the book [1] was published containing a collection of papers in Rothe's honour. Perhaps, most remarkably, in 1986 at the age of 91 he published the 242-page book *Introduction to various aspects of degree theory in Banach spaces* which was published by the American Mathematical Society. Christian Fenske writes in a review:-

Following Rothe's death in 1988, Donald John Lewis (1926-2015), then the Chair of Mathematics at the University of Michigan and known as D.J., wrote:-This is a highly detailed introduction to degree theory of compact maps in Banach spaces, written by one of the pioneers of the field. The author concentrates on the analytic approach to degree theory and restricts the discussion to Banach spaces. Of course, much more could be said about degree theory, but the author leaves the reader in no doubt about his choice of topics: at the very beginning he gives a list of subjects not treated in this monograph. ... Most of the text deals with degree theory in finite dimensions. ... The text should be easily accessible to everyone with a moderate background in functional analysis(including some spectral theory up to the Dunford integral). The proofs are unusually detailed and technical arguments are in most cases delegated to notes complementing the chapters. For beginners or non-specialists this is perhaps the best introductory text on degree theory.

Rothe was a scholar of the old school. He was very broadly educated ... He was a wise and judicious man of much wit. His companionship was very much in demand.

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