Ernst Zermelo

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Ernst Zermelo, Freiburg 1953

Ernst Friedrich Ferdinand Zermelo [ t͡sɛrˈmeːlo ] (born July 27, 1871 in Berlin , † May 21, 1953 in Freiburg im Breisgau ) was a German mathematician .


Zermelo was the son of a high school professor and attended the Luisenstädtische Gymnasium in Berlin until his Abitur in 1889. He studied mathematics , physics and philosophy at the universities of Berlin, Halle (Saale) and Freiburg and received his doctorate in 1894 at the University of Berlin under Hermann Amandus Schwarz with distinction with investigations on the calculus of variations , in which he expanded Weierstrass' theory. In Berlin he studied under Max Planck , whose assistant he was. In the years 1896 and 1897 he was involved in a debate with Ludwig Boltzmann because he saw a contradiction between Poincaré's return theorem and the second law of thermodynamics, which Boltzmann believed to have derived from mechanics. In 1897 Zermelo went to Göttingen , at that time the world center of mathematics, where he submitted his habilitation on a hydrodynamic topic (vortex movements on the spherical surface). In 1904 he formulated the axiom of choice and thus proved the well-order theorem , which says that any amount can be well ordered. This attracted so much attention that he was appointed professor in Göttingen in 1905. But his proof also generated severe criticism, so that in 1908 he gave a new proof. As a result he founded the axiomatic set theory with the axioms of the Zermelo set theory 1907/08, the basis for the Zermelo-Fraenkel set theory , which is now established as the standard approach. In 1910 Zermelo got the chair for mathematics at the University of Zurich . In 1913 he proved that finite games like chess (there are certain game termination conditions so that no game can last indefinitely) have a unique solution. That means: either White has a winning strategy , as in a chess composition (or chess problem) , or Black has one, or each of the two players can force at least one draw. This result was one of the first in mathematical game theory . In 1916 he received the Ackermann-Teubner Memorial Prize .

Because of some health problems, he gave up his professorship in Zurich in 1916 and took up residence in the Black Forest . From 1926 he worked as an honorary professor at the Albert-Ludwigs-Universität in Freiburg im Breisgau , but had to give up this work again in 1935 because he refused to start the lectures with the Hitler salute, something from colleagues ( Gustav Doetsch and his assistant Eugen Schlotter ) was denounced. After the Second World War he took up his position as honorary professor again, but was unable to hold lectures due to his health.

Zermelo is buried in the Günterstal cemetery in Freiburg.

In April 2018, the Eckerstraße in Freiburg , where the Mathematical Institute of the Albert-Ludwigs-Universität Freiburg is located, was renamed Ernst-Zermelo-Straße in his honor.


Ernst Zermelo in the 1900s

Zermelo was known to be sharp-tongued. Wolfgang Pauli told the following anecdote from Ernst Zermelo: In a lecture on logic in Göttingen, Zermelo posed the following paradox: There are two classes of mathematicians in Göttingen. The first class includes those who would do what Felix Klein wanted but did not like. The second class included those who did what they liked but didn't like Felix Klein. What class does Felix Klein belong to? When the students remained silent (Felix Klein held a prominent position in mathematics in Göttingen and elsewhere in Germany and was also the superior of Zermelo, who taught as a private lecturer in Göttingen), he said the answer would be terribly simple: Felix Klein would be no mathematician at all (in fact, in his later career Klein was known for dealing a lot with physical applications, and he was accused of poor mathematical rigor , especially by the Berlin maths school, from which Zermelo came ). It can be added to the anecdote that Zermelo independently discovered Russell's antinomy before the publication by Bertrand Russell (1903) and used it in lectures (through which it was known to David Hilbert , among others ).



Web links

Commons : Ernst Zermelo  - Collection of images, videos and audio files

Individual evidence

  1. Ernst Zermelo: About a set of dynamics and the mechanical heat theory , Annalen der Physik, Vol. 57, 1896, pp. 485–494; About mechanical explanations of irreversible processes , Annalen der Physik, Vol. 59, 1896, pp. 793-801. Boltzmann's answer in Wiedemann's Annalen Vol. 57, 1896, p. 772, Vol. 60, 1897, p. 392, partly reprinted in Stephen Brush: Kinetic Theory , WTB 1970
  2. Ernst Zermelo, On an application of set theory to the theory of the chess game , Proceedings of the Fifth International Congress of Mathematicians, 1913, pp. 501–504 ( Memento from March 24, 2016 in the Internet Archive )
  3. Eckerstraße is renamed Ernst-Zermelo-Straße. City of Freiburg, April 6, 2018, accessed April 25, 2018 .
  4. Schuecking: Jordan, Pauli, Politics, Brecht and a variable gravitational constant. Physics Today, October 1999, p. 28 f.