Ernst Friedrich Ferdinand Zermelo (July 27, 1871, Berlin, German Empire – May 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. Events 1214 - Battle of Bouvines: In France, Philip II of France defeats John of England. Year 1871 ( MDCCCLXXI) was a Common year starting on Sunday (link will display the full calendar of the Gregorian calendar (or a Common Berlin is the capital city and one of sixteen states of Germany. The German Empire is the name commonly used in English to describe Germany from 1871 to 1918 when it was a semi- Constitutional monarchy: beginning with the Unification Events 878 - Syracuse Italy is captured by the Muslim sultan of Sicily. Year 1953 ( MCMLIII) was a Common year starting on Thursday (link will display full calendar of the Gregorian calendar. West Germany ( Inf German: Westdeutschland or West-Deutschland) was the common English name for the Federal Republic of Germany ( Germany, officially the Federal Republic of Germany ( ˈbʊndəsʁepuˌbliːk ˈdɔʏtʃlant is a Country in Central Europe. A mathematician is a person whose primary area of study and research is the field of Mathematics. Foundations of mathematics is a term sometimes used for certain fields of Mathematics, such as Mathematical logic, Axiomatic set theory, Proof theory Philosophy is the study of general problems concerning matters such as existence knowledge truth beauty justice validity mind and language
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Life
He graduated from Berlin's Luisenstädtisches Gymnasium in 1889. Year 1889 ( MDCCCLXXXIX) was a Common year starting on Tuesday (link will display the full calendar of the Gregorian calendar (or a Common He then studied mathematics, physics and philosophy at the universities of Berlin, Halle and Freiburg. Mathematics is the body of Knowledge and Academic discipline that studies such concepts as Quantity, Structure, Space and Physics (Greek Physis - φύσις in everyday terms is the Science of Matter and its motion. Philosophy is the study of general problems concerning matters such as existence knowledge truth beauty justice validity mind and language Berlin is the capital city and one of sixteen states of Germany. Halle is the largest city in the German State of Saxony-Anhalt. He finished his doctorate in 1894 at the University of Berlin, awarded for a dissertation on the calculus of variations (Untersuchungen zur Variationsrechnung). Year 1894 ( MDCCCXCIV) was a Common year starting on Monday (link will display the full calendar of the Gregorian calendar (or a Common Calculus of variations is a field of Mathematics that deals with functionals, as opposed to ordinary Calculus which deals with functions. Zermelo remained at the University of Berlin, where he was appointed assistant to Planck, under whose guidance he began to study hydrodynamics. Fluid dynamics is the sub-discipline of Fluid mechanics dealing with fluid flow: Fluids ( Liquids and Gases in motion 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. Year 1897 ( MDCCCXCVII) was a Common year starting on Friday (link will display the full calendar of the Gregorian Calendar (or a Common Göttingen ( ˈgœtɪŋən, Low German: Chöttingen is a College town in Lower Saxony, Germany. Habilitation is the highest academic qualification a person can achieve by their own pursuit in certain European and Asian countries Year 1899 ( MDCCCXCIX) was a Common year starting on Sunday (link will display the full calendar of the Gregorian calendar (or a Common
In 1910, Zermelo left Göttingen upon being appointed to the chair of mathematics at Zurich University, which he resigned in 1916. Year 1910 ( MCMX) was a Common year starting on Saturday (link will display calendar of the Gregorian calendar (or a Common year starting The University of Zurich ( German: Universität Zürich) located in the city of Zurich, is the largest University in Switzerland Year 1916 ( MCMXVI) was a Leap year starting on Saturday (link will display the full calendar of the Gregorian calendar (or a Leap year 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. Year 1926 ( MCMXXVI) was a Common year starting on Friday (link will display the full calendar of the Gregorian calendar. Year 1935 ( MCMXXXV) was a Common year starting on Tuesday (link will display full calendar of the Gregorian calendar. At the end of World War II and at his request, Zermelo was reinstated to his honorary position in Freiburg. World War II, or the Second World War, (often abbreviated WWII) was a global military conflict which involved a majority of the world's nations, including
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. Year 1900 ( MCM) was an exceptional Common year starting on Monday (link will display the full calendar of the Gregorian calendar The International Congress of Mathematicians (ICM is the largest congress in the Mathematics community David Hilbert ( January 23, 1862 &ndash February 14, 1943) was a German Mathematician, recognized as one of the most Hilbert's problems are a list of twenty-three problems in Mathematics put forth by German Mathematician David Hilbert at the Paris The first of these, a problem of set theory, was the continuum hypothesis introduced by Cantor in 1878. In Mathematics, the continuum hypothesis (abbreviated CH) is a Hypothesis, advanced by Georg Cantor, about the possible sizes of Infinite Georg Ferdinand Ludwig Philipp Cantor ( – January 6 1918) was a German Mathematician, born in Russia. Year 1878 ( MDCCCLXXVIII) was a Common year starting on Tuesday (link will display the full calendar of the Gregorian calendar (or a Common
Zermelo began to work on the problems of set theory and in 1902 published his first work concerning the addition of transfinite cardinals. Year 1902 ( MCMII) was a Common year starting on Wednesday (link will display calendar of the Gregorian calendar (or a Common year starting This article describes cardinal numbers in mathematics For cardinals in linguistics see Names of numbers in English. 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). In Mathematics, the continuum hypothesis (abbreviated CH) is a Hypothesis, advanced by Georg Cantor, about the possible sizes of Infinite The well-ordering theorem (not to be confused with the Well-ordering axiom) states that every set can be Well-ordered This is important because it makes This result brought fame to Zermelo, who was appointed Professor in Göttingen, in 1905. Year 1905 ( MCMV) was a Common year starting on Sunday (link will display full calendar of the Gregorian calendar (or a Common year starting 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. The well-ordering theorem (not to be confused with the Well-ordering axiom) states that every set can be Well-ordered This is important because it makes In Mathematics, the axiom of choice, or AC, is an Axiom of Set theory. In Mathematics, an axiomatic system is any set of Axioms from which some or all axioms can be used in conjunction to logically derive Theorems In 1908, Zermelo succeeded in producing a much more widely-accepted proof. Year 1908 ( MCMVIII) was a Leap year starting on Wednesday (link will display the full calendar of the Gregorian calendar (or a Leap year
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. Year 1905 ( MCMV) was a Common year starting on Sunday (link will display full calendar of the Gregorian calendar (or a Common year starting Year 1908 ( MCMVIII) was a Leap year starting on Wednesday (link will display the full calendar of the Gregorian calendar (or a Leap year See the article on Zermelo set theory for an outline of this paper, together with the original axioms, with the original numbering. 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. Year 1922 ( MCMXXII) was a Common year starting on Sunday of the Gregorian calendar. Abraham Halevi (Adolf Fraenkel (אברהם הלוי (אדולף פרנקל February 17 1891 Munich, Germany – October 15 Thoralf Albert Skolem ( May 23, 1887 – March 23, 1963) (ˈtɔɾɑlf ˈskuləm was a Norwegian Mathematician known The resulting 10 axiom system, now called Zermelo-Fraenkel axioms (ZF), is now the most commonly used system for axiomatic set theory. Zermelo–Fraenkel set theory with the axiom of choice, commonly abbreviated ZFC, is the standard form of Axiomatic set theory and as such is the most common
Zermelo's Navigation Problem
Proposed in 1913, the Zermelo's Navigation Problem is a classic optimal control problem. Optimal control theory, a modern extension of the Calculus of variations, is a mathematical optimization method for deriving control policies. The problems 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 to follow a straight line segment from O to D. WIth consideration of current and wind, the shortest path from O to D is in fact, not the optimal solution.
See also
Bibliography
Primary literature in English translation:
- Jean van Heijenoort, 1967. Zermelo–Fraenkel set theory with the axiom of choice, commonly abbreviated ZFC, is the standard form of Axiomatic set theory and as such is the most common Jean Louis Maxime Van Heijenoort (pronounced highenort) ( July 23 1912, Creil France - March 29 1986, Mexico City 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:
- Ivor Grattan-Guinness, 2000. Ivor Grattan-Guinness (Born 23 June 1941 Bakewell, England is a Historian of mathematics and Logic. The Search for Mathematical Roots 1870-1940. Princeton Uni. Press.
External links
- O'Connor, John J. & Robertson, Edmund F. , “Ernst Zermelo”, MacTutor History of Mathematics archive
- Ernst Zermelo at the Mathematics Genealogy Project
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