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C H A P T E R S E V E N Ludwig Bieberbach and “Deutsche Mathematik” THE figure of Ludwig Bieberbach has already appeared frequently in the preceding pages.1 He was a mathematician of high repute who, in 1915, when he was twenty-eight, was described by Georg Frobenius, one of the leading figures of the preceding generation of mathematicians as someone who attacked with his unusual mathematical acuity always the deepest and most difficult problems , and might be the most sharp-witted and penetrating thinker of his generation .2 He was also, among mathematicians, a leading proponent of Nazi ideology . Yet, somewhat earlier, he had had a reputation as an academic who was politically of a relatively liberal cast, and during and after the First World War was a member of the faculty of one of the reputedly “politically more liberal” universities (and one with a high percentage of Jewish faculty). Ludwig Bieberbach was born on December 4, 1886, in Goddelau, a town near Frankfurt-am-Main. In secondary school he was already interested in mathematics, being particularly influenced by a teacher who “knew how to lecture very interestingly on his topics.”3 In 1905 in military service in Heidelberg , on the side he heard lectures by Leo Königsberger, “a completely excellent teacher,” then near the end of a long career. He reviewed the lecture announcements of the various universities as published in the JDMV and noticed that Hermann Minkowski had announced lectures on invariant theory.4 Unaware of Göttingen’s general mathematical reputation, but having progressed far enough in his studies to be able to listen to Minkowski, whose announcement sounded attractive, he decided to attend. Arriving in Göttingen, he became “fascinated” with Felix Klein—the way he lectured and the way he interested students in mathematical matters. Already prepared by material he had heard from Königsberger , he listened to Klein’s lectures on elliptic functions. Bieberbach had been attracted to Göttingen by his interest in algebra, and Minkowski’s announcement ; however, Klein influenced him in an analytic direction. Four years older than Bieberbach, and already “habilitated” in 1907 at Göttingen, was Paul 1 The title of this chapter is also the title of an article by Herbert Mehrtens (Mehrtens 1987). 2 See Edgar Bonjour, Die Universität Basel von den Anfängen bis zur Gegenwart, 1460–1960 (1960), 753–754. The writer was F. G. Frobenius on February 6, 1913 (ibid.: 765 n. 112). Bieberbach was succeeded by Erich Hecke, again with Frobenius’s recommendation (ibid.: 754 and 765 n. 116). 3 On September 21, 1981, Bieberbach (then nearly ninety-five) was interviewed by Herbert Mehrtens. The interview was tape-recorded and partially transcribed. I have a copy of that partial transcription thanks to Prof. Mehrtens. This memory, including the direct quote, comes from that interview, hereafter cited as BI. 4 BI. Invariant theory was one of the most actively pursued research areas of the day. While its death was once presumed as a result of new interpretations of its problems, and even analyzed by historians of science (see above, chapter 2), it has apparently been reborn in recent years. L U D W I G B I E B E R B A C H 335 Koebe. Koebe would become famous as an analyst who did fundamental work in complex function theory, and infamous as one who was vain and whose papers were not models of clear exposition. The young Koebe also influenced Bieberbach’s interest in analysis. In his own words, Bieberbach had, “so to speak, two souls in one breast”:5 Klein’s automorphic functions on one side and more algebraic things on the other. Bieberbach satisfied the first side by writing a dissertation under Klein on automorphic functions. Ernst Zermelo had been a “habilitated” Privatdozent rather longer than usual at Göttingen, and was chosen as Erhard Schmidt’s successor in Zürich, when Schmidt left for Erlangen in 1910. Zermelo wanted some new doctorand to go with him, and he chose Bieberbach. In 1910 also Bieberbach announced a result from his “algebraic soul” that would initially make him famous. In 1900 David Hilbert had given a well-known lecture in Paris in which he mentioned twentythree mathematical problems that he thought important for the future. Some of the problems had several parts, and some were not precisely formulated, but by and large they have indeed indicated the directions of...


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