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Created page with "'''Home * People * Ernst Zermelo''' '''Ernst Friedrich Ferdinand Zermelo''', (July 27, 1871 – May 21, 1953) File:Zermelo.jpeg|thumb|right|link=http://ww..."
'''[[Main Page|Home]] * [[People]] * Ernst Zermelo'''
'''Ernst Friedrich Ferdinand Zermelo''', (July 27, 1871 – May 21, 1953) [[File:Zermelo.jpeg|thumb|right|link=http://www-history.mcs.st-andrews.ac.uk/PictDisplay/Zermelo.html|Ernst Zermelo <ref>Image from [http://www-history.mcs.st-andrews.ac.uk/PictDisplay/Zermelo.html Zermelo Portraits] from [http://www-history.mcs.st-andrews.ac.uk/ MacTutor History of Mathematics] created by [http://www-history.mcs.st-and.ac.uk/~john/ John J O'Connor] and [http://www-history.mcs.st-and.ac.uk/~edmund/ Edmund F. Robertson]</ref> ]]
a German mathematician and pioneer in [https://en.wikipedia.org/wiki/Set_theory set-] and [https://en.wikipedia.org/wiki/Game_theory game theory]. His university bibliography includes the [https://en.wikipedia.org/wiki/Humboldt_University_of_Berlin Humboldt University of Berlin] 1894, the [https://en.wikipedia.org/wiki/University_of_G%C3%B6ttingen University of Göttingen] 1899, honorary professorship in [https://en.wikipedia.org/wiki/Z%C3%BCrich Zürich] 1910, and the [https://en.wikipedia.org/wiki/University_of_Freiburg University of Freiburg] since 1926. During the [https://en.wikipedia.org/wiki/Nazi_Germany Third Reich], in 1935 disciplinary actions were initiated against him, because he refused the [https://en.wikipedia.org/wiki/Hitler_salute Hitler salute]. To preempt of his dismissal, as a result he withdrew voluntarily. In 1946 he was reinstated in Freiburg <ref>[http://www5.in.tum.de/lehre/seminare/math_nszeit/SS03/vortraege/verfolgt/#Zermelo Seminar für überfachliche Grundlagen: Mathematiker in der NS-Zeit] (German) Zermelo refuses [https://en.wikipedia.org/wiki/Hitler_salute Hitler salute]</ref>.
=Set Theory=
In 1900, Zermelo proved the [https://en.wikipedia.org/wiki/Well-ordering_theorem 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 [https://en.wikipedia.org/wiki/Axiom_of_choice axiom of choice] <ref>Ernst Zermelo ('''1904'''). ''[https://www.zvab.com/servlet/BookDetailsPL?bi=22763242989 Beweis, daß jede Menge wohlgeordnet werden kann]''. [https://en.wikipedia.org/wiki/Mathematische_Annalen Mathematische Annalen] 59: 514–16 (German)</ref>, 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 [[Mathematician#Cantor|Georg Cantor's]] theory of sets <ref>[https://en.wikipedia.org/wiki/Controversy_over_Cantor%27s_theory Controversy over Cantor's theory from Wikipedia]</ref> - were made by Zermelo in 1908.
=Game Theory=
In [[Timeline#1912|1912]], Zermelo proved the determinism of games like chess and that rational players were able to utilize all information to develop an optimal strategy <ref>Ernst Zermelo ('''1913'''). ''Über eine Anwendung der Mengenlehre auf die Theorie des Schachspiels''. Proc. Fifth Congress Mathematicians, [https://en.wikipedia.org/wiki/Cambridge_University_Press Cambridge University Press] 1913, 501–504. Translation: ''On an Application of Set Theory to the Theory of the Game of Chess''.</ref>. [https://en.wikipedia.org/wiki/Zermelo%27s_theorem_%28game_theory%29 Zermelo's theorem] is the mathematical justification for the [[Retrograde Analysis|retrograde analysis]] chess algorithm <ref>[[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''. [[ICGA Journal#9_4|ICCA Journal, Vol. 9, No. 4]]</ref> <ref>[[Lewis Stiller]] ('''1995'''). ''Exploiting symmetry on parallel architectures''. Ph.D. Thesis</ref>.
=Tournament Results=
Zermelo published a paper about "The calculation of the tournament results as a maximum problem of the probability calculus" in 1929 <ref>Ernst Zermelo ('''1929'''). ''Die Berechnung der Turnier-Ergebnisse als ein Maximumproblem der Wahrscheinlichkeitsrechnung''. [http://gdz.sub.uni-goettingen.de/dms/load/img/?IDDOC=82727 pdf] (German)</ref> .
=See also=
* [[Retrograde Analysis]]
* [[History|History of Computer Chess]]
=Publications=
* Ernst Zermelo ('''1904'''). ''[https://www.zvab.com/servlet/BookDetailsPL?bi=22763242989 Beweis, daß jede Menge wohlgeordnet werden kann]''. [https://en.wikipedia.org/wiki/Mathematische_Annalen Mathematische Annalen] 59: 514–16 (German)
* Ernst Zermelo ('''1908'''). ''[http://www.digizeitschriften.de/main/dms/img/?PPN=GDZPPN002262002 Untersuchungen über die Grundlagen der Mengenlehre I]''. [https://en.wikipedia.org/wiki/Mathematische_Annalen Mathematische Annalen] 65: 261–81 (German)
* Ernst Zermelo ('''1913'''). ''Über eine Anwendung der Mengenlehre auf die Theorie des Schachspiels''. Proc. Fifth Congress Mathematicians, [https://en.wikipedia.org/wiki/Cambridge_University_Press Cambridge University Press] 1913, 501–504. Translation: ''On an Application of Set Theory to the Theory of the Game of Chess''. <ref>see Appendix in [https://www.uni-hohenheim.de/organization/person/prof-dr-ulrich-schwalbe Ulrich Schwalbe], [http://www.econ.canterbury.ac.nz/personal_pages/paul_walker/psw.htm Paul Walker] ('''1997'''). ''Zermelo and the early history of game theory''. [http://abel.math.harvard.edu/~elkies/FS23j.03/zermelo.pdf pdf]</ref>
* [[Mathematician#DenesKoenig|Dénes Kőnig]] ('''1927'''). ''[http://acta.fyx.hu/acta/showCustomerArticle.action?id=5131&dataObjectType=article&returnAction=showCustomerVolume&sessionDataSetId=2b29ea26fa2c9ba Über eine Schlussweise aus dem Endlichen ins Unendliche]''. [http://acta.fyx.hu/acta/home.action?noDataSet=true Acta Scientiarum Mathematicarum] ([https://en.wikipedia.org/wiki/University_of_Szeged University of Szeged])
* Ernst Zermelo ('''1929'''). ''Die Berechnung der Turnier-Ergebnisse als ein Maximumproblem der Wahrscheinlichkeitsrechnung''. [http://gdz.sub.uni-goettingen.de/dms/load/img/?IDDOC=82727 pdf] (German)
* [https://www.uni-hohenheim.de/organization/person/prof-dr-ulrich-schwalbe Ulrich Schwalbe], [http://www.econ.canterbury.ac.nz/personal_pages/paul_walker/psw.htm Paul Walker] ('''1997'''). ''Zermelo and the early history of game theory''. [http://abel.math.harvard.edu/~elkies/FS23j.03/zermelo.pdf pdf]
* [http://www.wirtschaftsdienst.eu/archiv/autor/615/?PHPSESSID=d26b5dc217fd5572c940a629eeced7d5 Christoph Eichhorn] <ref>[http://www.mathematik.uni-muenchen.de/%7Espielth/artikelFrame.html Artikel zur Vorlesung "Spieltheorie"] (German)</ref> ('''2004'''). ''Der Beginn der Formalen Spieltheorie: Zermelo (1913)''. [http://www.mathematik.uni-muenchen.de/%7Espielth/artikel/Zermelo.pdf pdf] (German)
* [http://home.mathematik.uni-freiburg.de/hde/Ebbinghaus.html Heinz-Dieter Ebbinghaus] ('''2007'''). ''Ernst Zermelo: An Approach to his Life and Work''. Springer, 1 edition, [http://www.amazon.com/Ernst-Zermelo-Approach-Life-Work/dp/3540495517 amazon]
* [[Dan Heisman]] ('''2009'''). ''Steinitz, Zermelo, and Elkies''. [http://www.chesscafe.com/text/skittles358.pdf pdf] from [https://en.wikipedia.org/wiki/ChessCafe.com ChessCafe.com], on [https://en.wikipedia.org/wiki/Wilhelm_Steinitz Wilhelm Steinitz], Ernst Zermelo and [[Noam Elkies]]
* [[Daniel Andersson]] ('''2009''') ''Perfect-Information Games with Cycles''. Ph.D. thesis, [https://en.wikipedia.org/wiki/Aarhus_University Aarhus University], advisor [[Mathematician#Miltersen|Peter Bro Miltersen]], [http://www.cs.au.dk/~koda/thesis.pdf pdf]
=External Links=
* [https://en.wikipedia.org/wiki/Ernst_Zermelo Ernst Zermelo from Wikipedia]
* [https://en.wikipedia.org/wiki/Well-ordering_theorem Well-ordering theorem from Wikipedia]
* [https://en.wikipedia.org/wiki/Zermelo%27s_theorem_%28game_theory%29 Zermelo's theorem (game theory) from Wikipedia]
* [https://en.wikipedia.org/wiki/Zermelo%E2%80%93Fraenkel_set_theory Zermelo–Fraenkel set theory from Wikipedia] » [[Mathematician#AbrahamFraenkel|Abraham Fraenkel]]
* [http://encyclopedia.farlex.com/Zermelo,+Ernst+Friedrich+Ferdinand Zermelo, Ernst Friedrich Ferdinand from The Free Dictionary]
* [http://www-groups.dcs.st-and.ac.uk/%7Ehistory/Biographies/Zermelo.html Ernst Zermelo biography from JOC/EFR © February 1999]
* [http://www.genealogy.math.ndsu.nodak.edu/id.php?id=46828 Ernst Zermelo from the Mathematics Genealogy Project]]
* [http://owpdb.mfo.de/person_detail?id=4654 Details for Ernst Zermelo - Oberwolfach Photo Collection]
* [http://www.mathematik.de/ger/information/kalenderblatt/zermelo/zermelo.html Ernst Zermelo publiziert sein Axiomensystem der Mengenlehre] (German)
* 15. [https://en.wikipedia.org/wiki/Backward_induction Backward induction]: chess, strategies, and credible threats, [https://en.wikipedia.org/wiki/YouTube YouTube] Video
: [http://oyc.yale.edu/ Yale Course] by [https://en.wikipedia.org/wiki/Benjamin_Polak Ben Polak], covers Zermelo's theorem
: {{#evu:https://www.youtube.com/watch?v=Bm8lM73lTmk|alignment=left|valignment=top}}
=References=
<references />
=What links here?=
'''[[People|Up one level]]'''
'''Ernst Friedrich Ferdinand Zermelo''', (July 27, 1871 – May 21, 1953) [[File:Zermelo.jpeg|thumb|right|link=http://www-history.mcs.st-andrews.ac.uk/PictDisplay/Zermelo.html|Ernst Zermelo <ref>Image from [http://www-history.mcs.st-andrews.ac.uk/PictDisplay/Zermelo.html Zermelo Portraits] from [http://www-history.mcs.st-andrews.ac.uk/ MacTutor History of Mathematics] created by [http://www-history.mcs.st-and.ac.uk/~john/ John J O'Connor] and [http://www-history.mcs.st-and.ac.uk/~edmund/ Edmund F. Robertson]</ref> ]]
a German mathematician and pioneer in [https://en.wikipedia.org/wiki/Set_theory set-] and [https://en.wikipedia.org/wiki/Game_theory game theory]. His university bibliography includes the [https://en.wikipedia.org/wiki/Humboldt_University_of_Berlin Humboldt University of Berlin] 1894, the [https://en.wikipedia.org/wiki/University_of_G%C3%B6ttingen University of Göttingen] 1899, honorary professorship in [https://en.wikipedia.org/wiki/Z%C3%BCrich Zürich] 1910, and the [https://en.wikipedia.org/wiki/University_of_Freiburg University of Freiburg] since 1926. During the [https://en.wikipedia.org/wiki/Nazi_Germany Third Reich], in 1935 disciplinary actions were initiated against him, because he refused the [https://en.wikipedia.org/wiki/Hitler_salute Hitler salute]. To preempt of his dismissal, as a result he withdrew voluntarily. In 1946 he was reinstated in Freiburg <ref>[http://www5.in.tum.de/lehre/seminare/math_nszeit/SS03/vortraege/verfolgt/#Zermelo Seminar für überfachliche Grundlagen: Mathematiker in der NS-Zeit] (German) Zermelo refuses [https://en.wikipedia.org/wiki/Hitler_salute Hitler salute]</ref>.
=Set Theory=
In 1900, Zermelo proved the [https://en.wikipedia.org/wiki/Well-ordering_theorem 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 [https://en.wikipedia.org/wiki/Axiom_of_choice axiom of choice] <ref>Ernst Zermelo ('''1904'''). ''[https://www.zvab.com/servlet/BookDetailsPL?bi=22763242989 Beweis, daß jede Menge wohlgeordnet werden kann]''. [https://en.wikipedia.org/wiki/Mathematische_Annalen Mathematische Annalen] 59: 514–16 (German)</ref>, 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 [[Mathematician#Cantor|Georg Cantor's]] theory of sets <ref>[https://en.wikipedia.org/wiki/Controversy_over_Cantor%27s_theory Controversy over Cantor's theory from Wikipedia]</ref> - were made by Zermelo in 1908.
=Game Theory=
In [[Timeline#1912|1912]], Zermelo proved the determinism of games like chess and that rational players were able to utilize all information to develop an optimal strategy <ref>Ernst Zermelo ('''1913'''). ''Über eine Anwendung der Mengenlehre auf die Theorie des Schachspiels''. Proc. Fifth Congress Mathematicians, [https://en.wikipedia.org/wiki/Cambridge_University_Press Cambridge University Press] 1913, 501–504. Translation: ''On an Application of Set Theory to the Theory of the Game of Chess''.</ref>. [https://en.wikipedia.org/wiki/Zermelo%27s_theorem_%28game_theory%29 Zermelo's theorem] is the mathematical justification for the [[Retrograde Analysis|retrograde analysis]] chess algorithm <ref>[[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''. [[ICGA Journal#9_4|ICCA Journal, Vol. 9, No. 4]]</ref> <ref>[[Lewis Stiller]] ('''1995'''). ''Exploiting symmetry on parallel architectures''. Ph.D. Thesis</ref>.
=Tournament Results=
Zermelo published a paper about "The calculation of the tournament results as a maximum problem of the probability calculus" in 1929 <ref>Ernst Zermelo ('''1929'''). ''Die Berechnung der Turnier-Ergebnisse als ein Maximumproblem der Wahrscheinlichkeitsrechnung''. [http://gdz.sub.uni-goettingen.de/dms/load/img/?IDDOC=82727 pdf] (German)</ref> .
=See also=
* [[Retrograde Analysis]]
* [[History|History of Computer Chess]]
=Publications=
* Ernst Zermelo ('''1904'''). ''[https://www.zvab.com/servlet/BookDetailsPL?bi=22763242989 Beweis, daß jede Menge wohlgeordnet werden kann]''. [https://en.wikipedia.org/wiki/Mathematische_Annalen Mathematische Annalen] 59: 514–16 (German)
* Ernst Zermelo ('''1908'''). ''[http://www.digizeitschriften.de/main/dms/img/?PPN=GDZPPN002262002 Untersuchungen über die Grundlagen der Mengenlehre I]''. [https://en.wikipedia.org/wiki/Mathematische_Annalen Mathematische Annalen] 65: 261–81 (German)
* Ernst Zermelo ('''1913'''). ''Über eine Anwendung der Mengenlehre auf die Theorie des Schachspiels''. Proc. Fifth Congress Mathematicians, [https://en.wikipedia.org/wiki/Cambridge_University_Press Cambridge University Press] 1913, 501–504. Translation: ''On an Application of Set Theory to the Theory of the Game of Chess''. <ref>see Appendix in [https://www.uni-hohenheim.de/organization/person/prof-dr-ulrich-schwalbe Ulrich Schwalbe], [http://www.econ.canterbury.ac.nz/personal_pages/paul_walker/psw.htm Paul Walker] ('''1997'''). ''Zermelo and the early history of game theory''. [http://abel.math.harvard.edu/~elkies/FS23j.03/zermelo.pdf pdf]</ref>
* [[Mathematician#DenesKoenig|Dénes Kőnig]] ('''1927'''). ''[http://acta.fyx.hu/acta/showCustomerArticle.action?id=5131&dataObjectType=article&returnAction=showCustomerVolume&sessionDataSetId=2b29ea26fa2c9ba Über eine Schlussweise aus dem Endlichen ins Unendliche]''. [http://acta.fyx.hu/acta/home.action?noDataSet=true Acta Scientiarum Mathematicarum] ([https://en.wikipedia.org/wiki/University_of_Szeged University of Szeged])
* Ernst Zermelo ('''1929'''). ''Die Berechnung der Turnier-Ergebnisse als ein Maximumproblem der Wahrscheinlichkeitsrechnung''. [http://gdz.sub.uni-goettingen.de/dms/load/img/?IDDOC=82727 pdf] (German)
* [https://www.uni-hohenheim.de/organization/person/prof-dr-ulrich-schwalbe Ulrich Schwalbe], [http://www.econ.canterbury.ac.nz/personal_pages/paul_walker/psw.htm Paul Walker] ('''1997'''). ''Zermelo and the early history of game theory''. [http://abel.math.harvard.edu/~elkies/FS23j.03/zermelo.pdf pdf]
* [http://www.wirtschaftsdienst.eu/archiv/autor/615/?PHPSESSID=d26b5dc217fd5572c940a629eeced7d5 Christoph Eichhorn] <ref>[http://www.mathematik.uni-muenchen.de/%7Espielth/artikelFrame.html Artikel zur Vorlesung "Spieltheorie"] (German)</ref> ('''2004'''). ''Der Beginn der Formalen Spieltheorie: Zermelo (1913)''. [http://www.mathematik.uni-muenchen.de/%7Espielth/artikel/Zermelo.pdf pdf] (German)
* [http://home.mathematik.uni-freiburg.de/hde/Ebbinghaus.html Heinz-Dieter Ebbinghaus] ('''2007'''). ''Ernst Zermelo: An Approach to his Life and Work''. Springer, 1 edition, [http://www.amazon.com/Ernst-Zermelo-Approach-Life-Work/dp/3540495517 amazon]
* [[Dan Heisman]] ('''2009'''). ''Steinitz, Zermelo, and Elkies''. [http://www.chesscafe.com/text/skittles358.pdf pdf] from [https://en.wikipedia.org/wiki/ChessCafe.com ChessCafe.com], on [https://en.wikipedia.org/wiki/Wilhelm_Steinitz Wilhelm Steinitz], Ernst Zermelo and [[Noam Elkies]]
* [[Daniel Andersson]] ('''2009''') ''Perfect-Information Games with Cycles''. Ph.D. thesis, [https://en.wikipedia.org/wiki/Aarhus_University Aarhus University], advisor [[Mathematician#Miltersen|Peter Bro Miltersen]], [http://www.cs.au.dk/~koda/thesis.pdf pdf]
=External Links=
* [https://en.wikipedia.org/wiki/Ernst_Zermelo Ernst Zermelo from Wikipedia]
* [https://en.wikipedia.org/wiki/Well-ordering_theorem Well-ordering theorem from Wikipedia]
* [https://en.wikipedia.org/wiki/Zermelo%27s_theorem_%28game_theory%29 Zermelo's theorem (game theory) from Wikipedia]
* [https://en.wikipedia.org/wiki/Zermelo%E2%80%93Fraenkel_set_theory Zermelo–Fraenkel set theory from Wikipedia] » [[Mathematician#AbrahamFraenkel|Abraham Fraenkel]]
* [http://encyclopedia.farlex.com/Zermelo,+Ernst+Friedrich+Ferdinand Zermelo, Ernst Friedrich Ferdinand from The Free Dictionary]
* [http://www-groups.dcs.st-and.ac.uk/%7Ehistory/Biographies/Zermelo.html Ernst Zermelo biography from JOC/EFR © February 1999]
* [http://www.genealogy.math.ndsu.nodak.edu/id.php?id=46828 Ernst Zermelo from the Mathematics Genealogy Project]]
* [http://owpdb.mfo.de/person_detail?id=4654 Details for Ernst Zermelo - Oberwolfach Photo Collection]
* [http://www.mathematik.de/ger/information/kalenderblatt/zermelo/zermelo.html Ernst Zermelo publiziert sein Axiomensystem der Mengenlehre] (German)
* 15. [https://en.wikipedia.org/wiki/Backward_induction Backward induction]: chess, strategies, and credible threats, [https://en.wikipedia.org/wiki/YouTube YouTube] Video
: [http://oyc.yale.edu/ Yale Course] by [https://en.wikipedia.org/wiki/Benjamin_Polak Ben Polak], covers Zermelo's theorem
: {{#evu:https://www.youtube.com/watch?v=Bm8lM73lTmk|alignment=left|valignment=top}}
=References=
<references />
=What links here?=
'''[[People|Up one level]]'''
