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Mathematics in Nazi Germany

Mathematics in Nazi Germany is a mathematics topic covered in the lgStudy science library. This page brings together a partial reference excerpt, illustrations, worked examples, real-world applications and a short study plan, so you can understand Mathematics in Nazi Germany rather than just read about it. In short: Mathematics in Nazi Germany was heavily affected by Nazi policies. Though Jews had previously faced discrimination in academic institutions, the Civil Service Law of 1933 led to the dismissal of many Jewish mathematics professors and lecturers at German universities.

Mathematics in Nazi Germany — main illustration
Mathematics in Nazi Germany — illustration

Key takeaways

  • Mathematics in Nazi Germany belongs to mathematics; place it in that map before memorising details.
  • Learn the definition first, then one example that makes the definition concrete.
  • Connect Mathematics in Nazi Germany to a quantity you can measure, compute or draw — that is where exam questions come from.
  • Reproduce the core statement of Mathematics in Nazi Germany from memory before moving on to harder problems.

Reference excerpt

Mathematics in Nazi Germany was heavily affected by Nazi policies. Though Jews had previously faced discrimination in academic institutions, the Civil Service Law of 1933 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. Before the Nazi rise to power, some Jewish mathematicians like Hermann Minkowski and Edmund Landau had achieved success and even were appointed to full professorships with the support of David Hilbert.

University of Göttingen Göttingen was, along with Berlin, one of Germany's two main centers for mathematical research. Prior to Nazi rule, the University of Göttingen already had a long and productive history of mathematical research that included prolific mathematicians like Gauss, Riemann, David Hilbert, Dirichlet, Hermann Minkowski, and Felix Klein.

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. Like Hilbert himself, Minkowski had first been appointed by Felix Klein. 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. 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. Intuition (Anschauung) was contrasted with "modern abstract" mathematics like formalism. There was a rivalry in those years between Berlin and Göttingen, and Berlin sided with Brouwer against Hilbert in the dispute. 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. Though Jewish academics had experienced prejudice prior to 1933, Hilbert had been supportive of Jewish mathematicians and 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. 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. Other lower ranking professors and lecturers included Paul Bernays, Emmy Noether, Hans Lewy, Otto Neugebauer, Herbert Busemann, Werner Fenchel, Franz Rellich, and Wilhelm Magnus. 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. Otto Blumenthal, who had converted to Protestantism when he was 18, lost his position at RWTH Aachen University.

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. 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. 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. Some emigrated to the United States, others to European countries; Heinz Hopf spent the years of Nazi rule in Zürich, Switzerland. Hans Rademacher obtained a position at the University of Pennsylvania after he was dismissed from the University of Breslau by the Nazis. 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.

Deutsche Mathematik

… excerpt ends here. Continue reading the full article.

Worked examples

Example 1 — a first encounter with Mathematics in Nazi Germany

Start with the simplest possible case. Write down what Mathematics in Nazi Germany claims or describes in one sentence, then invent the smallest concrete situation in which that sentence is true. In mathematics, the smallest case is usually a single object, a single equation or a single measurement. Check that every symbol or term in your sentence has a meaning in that case.

Example 2 — changing one variable

Take the situation from Example 1 and change exactly one quantity: double it, halve it, or set it to zero. Predict what should happen to Mathematics in Nazi Germany before you calculate. Comparing your prediction with the result is the fastest way to find out whether you understand the idea or only the words.

Example 3 — an exam-style question

Typical questions about Mathematics in Nazi Germany ask you to (a) state it precisely, (b) apply it to given data, and (c) explain a limitation. Practise writing all three answers in under five minutes; the third part is what separates a full-mark answer from an average one.

Applications of Mathematics in Nazi Germany

In research
Mathematics in Nazi Germany appears in mathematics research whenever the underlying quantities have to be modelled precisely. Papers usually cite it as a starting assumption and then explore where it breaks down.
In technology and industry
Engineering practice reuses Mathematics in Nazi Germany in design rules, simulations and safety margins. Knowing the idea lets you read a specification sheet and understand why the numbers look the way they do.
In the classroom
Mathematics in Nazi Germany is common in secondary-school and first-year university syllabi. It links to neighbouring topics 20th century in mathematics, Mathematics in Germany, Science and technology in Nazi Germany, so understanding it makes those chapters shorter.
In everyday life
Look for Mathematics in Nazi Germany outside the textbook — in sport, cooking, traffic, electronics or the sky above you. An example you found yourself is remembered far longer than one you were given.

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How to study Mathematics in Nazi Germany in 20 minutes

  1. Read the reference excerpt below once, without taking notes.
  2. Close the page and write down what Mathematics in Nazi Germany means in your own words.
  3. Compare your version with the excerpt and mark what you missed.
  4. Work through the three examples above with pen and paper.
  5. Explain Mathematics in Nazi Germany out loud to somebody else — or to Teacher Smith in the lgStudy chat.

Frequently asked questions

What is Mathematics in Nazi Germany in simple terms?

Mathematics in Nazi Germany was heavily affected by Nazi policies. Though Jews had previously faced discrimination in academic institutions, the Civil Service Law of 1933 led to the dismissal of many Jewish mathematics professors and lecturers at German universities.

Why does Mathematics in Nazi Germany matter?

Because it connects several mathematics ideas at once: it gives you a definition you can apply, a quantity you can calculate, and a way to check whether a result is plausible.

How should I study Mathematics in Nazi Germany?

Read the excerpt, restate it from memory, then work through the examples and applications listed on this page. The five-step study plan above takes about twenty minutes.

What does this page cover?

It gives you a compact reference excerpt plus original lgStudy explanations, examples, applications and study material on Mathematics in Nazi Germany.

Tags

  • 20th century in mathematics
  • Mathematics in Germany
  • Science and technology in Nazi Germany

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