Ernst Zermelo

Home * People * Ernst Zermelo

Ernst Friedrich Ferdinand Zermelo, (July 27, 1871 – May 21, 1953) a German mathematician and pioneer in set- and game theory. His university bibliography includes the Humboldt University of Berlin 1894, the University of Göttingen 1899, honorary professorship in Zürich 1910, and the University of Freiburg since 1926. During the Third Reich, in 1935 disciplinary actions were initiated against him, because he refused the Hitler salute. To preempt of his dismissal, as a result he withdrew voluntarily. In 1946 he was reinstated in Freiburg.

=Set Theory= In 1900, Zermelo proved the well-ordering theorem, which states that every set can be well ordered. This gave rise to the Zermelo axiom that every class can be well ordered. In 1904 Zermelo defined the axiom of choice, the use of which had previously been unrecognized in mathematical reasoning. The first formulations of axioms for set theory - an axiom system for German mathematician Georg Cantor's theory of sets - were made by Zermelo in 1908.

=Game Theory= In 1912, Zermelo proved the determinism of games like chess and that rational players were able to utilize all information to develop an optimal strategy. Zermelo's theorem is the mathematical justification for the retrograde analysis chess algorithm.

=Tournament Results= Zermelo published a paper about "The calculation of the tournament results as a maximum problem of the probability calculus" in 1929.

=See also=
 * Retrograde Analysis
 * History of Computer Chess

=Publications=
 * Ernst Zermelo (1904). Beweis, daß jede Menge wohlgeordnet werden kann. Mathematische Annalen 59: 514–16 (German)
 * Ernst Zermelo (1908). Untersuchungen über die Grundlagen der Mengenlehre I. Mathematische Annalen 65: 261–81 (German)
 * Ernst Zermelo (1913). Über eine Anwendung der Mengenlehre auf die Theorie des Schachspiels. Proc. Fifth Congress Mathematicians, Cambridge University Press 1913, 501–504. Translation: On an Application of Set Theory to the Theory of the Game of Chess.
 * Dénes Kőnig (1927). Über eine Schlussweise aus dem Endlichen ins Unendliche. Acta Scientiarum Mathematicarum (University of Szeged)
 * Ernst Zermelo (1929). Die Berechnung der Turnier-Ergebnisse als ein Maximumproblem der Wahrscheinlichkeitsrechnung. pdf (German)
 * Ulrich Schwalbe, Paul Walker (1997). Zermelo and the early history of game theory. pdf
 * Christoph Eichhorn (2004). Der Beginn der Formalen Spieltheorie: Zermelo (1913). pdf (German)
 * Heinz-Dieter Ebbinghaus (2007). Ernst Zermelo: An Approach to his Life and Work. Springer, 1 edition, amazon
 * Dan Heisman (2009). Steinitz, Zermelo, and Elkies. pdf from ChessCafe.com, on Wilhelm Steinitz, Ernst Zermelo and Noam Elkies
 * Daniel Andersson (2009) Perfect-Information Games with Cycles. Ph.D. thesis, Aarhus University, advisor Peter Bro Miltersen, pdf

=External Links=
 * Ernst Zermelo from Wikipedia
 * Well-ordering theorem from Wikipedia
 * Zermelo's theorem (game theory) from Wikipedia
 * Zermelo–Fraenkel set theory from Wikipedia » Abraham Fraenkel
 * Zermelo, Ernst Friedrich Ferdinand from The Free Dictionary
 * Ernst Zermelo biography from JOC/EFR © February 1999
 * Ernst Zermelo from the Mathematics Genealogy Project]
 * Details for Ernst Zermelo - Oberwolfach Photo Collection
 * Ernst Zermelo publiziert sein Axiomensystem der Mengenlehre (German)
 * 15. Backward induction: chess, strategies, and credible threats, YouTube Video
 * Yale Course by Ben Polak, covers Zermelo's theorem

=References= =What links here?=

Up one level