Mathematics in Nazi Germany

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Mathematics in Nazi Germany was governed by racist Nazi policies like the Civil Service Law of 1933, which led to the dismissal of many Jewish mathematics professors and lecturers at German universities. During this time many Jewish mathematicians left Germany and took positions at American universities. Jews had faced discrimination in academic institutions before 1933, yet before the Nazi rise to power, some Jewish mathematicians like Hermann Minkowski and Edmund Landau had achieved success and even been appointed to full professorships with the support of David Hilbert at the University of Göttingen.

University of Göttingen

Göttingen was, along with Berlin, one of Germany's two main centers for mathematical research.[1] Prior to Nazi rule, the University of Göttingen already had an illustrious mathematics tradition that included distinguished mathematicians like Gauss, Riemann, David Hilbert, Dirichlet, Hermann Minkowski and Felix Klein.[2]

Abraham Fraenkel has written that Hilbert was "the most significant mathematician in the world" during those years. Fraenkel writes that Hilbert "always remained free of all national and racist prejudices" and had been influenced by two Jewish mathematicians, Adolf Hurwitz and Minkowski. Though prejudice against appointing Jews to academic positions existed before the Nazi era, Hilbert had supported the successful appointments of two Jewish mathematicians to full professorships: Minkowski in 1902 and Edmund Landau in 1909.[3] Like Hilbert himself, Minkowski had first been appointed by Felix Klein.[1] When Klein retired, Hilbert appointed the German Jewish mathematician Richard Courant to replace him. (Courant moved to New York University in 1933 where the Courant Institute of Mathematical Sciences is named after him). Hilbert also supported Emmy Noether, a Jewish woman whose postdoctoral candidacy had been opposed, mostly on account of her gender, even by Jews.[3]

In the 1920s, Hilbert became involved in a dispute with L.E.J. Brouwer, a Dutch mathematician whose support for intuitionism had not been widely accepted by Germany's mathematical establishment.[3] Intuition (Anschauung) was contrasted with "modern abstract" mathematics like formalism.[1] There was a rivalry in those years between Berlin and Göttingen, and Berlin sided with Brouwer against Hilbert in the dispute.[4] The dispute took on an ideological dimension as Brouwer presented himself as a "champion of Aryan Germanness". When Brouwer objected to Ostjuden (German Jews of Eastern European descent) writing for the journal Mathematische Annalen, Hilbert removed Brouwer from his position as editor. The Nazis offered Brouwer a position at the University of Berlin in 1933, which he declined. Even so, the Dutch government suspended Brouwer in 1945 because of his connections to the Party; he was, however, eventually reinstated.[3]

Though Jewish academics had experienced prejudice prior to 1933, Hilbert had been supportive of Jewish mathematicians and supported their advancement. When the Civil Service Law of 1933 mandated the dismissal of Jews from the civil service, including university professors and Privatdozent, Landau and Courant were still teaching.[5] Hermann Weyl, who had succeeded Hilbert in 1931, and Gustav Herglotz were not of Jewish descent. Weyl, whose wife was Jewish, chose to accept a position at the Institute for Advanced Study in Princeton in the United States.[6] Other lower ranking professors and lecturers included Paul Bernays, Emmy Noether, Hans Lewy, Otto Neugebauer, Herbert Busemann, Werner Fenchel, Franz Rellich, and Wilhelm Magnus.[7]

Paul Bernays was among the scholars who had to leave their positions at Göttingen in 1933. Together with Hilbert, Bernays had co-authored a seminal text on mathematical logic called Grundlagen der Mathematik. The collaboration on the second volume of that work, published in 1939, continued even after 1933; face to face collaboration ceased sometime in 1934 when Bernays moved to Zürich.[8] Otto Blumenthal, who had converted to Protestantism when he was 18, lost his position at RWTH Aachen University.[9]

NSDAP

In the mid-1930s, racist Nazi policies that limited the participation of Jewish mathematicians were imposed on the German mathematics journal Zentralblatt für Mathematik. Ivan Niven identified this as a turning point for the journal saying it began to "deteriorate". Otto Neugebauer, who had been a key figure in founding Zentralblatt, had moved to the United States and taken a position at Brown University. With his expertise a new reviewing journal, Mathematical Reviews, was established in the United States.[10] During the years of Nazi rule, many classes in German universities would begin with a Nazi salute, a practice that Erich Hecke declined to implement in his classroom.[11]

Even before Hitler's rise to power, some mathematicians had already emigrated to the United States for various reasons. John von Neumann had taken a position at the California Institute of Technology in 1929 because he felt anti-semitism in Germany was affecting his career. By 1933, von Neumann had a position at Princeton; though he had maintained ties with Germany until then, he canceled his scheduled lectures in Berlin after Hitler became Chancellor. Other early emigrants from Germany included Theodor Estermann, Hans Freudenthal, Eberhard Hopf, Heinz Hopf, Herman Müntz, Wilhelm Meyer and Abraham Plessner.[12] Some emigrated to the United States, others to European countries; Heinz Hopf spent the years of Nazi rule in Zürich, Switzerland.[13] Hans Rademacher obtained a position at the University of Pennsylvania after he was dismissed from the University of Breslau by the Nazis.[14]

In 1933, when Hitler came to power, the following topologists held positions in German universities: Max Dehn, Herbert Seifert, Hans Freudenthal, Hellmuth Kneser, Georg Feigl, Kurt Reidemeister, William Threlfall, Heinrich Tietze, Hermann Künneth, Leopold Vietoris and Felix Hausdorff.[13]

Deutsche Mathematik

The journal Deutsche Mathematik, published between 1936-1943, was edited by Theodor Vahlen and Ludwig Bieberbach. Bieberbach was a distinguished mathematician who first taught in Königsberg in 1910, moving to Basel in 1913 and Berlin in 1921; Ferdinand Georg Frobenius called him "the most insightful and penetrating mathematician of his generation".[15] Though Bieberbach had himself espoused formalistic ideas in the early years of his career, by the 1920s he had become critical of Hilbert's formalism.[1] In later years, during Nazi rule, Bieberbach became a strong supporter of the "Aryanization" of mathematics. Nazi ideology about mathematics had determined that "Aryan mathematics" would emphasize geometric math and probability theory. Abstract axiomatics were denounced as "Franco-Jewish". Felix Klein, who had already passed away, became an unwilling paragon of Aryan math. David Hilbert and Richard Dedekind were also accepted even though their work did not actually fit the Aryan mold. Bieberbach, for his part, condemned Cantorian set theory and measure theory as un-Germanic. Even abstract algebra was suspect.[13]

Vahlen had studied under Frobenius and written his dissertation on additive number theory. He had been published in mathematical journals like Crelle's Journal and Acta Mathematica. Vahlen's mathematical interests included partition theory, non-Euclidean geometry and differential equations. His published works on applied mathematics included papers on ballistics, aerodynamics, the magnetic compass and celestial mechanics. By 1911 Vahlen was teaching in Greifswald. Between 1914 and 1915 he served on the Western Front of World War I. He was wounded during his service on the Eastern Front (1916-1919) and left the army a decorated, high-ranking officer. He joined the Nazi Party after the failed Beer Hall Putsch and visited Hitler at Landsburg prison in 1924. He lost his teaching position after taking down the Weimar flag at the University of Greifswald. After living in Vienna for a time, Vahlen returned to Germany only after Hitler became Chancellor in 1933. Bernhard Rust had become the Reich education minister and supported Vahlen's return.[15]

Notes

  1. ^ a b c d Dalen 2013, p. 496.
  2. ^ Lane 1995, p. 1134.
  3. ^ a b c d Fraenkel 2017.
  4. ^ Dalen 2013, p. 497.
  5. ^ Lane 1995, p. 1136.
  6. ^ Dalen 2013, p. 620.
  7. ^ Lane 1995, pp. 1134–1135.
  8. ^ Parsons 2009, pp. 129–150.
  9. ^ Holfter 2015, p. 124.
  10. ^ Krantz, Steven G. (2002-09-12). "Utter Sagacity". Mathematical Apocrypha: Stories and Anecdotes of Mathematicians and the Mathematical. MAA. pp. 89–115. ISBN 978-0-88385-539-3.
  11. ^ Krantz, Steven G. (2002-09-12). "Utter Seriousness". Mathematical Apocrypha: Stories and Anecdotes of Mathematicians and the Mathematical. MAA. pp. 145–182. ISBN 978-0-88385-539-3.
  12. ^ Siegmund-Schultze, Reinhard (2009). "1. The Terms "German-speaking Mathematician," "Forced," and "Voluntary Emigration"". Mathematicians Fleeing from Nazi Germany: Individual Fates and Global Impact. Princeton University Press. pp. 1–12. ISBN 978-0-691-12593-0.
  13. ^ a b c James, I. M. (1999-08-24). "30. Topologists in Hitler's Germany". History of Topology. Elsevier. pp. 849–861. ISBN 978-0-08-053407-7.
  14. ^ Krantz, Steven G. (2002-09-12). "Utter Sanguinuity". Mathematical Apocrypha: Stories and Anecdotes of Mathematicians and the Mathematical. MAA. pp. 116–144. ISBN 978-0-88385-539-3.
  15. ^ a b Segal 1986, pp. 118–135.

References

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