**Karl Dörge**'s father, Friedrich Wilhelm Karl Dörge, was a pastor in Müllerdorf which is close to Halle. Friedrich Dörge was born in Eickendorf near Haldensleben on 16 May 1864. Friedrich's father was a landowner known locally as a "Halbspänner" meaning he was a small farmer, owning between 12 to 24 hectares, and he had to provide, along with other farmers, a complete team for their larger landlords. Friedrich attended real gymnasium in Halberstadt, the gymnasium in Mühlhausen, and the University of Halle from 1886 to 1889. He was ordained on 13 February 1895, then became a pastor in Müllerdorf. On 11 March 1895, in Bornstedt in the Mansfelder Land district, he married the daughter of a mining officer. Karl spent the first five years of his life in Müllerdorf.

In 1905 the family moved to Seyda, a village in the district of Wittenberg, where again Dörge's father Friedrich was the local pastor. Friedrich had been successful in the selection process run by the Seyda Churches. There were many applicants for the position and selection followed the usual procedure of giving a trial sermon and being interviewed. Because of his upbringing on a farm, it was assumed that the new rector would be familiar with living conditions in Seyda, as his wife would be in the Mansfelder Land region.

Until he was thirteen years old, Karl was educated by private tutors. His own father, in his position as a pastor, ran a school and played a role in the education of his own son. From his father, Karl learnt religion, mathematics, history and German. When World War I began in July 1914, Dörge was fourteen years old and attending school. Because of the war, Germany introduced a new qualification, the Notabitur (an emergency Abitur), for boys studying at a Gymnasium who voluntarily enlisted for military service before graduation. Dörge followed this route, enlisted for the army and he passed the Notabitur in Torgau in 1915. Torgau is a town on the banks of the Elbe in northwestern Saxony about 45 km south of the village of Seyda. Dörge served in the army for the duration of World War I, reaching the rank of Lieutenant and being awarded the Iron Cross I and II Class for bravery. Throughout the hard war years his father continued to support the Seyda community as their pastor.

In 1919, now nearly twenty years old, Dörge was able to continue his education which had been disrupted by the war. In that year he entered the Friedrich-Wilhelm University in Berlin. Today this university is known as the Humboldt University. He studied mathematics attending courses by leading mathematicians such as Issai Schur, Richard von Mises, Erhard Schmidt and Ludwig Bieberbach. He also studied physics and took courses by Albert Einstein, Max Planck and Heinrich Rubens (1865-1922). He continued to study for his doctorate advised by Issai Schur and he was awarded the degree in 1925 for his 15-page dissertation *Über die ganzen rationalen Lösungspaare von algebraischen Gleichungen in zwei Variablen* . He corresponded with David Hilbert, for example writing a letter to him in 1925, and also with Emmy Noether. Dörge's years of study at university had been difficult one since Germany went through a period of hyperinflation which made life close to impossible. In particular towards the end of 1923 Germany suffered a total economic collapse.

Dörge habilitated at the University of Cologne in 1926. He published several papers in 1925-27, namely: *Zum Hilbertschen Irreduzibilitätssatz* ; *Über die seltenheit der reduziblen Polynome und der Normalgleichungen* ; *Ein Beitrag zur Theorie der diophantischen Gleichungen mit zwei unbekannten * (a polished version of his thesis); and *Einfacher Beweis des Hilbertschen Irreduzibilitätssatzes* . His father, who had continued to support his parishioners throughout the years of crippling hyperinflation, retired as pastor at Seyda in 1926 but he did not stop work for he continued to manage the parishes of Wolteritz and Hayna. In 1932 Dörge was promoted to extraordinary professor at the University of Cologne. He had published four papers in 1930, namely *Zur Verteilung der quadratischen Reste* , *Bemerkung zum Hilbertschen Irreduzibilitätssatz* , *Über die Reduzibilität von Polynomen im Körper der reellen Zahlen* , and *Zu der von R von Mises gegebenen Begründung der Wahrscheinlichkeitsrechnung. Erste Mitteilung: Theorie des Glücksspiels* .

On 30 January 1933 Hitler came to power and on 7 April 1933 the Civil Service Law provided the means of removing Jewish teachers from the universities, and of course removing those of Jewish descent from other roles. This did not directly affect Dörge but, of course, the large impact on mathematics throughout Germany had an indirect impact on everyone. Felix Hausdorff was forced to retire from his chair in Bonn by the Nazi regime in 1935. (He committed suicide on 26 January 1942 when it was clear he was about to be sent to a concentration camp.) On 26 February 1936 the University of Bonn submitted the following names for the Hausdorff succession to the Ministry of Education: Ernst Kähler, Konrad Knopp and Karl Dörge. By this time, however, the Ministry of Education was more interested in how enthusiastic the candidates were for the Nazi policies rather than their mathematical expertise. As a consequence the Ministry of Education rejected all three names and none of the three was appointed. Dörge remained in Cologne and, perhaps as a consequence of being recommended for a full chair in Bonn, he was appointed to a full chair at Cologne later in 1936.

Dörge continued working on algebra and number theory. On 9 June 1935 he wrote to Otto Toeplitz reporting on his own results for estimating the number of primes below 2^{n}. In the same letter he reports on other results on the same problem and compares his own results with those of other mathematicians. He published *Zu der von R von Mises gegebenen Begründung der Wahrscheinlichkeitsrechnung *(*zweite Mitteilung: Allgemeine Wahrscheinlichkeitstheorie*) in 1936. It was in that year that he was made director of Mathematical Seminars at Cologne.

In 1938 Dörge's father, by this time 74 years old, came to live with his son at his home in Lindenthal on the west side of Cologne. Friedrich Dörge spent the last five years of his life living with his son and died on 28 May 1943.

Dörge published a number of books. He published *Über den Fundamentalsatz der Algebra* in 1928. The first edition of *Wahrscheinlichkeitsrechnung für Nichtmathematiker* , co-authored with Hans Klein, was published in 1939 and the second edition, after World War II, in 1947. He also published the first volume of *Differential- und Integralrechnung* in 1948. This volume was subtitled *Elemente der Differential- und Integralrechnung einer Veränderlichen, unendliche Folgen und Reihen mit konstanten Gliedern* .

Klaus Wagner (31 March 1910 - 6 February 2000) was Dörge's most famous student. He received his Ph.D. from the University of Cologne in 1937 advised by Dörge, and taught at Cologne for many years becoming head of the Cologne graph theory school. In 1970, he moved to the University of Duisburg, where he remained until his retirement in 1978.

Later in his career Dörge studied universal algebra. For example in *Bemerkung über Elimination in beliebigen Mengen mit Operationen* (1951/52) he studied infinitary operations. Also in (with Heinz Adolf Jung) *Abschliessungen in Klassen strukturierter Mengen* (1970) the authors find various conditions for existence and uniqueness of algebraic closures in a given class of structures. However, he continued to study topics that had interested him throughout his career. For example he published (with Heinz Adolf Jung) *Über die Seltenheit der reduziblen Polynome* (1968) which referenced his earlier papers *Über die Seltenheit der reduziblen Polynome und der Normalgleichungen* (1925), *Einfacher Beweis des Hilbertschen Irreduzibilitätssatzes* (1926), *Bemerkung zum Hilbertschen Irreduzibilitätssatz* (1929), and *Abschätzung der Anzahl der reduziblen Polynome* (1965).

We should add one further fact about Dörge, namely his passion for art. He collected both classical art as well as works of contemporary artists. The most notable painting that he owned was a superb copy of Annibale Carracci's *The mystic marriage of Saint Catherine* (1585-1587). Dörge's copy was made in 1600 while the original now hangs in the Museo Nazionale di Capodimonte in Naples. His favourite contemporary artist was Joan Miró i Ferrà (1893-1983) who was born in Barcelona. Miró declared that he wanted to assassinate painting by upsetting the visual elements of established painting.

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