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.
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 ).
- Investigations on the calculus of variations , Gustav Schade (Otto Francke), Berlin 1894 (dissertation; with a Latin curriculum vitae)
- On the theory of the shortest lines , annual report of the DMV 11, 1902, pp. 184–187
- with Hans Hahn : Further development of the calculus of variations in recent years , Encyclopedia of Mathematical Sciences, Volume 2 (Analysis), 1904, pp. 626–641
- Proof that any amount can be well ordered , Mathematische Annalen 59, 1904, pp. 514-516
- New evidence for the possibility of a well-ordered system , Mathematische Annalen 65, 1908, pp. 107–128
- Investigations into the basics of set theory. I , Mathematische Annalen 65, 1908, pp. 261-281
- The calculation of the tournament results as a maximum problem of the probability calculation , Mathematische Zeitschrift 29, 1929, pp. 436-460
- About limit numbers and quantity ranges ( PDF file, 1.5 MB), Fundamenta Mathematicae 16, 1930, pp. 29–47
- Jean van Heijenoort (Ed.): From Frege to Gödel , Cambridge Mass. 1966 (including English translations of three articles Zermelos by Stefan Bauer-Mengelberg)
- Heinz-Dieter Ebbinghaus , Craig G. Fraser, Akihiro Kanamori (eds.): Ernst Zermelo. Collected Works. Collected Works Volume 1 (set theory, varia), Heidelberg 2010, ISBN 978-3-540-79383-0 , doi: 10.1007 / 978-3-540-79384-7 ; Volume 2 (Calculus of Variations, Applied Mathematics and Physics), Heidelberg 2013, ISBN 978-3-540-70855-1 , doi: 10.1007 / 978-3-540-70856-8
- M. Pinl : Ernst Zermelo in Colleagues in a Dark Time (Part 1), Annual Report of DMV 71, 1969, p. 221f.
- Volker Peckhaus : 'I was careful not to fire all the cartridges at once'. Ernst Zermelo in Göttingen , History and Philosophy of Logic 11, 1990, pp. 19–58 ( Zentralblatt review )
- Ernst Zermelo in Sanford L. Segal: Mathematicians under the Nazis , Princeton University Press, 2003, pp. 467–469 (English)
- Volker Peckhaus: "But maybe there will come a time when my work will also be discovered and read again": The failed career of Ernst Zermelo in Wolfgang Hein, Peter Ullrich (ed.): Mathematik im Fluss der Zeit , Erwin Rauner, Augsburg 2004 , ISBN 3-936905-02-9 , pp. 325-339
- Heinz-Dieter Ebbinghaus , Volker Peckhaus: Ernst Zermelo. An approach to his life and work , Springer, Berlin 2007, ISBN 978-3-540-49551-2 (English; Zentralblatt review , review by Gregory Moore, Notices AMS, August 2009, pdf )
- Literature by and about Ernst Zermelo in the catalog of the German National Library
- Erwin Neuenschwander : Zermelo, Ernst. In: Historical Lexicon of Switzerland .
- John J. O'Connor, Edmund F. Robertson : Ernst Friedrich Ferdinand Zermelo. In: MacTutor History of Mathematics archive .
- Zermelo, Ernst Friedrich Ferdinand von Bob van Rootselaar in Complete Dictionary of Scientific Biography , Encyclopedia.com, 2008 (English)
- Hundred years of modern mathematics by Ralf Bülow and Peter-Michael Ziegler at heise online, February 13, 2008
- spectrum .de: Ernst Zermelo (1871–1953) May 1, 2019
- 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
- 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 )
- Eckerstraße is renamed Ernst-Zermelo-Straße. City of Freiburg, April 6, 2018, accessed April 25, 2018 .
- Schuecking: Jordan, Pauli, Politics, Brecht and a variable gravitational constant. Physics Today, October 1999, p. 28 f.
|ALTERNATIVE NAMES||Zermelo, Ernst Friedrich Ferdinand (full name)|
|BRIEF DESCRIPTION||German mathematician|
|DATE OF BIRTH||July 27, 1871|
|PLACE OF BIRTH||Berlin|
|DATE OF DEATH||May 21, 1953|
|Place of death||Freiburg in Breisgau|