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Encyclopedia > Ernst Zermelo

Ernst Friedrich Ferdinand Zermelo (July 27, 1871, Berlin, German EmpireMay 21, 1953, Freiburg im Breisgau, West Germany) was a German mathematician, whose work has major implications for the foundations of mathematics and hence on philosophy. July 27 is the 208th day (209th in leap years) of the year in the Gregorian Calendar, with 157 days remaining. ... 1871 (MDCCCLXXI) was a common year starting on Sunday (see link for calendar). ... Berlin is the capital city and a state of Germany. ... Motto: Gott mit Uns (German: God with us”) Anthem: Heil dir im Siegerkranz (unofficial) Territory of the German Empire in 1914, prior to World War I   Capital Berlin Official language(s) German Minor language(s) Polish (Posen, Upper Silesia, Masuria) French (Elsass-Lothringen) Government Constitutional Monarchy  - First Kaiser Wilhelm I... May 21 is the 141st day of the year in the Gregorian calendar (142nd in leap years). ... 1953 (MCMLIII) was a common year starting on Thursday (link is to a full 1953 calendar). ... This article is about Freiburg in Baden-Württemberg, Germany. ... To meet Wikipedias quality standards, this article or section may require cleanup. ... Foundations of mathematics is a term sometimes used for certain fields of mathematics itself, namely for mathematical logic, axiomatic set theory, proof theory, model theory, and recursion theory. ... To meet Wikipedias quality standards, this article may require cleanup. ...


He graduated from Berlin's Luisenstädtisches Gymnasium in 1889. He then studied mathematics, physics and philosophy at the universities of Berlin, Halle and Freiburg. He finished his doctorate in 1894 at the University of Berlin, awarded for a dissertation on the calculus of variations (Untersuchungen zur Variationsrechnung). Zermelo remained at the University of Berlin, where he was appointed assistant to Planck, under whose guidance he began to study hydrodynamics. In 1897, Zermelo went to Göttingen, at that time the leading centre for mathematical research in the world, where he completed his habilitation thesis in 1899. 1889 (MDCCCLXXXIX) was a common year starting on Tuesday (see link for calendar). ... For other meanings of mathematics or math, see mathematics (disambiguation). ... The first few hydrogen atom electron orbitals shown as cross-sections with color-coded probability density. ... To meet Wikipedias quality standards, this article may require cleanup. ... Berlin is the capital city and a state of Germany. ... Halle (also called Halle an der Saale in order to distinguish from Halle in North Rhine-Westphalia) is the largest town in the German Bundesland of Saxony-Anhalt. ... Freiburg city from Schlossberg Freiburg im Breisgau is a city in Baden-Württemberg, Germany, in the Breisgau region, on the western edge of the southern Black Forest (German: Schwarzwald) with about 214,000 inhabitants. ... 1894 (MDCCCXCIV) was a common year starting on Monday (see link for calendar). ... There is no institution called the University of Berlin, but there are four universities in Berlin, Germany: Humboldt University of Berlin (Humboldt-Universität zu Berlin) Technical University of Berlin (Technische Universität Berlin) Free University of Berlin (Freie Universität Berlin) Berlin University of the Arts (Universität der... Calculus of variations is a field of mathematics that deals with functions of functions, as opposed to ordinary calculus which deals with functions of numbers. ... Max Karl Ernst Ludwig Planck (April 23, 1858 – October 4, 1947) was a German physicist. ... Hydrodynamics is fluid dynamics applied to liquids, such as water, alcohol, oil, and blood. ... 1897 (MDCCCXCVII) was a common year starting on Friday (see link for calendar). ... Göttingen ( ) is a city in Lower Saxony, Germany. ... Habilitation is a term used within the university system in France, Germany, Austria, and some other European countries such as the German-speaking part of Switzerland, in Bulgaria, Poland, the Czech Republic, Slovakia, Hungary, Slovenia, and countries of former Soviet Union, such as Armenia, Azerbaijan, Moldova, Kirgizstan, Kazakhstan, Russia, Uzbekistan... 1899 (MDCCCXCIX) was a common year starting on Sunday (see link for calendar). ...


In 1900, in the Paris conference of the International Congress of Mathematicians, David Hilbert challenged the mathematical community with his famous Hilbert's problems, a list of 23 unsolved fundamental questions which mathematicians should attack during the coming century. The first of these, a problem of set theory, was the continuum hypothesis introduced by Cantor in 1878. 1900 (MCM) was an exceptional common year starting on Monday. ... The International Congress of Mathematicians (ICM) is the biggest congress in mathematics. ... David Hilbert (January 23, 1862, Wehlau, East Prussia – February 14, 1943, Göttingen, Germany) was a German mathematician, recognized as one of the most influential mathematicians of the 19th and early 20th centuries. ... Hilberts problems are a list of twenty-three problems in mathematics put forth by German mathematician David Hilbert at the Paris conference of the International Congress of Mathematicians in 1900. ... Set theory is the mathematical theory of sets, which represent collections of abstract objects. ... In mathematics, the continuum hypothesis is a hypothesis about the possible sizes of infinite sets. ... Georg Cantor Georg Ferdinand Ludwig Philipp Cantor (March 3, 1845, St. ... 1878 (MDCCCLXXVIII) was a common year starting on Tuesday (see link for calendar). ...


Zermelo began to work on the problems of set theory and in 1902 published his first work concerning the addition of transfinite cardinals. In 1904, he succeeded in taking the first step suggested by Hilbert towards the continuum hypothesis when he proved the well-ordering theorem (every set can be well ordered). This result brought fame to Zermelo, who was appointed Professor in Göttingen, in 1905. His proof of the well-ordering theorem, based on the axiom of choice, was not accepted by all mathematicians, partly because set theory was not axiomatized at this time. In 1908, Zermelo succeeded in producing a much more widely-accepted proof. 1902 (MCMII) was a common year starting on Wednesday (see link for calendar). ... Alternative meaning: number of pitch classes in a set. ... The well-ordering theorem (not to be confused with the well-ordering axiom) states that every set can be well-ordered. ... 1905 (MCMV) was a common year starting on Sunday (see link for calendar). ... In mathematics, the axiom of choice, or AC, is an axiom of set theory. ... Set theory is the mathematical theory of sets, which represent collections of abstract objects. ... In mathematics, axiomatization is the process of defining the basic axiomatic systems from which mathematical theories can be derived. ... 1908 (MCMVIII) was a leap year starting on Wednesday (link will take you to calendar). ...


In 1905, Zermelo began to axiomatize set theory; in 1908, he published his results despite his failure to prove the consistency of his axiomatic system. See the article on Zermelo set theory for an outline of this paper, together with the original axioms, with the original numbering. 1905 (MCMV) was a common year starting on Sunday (see link for calendar). ... 1908 (MCMVIII) was a leap year starting on Wednesday (link will take you to calendar). ... Zermelo set theory, as set out in an important paper in 1908 by Ernst Zermelo, is the ancestor of modern set theory. ...


In 1922, Adolf Fraenkel and Thoralf Skolem independently improved Zermelo's axiom system. The resulting 10 axiom system, now called Zermelo-Fraenkel axioms (ZF), is now the most commonly used system for axiomatic set theory. 1922 (MCMXXII) was a common year starting on Sunday (see link for calendar). ... Adolf Abraham Halevi Fraenkel (February 17, 1891 - October 15, German / Israeli mathematician. ... Albert Thoralf Skolem (May 23, 1887 - March 23, 1963) was a Norwegian mathematician. ... Zermelo–Fraenkel set theory, with the axiom of choice, commonly abbreviated ZFC, is the most common form of axiomatic set theory, and as such is the most common foundation of mathematics. ... This article or section is in need of attention from an expert on the subject. ...


In 1910, Zermelo left Göttingen upon being appointed to the chair of mathematics at Zurich University, which he resigned in 1916. He was appointed to an honorary chair at Freiburg im Breisgau in 1926, which he resigned in 1935 because he disapproved of Hitler's regime. At the end of World War II and at his request, Zermelo was reinstated to his honorary position in Freiburg. 1910 (MCMX) was a common year starting on Saturday (see link for calendar) of the Gregorian calendar or a common year starting on Sunday of the 13-day slower Julian calendar. ... The University of Zurich (in German: Universität Zürich) is the largest university of Switzerland. ... 1916 (MCMXVI) was a leap year starting on Saturday (link will take you to calendar). ... This article is about Freiburg in Baden-Württemberg, Germany. ... 1926 (MCMXXVI) was a common year starting on Friday (link will take you to calendar). ... 1935 (MCMXXXV) was a common year starting on Tuesday (link will take you to calendar). ... This article is becoming very long. ...

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Bibliography

Primary literature in English translation:

  • Jean van Heijenoort, 1967. From Frege to Godel: A Source Book in Mathematical Logic, 1879-1931. Harvard Univ. Press.
    • 1904. "Proof that every set can be well-ordered," 139-41.
    • 1908. "A new proof of the possibility of well-ordering," 183-98.
    • 1908. "Investigations in the foundations of set theory I," 199-215.
  • 1930. "On boundary numbers and domains of sets: new investigations in the foundations of set theory" in Ewald, William B., ed., 1996. From Kant to Hilbert: A Source Book in the Foundations of Mathematics, 2 vols. Oxford Uni. Press: 1219-33.

Secondary: Jean van Heijenoort (prounounced highenort) (July 23, 1912, Creil France - March 29, 1986, Mexico City) was a pioneer historian of mathematical logic. ...

  • Ivor Grattan-Guinness, 2000. The Search for Mathematical Roots 1870-1940. Princeton Uni. Press.
[edit]

Ivor Grattan-Guiness is a prolific contemporary historian of mathematics and logic. ...

External links

  • O'Connor, John J., and Edmund F. Robertson. "Ernst Zermelo". MacTutor History of Mathematics archive.
  • Ernst Zermelo at the Mathematics Genealogy Project
  • Scientific Biography of Ernst Zermelo (1871-1953).

  Results from FactBites:
 
Ernst Zermelo - Wikipedia, the free encyclopedia (489 words)
Zermelo remained at the University of Berlin where he was appointed assistant to Planck and under his guidance began to study hydrodynamics.
Zermelo began to work on the problems of set theory and in 1902 published his first work concerning the addition of transfinite cardinals.
At the end of World War II Zermelo requested that he be reinstated to his honorary position in Freiburg and indeed he was reinstated to the post in 1946.
Zermelo set theory - Wikipedia, the free encyclopedia (986 words)
Zermelo set theory, as set out in an important paper in 1908 by Ernst Zermelo, is the ancestor of modern set theory.
Zermelo is of course referring to the "Russell antinomy".
Zermelo's paper is notable for what may be the first mention of Cantor's theorem explicitly and by name.
  More results at FactBites »

 
 

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