Ernst Zermelo  

Born  
Died  21 May 1953  (aged 81)
Nationality  German 
Alma mater  University of Berlin 
Known for  
Spouse  Gertrud Seekamp (1944 – death) 
Awards  Ackermann–Teubner Memorial Award (1916) 
Scientific career  
Fields  Mathematics 
Institutions  University of Zürich 
Doctoral advisor  
Doctoral students  Stefan Straszewicz 
Ernst Friedrich Ferdinand Zermelo (/zɜːrˈmɛloʊ/, German: [tsɛɐ̯ˈmeːlo]; 27 July 1871 – 21 May 1953) was a German logician and mathematician, whose work has major implications for the foundations of mathematics. He is known for his role in developing Zermelo–Fraenkel axiomatic set theory and his proof of the wellordering theorem. Furthermore, his 1929^{[1]} work on ranking chess players is the first description of a model for pairwise comparison that continues to have a profound impact on various applied fields utilizing this method.
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O Paradoxo de Russell derrubou a matemática, mas Ernst Zermelo a tirou do chão  #FanMunMat 39

Ernst Zermelo

ZermeloFraenkel Set Theory

A (very) Brief History of David Hilbert

Crisis in the Foundation of Mathematics  Infinite Series
Transcription
Life
Ernst Zermelo graduated from Berlin's Luisenstädtisches Gymnasium (now HeinrichSchliemannOberschulemathematics, physics and philosophy at the University of Berlin, the University of Halle, and the University of 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 the University of Göttingen, at that time the leading centre for mathematical research in the world, where he completed his habilitation thesis in 1899.
) in 1889. He then studiedIn 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 the University of Freiburg in 1926, which he resigned in 1935 because he disapproved of Adolf Hitler's regime.^{[2]} At the end of World War II and at his request, Zermelo was reinstated to his honorary position in Freiburg.
Research in set theory
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, and in the course of its statement Hilbert mentioned also the need to prove the wellordering theorem.
Zermelo began to work on the problems of set theory under Hilbert's influence and in 1902 published his first work concerning the addition of transfinite cardinals. By that time he had also discovered the socalled Russell paradox. In 1904, he succeeded in taking the first step suggested by Hilbert towards the continuum hypothesis when he proved the wellordering 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 wellordering theorem, based on the powerset axiom and the axiom of choice, was not accepted by all mathematicians, mostly because the axiom of choice was a paradigm of nonconstructive mathematics. In 1908, Zermelo succeeded in producing an improved proof making use of Dedekind's notion of the "chain" of a set, which became more widely accepted; this was mainly because that same year he also offered an axiomatization of set theory.
Zermelo began to axiomatize set theory in 1905; 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.
In 1922, Abraham Fraenkel and Thoralf Skolem independently improved Zermelo's axiom system. The resulting system, now called Zermelo–Fraenkel axioms (ZF), is now the most commonly used system for axiomatic set theory.
Proposed in 1931, the Zermelo's navigation problem is a classic optimal control problem. The problem deals with a boat navigating on a body of water, originating from a point O to a destination point D. The boat is capable of a certain maximum speed, and we want to derive the best possible control to reach D in the least possible time.
Without considering external forces such as current and wind, the optimal control is for the boat to always head towards D. Its path then is a line segment from O to D, which is trivially optimal. With consideration of current and wind, if the combined force applied to the boat is nonzero, the control for no current and wind does not yield the optimal path.
Publications
 Zermelo, Ernst (2013), Ebbinghaus, HeinzDieter; Fraser, Craig G.; Kanamori, Akihiro (eds.), Ernst Zermelo—collected works. Vol. I. Set theory, miscellanea, Schriften der MathematischNaturwissenschaftlichen Klasse der Heidelberger Akademie der Wissenschaften, vol. 21, Berlin: SpringerVerlag, doi:10.1007/9783540793847, ISBN 9783540793830, MR 2640544
 Zermelo, Ernst (2013), Ebbinghaus, HeinzDieter; Kanamori, Akihiro (eds.), Ernst Zermelo—collected works. Vol. II. Calculus of variations, applied mathematics, and physics, Schriften der MathematischNaturwissenschaftlichen Klasse der Heidelberger Akademie der Wissenschaften, vol. 23, Berlin: SpringerVerlag, doi:10.1007/9783540708568, ISBN 9783540708551, MR 3137671
 Jean van Heijenoort, 1967. From Frege to Gödel: A Source Book in Mathematical Logic, 1879–1931. Harvard Univ. Press.
 1904. "Proof that every set can be wellordered," 139−41.
 1908. "A new proof of the possibility of wellordering," 183–98.
 1908. "Investigations in the foundations of set theory I," 199–215.
 1913. "On an Application of Set Theory to the Theory of the Game of Chess" in Rasmusen E., ed., 2001. Readings in Games and Information, WileyBlackwell: 79–82.
 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 University Press: 1219–33.
Works by others:
 Zermelo's Axiom of Choice, Its Origins, Development, & Influence, Gregory H. Moore, being Volume 8 of Studies in the History of Mathematics and Physical Sciences, Springer Verlag, New York, 1982.
See also
 Axiom of choice
 Axiom of infinity
 Axiom of limitation of size
 Axiom of union
 Boltzmann brain
 Choice function
 Cumulative hierarchy
 Pairwise comparison
 Von Neumann universe
 14990 Zermelo, asteroid
References
 Dirk Van Dalen; HeinzDieter Ebbinghaus (June 2000). "Zermelo and the Skolem Paradox". The Bulletin of Symbolic Logic. 6 (2): 145–161. CiteSeerX 10.1.1.137.3354. doi:10.2307/421203. hdl:1874/27769. JSTOR 421203. S2CID 8530810.
 GrattanGuinness, Ivor (2000) The Search for Mathematical Roots 1870–1940. Princeton University Press.
 Kanamori, Akihiro (2004). "Zermelo and set theory". The Bulletin of Symbolic Logic. 10 (4): 487–553. doi:10.2178/bsl/1102083759. MR 2136635. S2CID 231795240.
 Schwalbe, Ulrich; Walker, Paul (2001). "Zermelo and the Early History of Game Theory" (PDF). Games and Economic Behavior. 34 (1): 123–137. doi:10.1006/game.2000.0794. Archived from the original (PDF) on 1 April 2017.
 Ebbinghaus, HeinzDieter (2007) Ernst Zermelo: An Approach to His Life and Work. Springer. ISBN 3642080502
Citations
 ^ Zermelo, Ernst (1929). "Die Berechnung der TurnierErgebnisse als ein Maximumproblem der Wahrscheinlichkeitsrechnung". Mathematische Zeitschrift. 29 (1): 436–460. doi:10.1007/BF01180541. S2CID 122877703.
 ^ KAPLANSKY, IRVING (2020). SET THEORY AND METRIC SPACES. PROVIDENCE: AMER MATHEMATICAL SOCIETY. pp. 36–37. ISBN 9781470463847.
External links
 Works by or about Ernst Zermelo at Internet Archive
 O'Connor, John J.; Robertson, Edmund F., "Ernst Zermelo", MacTutor History of Mathematics Archive, University of St Andrews
 Zermelo Navigation