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 [1] .
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[3] , 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 [4] - 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 [5]. Zermelo's theorem is the mathematical justification for the retrograde analysis chess algorithm [6][7] .
Tournament Results
Zermelo published a paper about "The calculation of the tournament results as a maximum problem of the probability calculus" in 1929 [8] .
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. [9]
^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.
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 [1] .
Table of Contents
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 [3] , 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 [4] - 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 [5]. Zermelo's theorem is the mathematical justification for the retrograde analysis chess algorithm [6] [7] .Tournament Results
Zermelo published a paper about "The calculation of the tournament results as a maximum problem of the probability calculus" in 1929 [8] .See also
Publications
External Links
Yale Course by Ben Polak, covers Zermelo's theorem
References
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