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 [2].
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
- 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. [9]
- 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 [10] (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
- ↑ Image from Zermelo Portraits from MacTutor History of Mathematics created by John J O'Connor and Edmund F. Robertson
- ↑ Seminar für überfachliche Grundlagen: Mathematiker in der NS-Zeit (German) Zermelo refuses Hitler salute
- ↑ Ernst Zermelo (1904). Beweis, daß jede Menge wohlgeordnet werden kann. Mathematische Annalen 59: 514–16 (German)
- ↑ Controversy over Cantor's theory from Wikipedia
- ↑ 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.
- ↑ Edward Komissarchik, Aaron L. Futer (1974). Ob Analize Ferzevogo Endshpilya pri Pomoshchi EVM. (Analysis of a queen endgame using an IBM computer) Problemy Kybernetiki, Vol. 29, pp. 211-220. English translation by Christian Posthoff, revised as Edward Komissarchik, Aaron L. Futer (1986). Computer Analysis of a Queen Endgame. ICCA Journal, Vol. 9, No. 4
- ↑ Lewis Stiller (1995). Exploiting symmetry on parallel architectures. Ph.D. Thesis
- ↑ Ernst Zermelo (1929). Die Berechnung der Turnier-Ergebnisse als ein Maximumproblem der Wahrscheinlichkeitsrechnung. pdf (German)
- ↑ see Appendix in Ulrich Schwalbe, Paul Walker (1997). Zermelo and the early history of game theory. pdf
- ↑ Artikel zur Vorlesung "Spieltheorie" (German)
