Ernst Zermelo

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

Life

Zermelo was the son of a high school professor and visited the Luisenstädtische Gymnasium in Berlin until graduation 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 with honors with studies on the calculus of variations in which he Weierstrass ' theory advanced. In Berlin, he studied under, among others Max Planck, whose assistant he was. 1896 and 1897 he was involved in a debate with Ludwig Boltzmann, when he saw a contradiction between the Poincare recurrence theorem and the second law of thermodynamics, the Boltzmann believed to have derived from mechanics. 1897 Zermelo went to Göttingen, then the world center of mathematics, where he a hydrodynamic topic submitted his habilitation ( vortices on the sphere ). In 1904 he formulated the axiom of choice and thus proved the theorem that every set can be well ordered. Thus he attracted so much attention that he was appointed professor in Göttingen in 1905. However, his evidence also generated strong criticism, so he gave in 1908 a new proof. As a result, he founded the axiomatic set theory with the axioms of Zermelo set theory in 1907/08, the basis for the Zermelo -Fraenkel set theory, which is now established as a standard access. 1910 Zermelo got the chair of mathematics at the University of Zurich. In 1913 he proved that finite games like chess ( there are certain game termination conditions, then no chess game take forever ) have a unique solution ( Proceedings of the Fifth International Congress of Mathematicians, pp. 501-504 ). This means that either has white like a chess composition (or chess problem ) has a winning strategy, or black has such, or each of the two players can force at least a draw. This result was one of the first in mathematical game theory. In 1916 he received the Ackermann- Teubner Memorial Prize.

Due to some health problems, he gave up his professorship in Zurich in 1916 and took up his residence in the Black Forest. He worked from 1926 with an honorary professorship in Freiburg im Breisgau, had to give up this work in 1935 but again, since he refused the lectures to begin with Hitler salute what colleagues ( Gustav Doetsch and his assistant Eugen Schlotter ) was denounced. After the Second World War he moved into his position as honorary professor again, but could not hold any more lectures due to his health condition.

Zermelo is buried in the cemetery in Günterstal in Freiburg.

Writings

• Studies on the Variations bill, Gustav Schade ( Otto Francke ), Berlin 1894 (Dissertation)
• On the theory of 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, Encyclopaedia of mathematical sciences Volume 2 (Analysis ), 1904, pp. 626-641
• Proof that every set can be well ordered, Mathematische Annalen 59, 1904, pp. 514-516
• New evidence for the possibility of a well-ordering, Mathematische Annalen 65, 1908, pp. 107-128
• Studies on the foundations of set theory. I, Mathematische Annalen 65, 1908, pp. 261-281
• The calculation of the tournament results than a maximum problem of probability theory, Mathematical Journal 29, 1929, pp. 436-460
• About marginal 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 ( in English translations of three articles Zermelo by Stefan Bauer- Mengelberg )
• Heinz -Dieter Ebbinghaus, Craig G. Fraser, Akihiro Kanamori (eds.): Ernst Zermelo. Collected Works. Collected Works Volume 1 ( Set Theory, Miscellaneous ); Volume 2 ( calculus of variations, Applied Mathematics and Physics), Springer, Heidelberg 2010, ISBN 978-3-540-79383-0