Bessel-Hagen attended the University of Berlin where he obtained a doctorate working under Constantin Carathéodory, with some help from Erhard Schmidt. He submitted his thesis on the calculus of variations Über eine Art singulärer Punkte der einfachen Variationsproblerme in der Ebene and was awarded the degree in 1920. Segal writes :-
Carathéodory thought Bessel-Hagen's disertation the first important advance in the theory of discontinuous solutions for problems in the calculus of variations since his own work in 1905. While at Berlin, however, Bessel-Hagen had also heard lectures from the famous classicist, Ulrich von Wilamowitz-Möllendorf, and was inspired by him to a life-long devotion to classical antiquity as well. He not only had a wide-ranging knowledge of various areas of mathematics, but also was well versed in classical Greek, Greek philosophy, and the history of Greek mathematics.
At Berlin, Bessel-Hagen met his fellow student Carl Siegel and the two became life-long friends. We shall say more of this friendship below. After graduating with his doctorate, Bessel-Hagen was appointed to Göttingen University. Dauben and Scriba write :-
Bessel-Hagen spent seven years in Göttingen where he met, among others, Otto Neugebauer .... Felix Klein had an exceptionally strong influence on him, for not only did Bessel-Hagen live in Klein's house, but he was Klein's private assistant from 1921 to 1923.During this period he published Über die Erhaltungssätze der Elektrodynamik (1921). Also, in collaboration with Neugebauer and Courant, he helped prepare Klein's lectures on the development of mathematics in the 19th century for publication. These appeared in 1926, a year after Klein's death, under the title Volesungen über fie Entwicklung der Mathematik im 19. Jahrhundert . Bessel-Hagen was one of a small number who had attended these lectures delivered in Klein's home.
The authors of  tell of the friendship between Carl Siegel and Bessel-Hagen during these seven years at Göttingen while Bessel-Hagen was working on his habilitation:-
Carl Siegel was joined in Göttingen by Schaffeld, Erich Bessel-Hagen and Maria (Siegel's girlfriend from Berlin). Braun says that Siegel and Bessel-Hagen first met as students in Berlin. Bessel-Hagen revered Siegel for his mathematical ability, and Siegel in turn was gratified to be admired by someone he could accept. They were friends all their lives, until Bessel-Hagen's early death in 1946. Bessel-Hagen walked with a slight limp - Braun thought because of polio. Schaffeld, Siegel, and Bessel-Hagen were united in their attitude towards marriage. Braun writes, "I do not know which of the three was more decided against ever marrying, but all three remained bachelors, expressing their views on marriage with varying degrees of theatricality." Schaffeld and Bessel-Hagen filled very different roles for Siegel. In later years Siegel would drop everything if Schaffeld appeared to go for a walk or go out to a restaurant. ... In contrast, Siegel couldn't resist baiting or playing sometimes cruel and humiliating practical jokes on Bessel-Hagen. He would then repent and do something to make it up to him. ...In 1927 Bessel-Hagen was appointed to a position at the University of Halle where he assisted Helmut Hasse. He then moved to the University of Bonn :-
Siegel had to review Bessel-Hagen's thesis for habilitation - perhaps as a friend, perhaps in some official capacity. However, it came to him at a time when he was deeply involved in his own research, and Bessel-Hagen's thesis was in a different area. Siegel felt burdened, and the longer he neglected the task the more burdened he felt. During this time he was required to travel somewhere by ship. At some point on the voyage Siegel's feelings overwhelmed him. Though he knew he was in possession of the only copy of the thesis, Siegel threw it overboard ... making due note of the coordinates. When he came home ... he told Bessel-Hagen he had done him a favour. It required months of work to reproduce the thesis, and eventually Siegel started feeling bad about what he had done. To make up, he invited Bessel-Hagen on a long vacation to Greece. Braun writes, "This journey made both of them very happy."
At Toeplitz's instigation, a salaried Lehrauftrag for "Mathematics with special consideration of its history and pedagogy" was established in Bonn and given to Erich Bessel-Hagen for the winter term 1928-29. ... Bessel-Hagen also played a major role in establishing the historical division, including an important library, as part of the mathematical seminar in Bonn. ... Bessel-Hagen was also involved in editing the works of Gauss. He had particularly close contacts with Otto Neugebauer, founder in 1931 of the Zentralblatt für Mathematik ... Bessel-Hagen wrote more than 200 reviews for Neugebauer's Zentralblatt.Béla Kerékjártó visited the University of Göttingen in 1922 and attended lectres by Bessel-Hagen. In the following year Kerékjártó published Vorlesungen über Topologie the index of which contains a reference to Bessel-Hagen. Turning to the indicated page, there is no mention of Bessel-Hagen. However, there is a diagram of a torus with large handles attached on the sides looking a bit like a face with oversized ears. In fact Bessel-Hagen was renowned for having large ears that stuck out of his head. At first this appears to be a rather cruel joke, but in fact Kerékjártó was merely following the teaching staff at Göttingen who all made jokes at Bessel-Hagen's expense. His friend Carl Siegel certainly played 'cruel and humiliating practical jokes' on him as we indicated above. Segal writes :-
Bessel-Hagen seems to have been a somewhat retiring personality who suffered from a severe constitutional illness; photographs show a face accentuated by large glasses. Certainly he was the butt of jokes among his colleagues; ... this author can recall, as a graduate student in the 1960s, hearing his name used as the object of mathematical jokes [20 years after his death!].This behaviour on the part of Bessel-Hagen's colleagues seems all the more cruel given Bessel-Hagen's nature :-
Bessel-Hagen, who was a devout Roman Catholic, in fact seems to have been one of the most honourable and honest of men. He seems to have represented the best sort of "inner emigration" during the Nazi period. After the great German and Jewish (but unreligious) mathematician Felix Hausdorff was retired ... in 1935, Bessel-Hagen seems to have been the only one of his former colleagues to visit him. In the Bonn catalogue of professors issued in 1968, [Bessel-Hagen] is described with unusual feeling as having been a "model of the noblest humanity. Unselfish goodness and purity of desire paired in him with an incorruptible love of truth and faithful friendship.In fact Bessel-Hagen was an excellent mathematician who, because of his shyness, did not publish much. This meant that his career was not nearly as successful as it might have been.
World War II was a difficult time for Bessel-Hagen. Although his illness meant that he was excused active service, nevertheless he had been forced to be an air-raid warden. Most of the other mathematicians at Bonn were conscripted so only Bessel-Hagen and Hans Beck remained to teach. This said, of course, most students were also conscripted so they did not have large numbers to teach. After Beck died in 1942, Bessel-Hagen essentially became a one-man department. Teaching materials were hard to come by, for example Bessel-Hagen even had to write to the Rektor of the university requesting writing paper in July 1941. He was asked to send copies of his work to soldiers on the front, but declined saying that he had not written anything that soldiers would find interesting. However, he did contribute to a little book about the University of Bonn which was specifically written to send to soldiers on the front.
Article by: J J O'Connor and E F Robertson