German mathematics

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Cover of the first issue (Jan. 20, 1936)
Students, in front , p. 5 from vol. 1, no. 1

The German mathematics was the attempt of the mathematician Ludwig Bieberbach in the Third Reich to put mathematics back on a clearly understood basis. Modern mathematics was most recently rejected as "Jewish". Deutsche Mathematik is also the title of a journal founded by Ludwig Bieberbach in 1936 and edited with Theodor Vahlen , which was published every two months up to and including 1941.

As with the phenomenon of German physics , a fundamental upheaval took place in basic mathematical research around 1900 that split mathematicians into supporters and opponents. Structural thinking prevailed, as did the axiomatic penetration of algebraic basic structures with terms such as “ body ”, “ group ” or “ ideal ”, the content of which defies concrete perception. With set theory , modern mathematics gained a formal, non-perceptual basis that prevailed between the world wars.

Ludwig Bieberbach rejected formalistic mathematics and in 1934 developed an anti-Semitic “type theory” based on the integration typology of the Marburg psychologist Erich Rudolf Jaensch . It deals with intellectual character types such as the unstable, weak and unstable "counter-type" or "S-type", which shows a tendency to confuse symbolic connections with real connections. In contrast, he stated an “ Aryan ” “J-type” whose strength is his will, character, deed and whose expressions of life come “from the depths”. With this, Bieberbach took up the " intuitionism dispute ". As early as 1926 in a lecture in Berlin, Bieberbach acknowledged the intuitionism of Brouwer and Weyl. According to Bieberbach, they represented the geometrically graphic foundations of mathematics (although he saw Felix Klein as a romantic forerunner of the direction, a representative of the descriptive direction connected with applications), the formalists, on the other hand, emphasized structural thinking and axiomatics, whereby intuition does not represent the formal system may influence. In his 1926 lecture he saw this only as a transition stage for a new mathematics to be built up on a clear basis. According to Bieberbach, the catastrophic consequences of the formalistic school would be to avert specific real problems in the applications. In particular, he also criticized - although he taught in Berlin - the main representatives of the old Berlin math school Karl Weierstrass and his pupil Hermann Amandus Schwarz , whom he accused of pedantry and excessive severity. In the "German Mathematics" the formalists were pushed into the negative S-type after Bieberbach. As a platform for his theses, Bieberbach founded the journal “Deutsche Mathematik” in 1936, which he headed as editor until the last issue in June 1944. Co-editor was the mathematician Theodor Vahlen (1869-1945), who tried to describe mathematics as a "mirror of the races".

Bieberbach, who, in his own opinion, represented the intuitionist view of "German mathematics", formulated accordingly:

"The racial affiliation expresses itself in the intellectual field in the style of creation and in the evaluation of the results and, I believe, in the attitude to the basic questions."

Bieberbach opposed the “ formalism that wants to establish an absolute realm of mathematical truths independently of human peculiarities” with “intuitionism” in his interpretation, “which assumes that mathematical thinking is a human activity and is therefore not detached from humans and their peculiarities can be".

Regularly published in the journal "Deutsche Mathematik" and a. the mathematicians Fritz Kubach , Erich Schönhardt , Werner Weber , Oswald Teichmüller (all vol.), Ernst August Weiß (vol. 1–6), Karl Dörge , Wilhelm Süss (vol. 1–5), Günther Schulz , Erhard Tornier ( Vol. 1-4), Georg Feigl , Gerhard Kowalewski (Vol. 2–6), Maximilian Krafft , Willi Rinow , Otfried Mittmann , Max Zacharias (Vol. 2–5).

Jaensch and Bieberbach differentiated between different "J types", between artistic (e.g. Felix Klein ), scientific ( Carl Friedrich Gauß , Johannes Kepler ) and soldier types ( David Hilbert , Karl Weierstrass ). Representatives of the abstract French school were named among the “S types” ( Augustin Louis Cauchy , Henri Poincaré ).

There are several causes for the seemingly occult phenomenon of German mathematics . After the collapse of the German Empire, the old intellectual elites turned against the modern in almost all areas of the basic sciences, with which formalistic mathematics was also connected. In the 1920s, new job profiles of insurance and business mathematicians emerged, which pushed mathematics into the background as a basic discipline. In the 1930s, the low birth rate from the First World War and the expulsion of Jewish scientists caused the number of students to collapse, and mathematics as a basic discipline was threatened.

Bieberbach used his anti-Semitic type theory under National Socialism to give the intuitionistic mathematics he represented more weight in a disciplinary way and to promote mathematics as a basic discipline in terms of scientific organization. A typical argument, for example, aimed at the pedagogical value for the "national whole":

“But what is far more important is the educational value that follows from mathematics' spiritual connection with the Third Reich. The basic attitude of both is the heroic. [...] Both demand service: mathematics the service of truth, sincerity, accuracy. [...] Both are anti-materialistic. [...] Both want order, discipline, both fight chaos, arbitrariness. "

The high point of the discussion about German mathematics was reached in 1938, it ultimately achieved no scientific significance and, like German physics, is located in the area of ​​tension between politics and science.

Mathematics was also affected by the synchronization in the Third Reich: a third of the scientific intelligentsia of the universities had to leave their positions. The Göttingen mathematician David Hilbert replied to an anecdote when asked by the Minister of Science Bernhard Rust whether the mathematical institute in Göttingen really suffered as a result of the synchronization (which led to the momentous forced emigration of Jewish professors):

"Jelitten? Dat did not suffer, Minister. There's more to it than that! "

The ideological influence of the magazine was assessed as follows in a situation report of the SD in the summer of 1939:

"In mathematics, however, one gradually begins to recognize the species-specific way of working of the mathematician, to which the journal 'Deutsche Mathematik', published with the support of the German Research Foundation , has made a significant contribution."

Main representative

literature

  • Paul Forman : Weimar Culture, Causality, and Quantum Theory, 1918–1927: Adaptation by German Physicists and Mathematicians to a Hostile Intellectual Environment. In: Historical Studies in the Physical Sciences. 3, 1971, pp. 1-115.
  • Abraham Fraenkel : Circles of Life. From the memories of a Jewish mathematician. German publishing house, Stuttgart 1967.
  • Georg Hamel : Mathematics in the Third Reich. In: teaching sheets for mathematics and science. 39, 1933, pp. 306-309.
  • Fritz Kubach : Students in the Front! In: German Mathematics. 1, 1936, pp. 5 , 6,7 , 8 .
  • Helmut Lindner: “German” and “counter-typical” mathematics. To justify a "native" mathematics in the "Third Reich" by Ludwig Bieberbach. In: Herbert Mehrtens & Steffen Richter (eds.): Natural science, technology and Nazi ideology. Contributions to the history of science in the Third Reich. Suhrkamp, ​​Frankfurt 1980, ISBN 3-518-07903-4 , pp. 88-115.
  • Herbert Mehrtens : Felix Hausdorff. A mathematician of his time. Student Council Mathematics at the University of Bonn, 1980.
  • ders .: Applied mathematics and applications of mathematics in National Socialist Germany. In: History and Society . 12th volume, H. 3, 1986, pp. 317-347.
  • Eckart Menzler-Trott : Gentzen's Problem. Mathematical Logic in National Socialist Germany. Birkhäuser, Basel / Boston / Berlin 2001, ISBN 3-7643-6574-9 .
  • Sanford Segal: Mathematicians under the Nazis. Princeton University Press, 2003.
  • Reinhard Siegmund-Schultze: Theodor Vahlen - on the part of the guilt of a German mathematician in the fascist abuse of science. In: NTM . Vol. 21, H. 1, 1984, pp. 17-32.
  • Volker Peckhaus: The National Socialist “new concept” of science using the example of “German Mathematics” - program, conception and political realization . August 1984 ( online [PDF] diploma thesis, RWTH Aachen).
Commons : Deutsche Mathematik  - Collection of images, videos and audio files

Individual evidence

  1. ^ Segal, Mathematicians under the Nazis , p. 345 f.
  2. ^ Styles of mathematical creation , Ludwig Bieberbach, p. 357.
  3. ↑ Contents .
  4. ^ Ludwig Bieberbach: styles of mathematical creation . In: Meeting reports of the Prussian Academy of Sciences , physical-mathematical class . Verlag der Akademie der Wissenschaften in commission from Walter de Gruyter & Co., 1934, p. 358-359 . Quoted from: Léon Poliakov and Josef Wulf (eds.): The Third Reich and its thinkers - documents . Arani-Verlags-GmbH, Berlin-Grunewald 1959. p. 313.
  5. ↑ Georg Hamel : Mathematics in the Third Reich. In: teaching sheets for mathematics and science. 39, 1933, p. 307.
  6. ↑ Abraham Fraenkel: Circles of Life. From the memories of a Jewish mathematician. Deutsche Verlagsanstalt, Stuttgart 1967, p. 159.
  7. ↑ Lothar Mertens : “Only politically worthy people”. DFG research funding in the Third Reich 1933–1937 . Oldenbourg Akademieverlag, 2004, ISBN 3-05-003877-2 . Here: p. 86. - Mertens cites " Messages from the Reich ", vol. 2, p. 253, which in turn refers to the 1st quarterly management report 1939 of the main security office, vol.