Ernst+Zermelo

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. || toc =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.
 * Home * People * Ernst Zermelo**
 * [[image:Zermelo.jpeg width="214" height="260" link="http://www-history.mcs.st-andrews.ac.uk/PictDisplay/Zermelo.html"]] ||~  || **Ernst Friedrich Ferdinand Zermelo**, (July 27, 1871 – May 21, 1953)
 * Ernst Zermelo ||~  ||^   ||

=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 1912), Cambridge Univ. 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] and [|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= > [|Yale Course] by [|Ben Polak], covers Zermelo's theorem > media type="custom" key="23820234"
 * [|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

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