Gyula Kőnig
   HOME

TheInfoList



OR:

Gyula Kőnig (16 December 1849 – 8 April 1913) was a
mathematician A mathematician is someone who uses an extensive knowledge of mathematics in their work, typically to solve mathematical problems. Mathematicians are concerned with numbers, data, quantity, mathematical structure, structure, space, Mathematica ...
from
Hungary Hungary is a landlocked country in Central Europe. Spanning much of the Pannonian Basin, Carpathian Basin, it is bordered by Slovakia to the north, Ukraine to the northeast, Romania to the east and southeast, Serbia to the south, Croatia and ...
. His mathematical publications in German appeared under the name Julius König. His son
Dénes Kőnig Dénes Kőnig (September 21, 1884 – October 19, 1944) was a Hungarian mathematician of Hungarian Jewish heritage who worked in and wrote the first textbook on the field of graph theory. Biography Kőnig was born in Budapest, the son of mathemat ...
was a graph theorist.


Biography

Gyula Kőnig was active literarily and mathematically. He studied medicine in
Vienna Vienna ( ; ; ) is the capital city, capital, List of largest cities in Austria, most populous city, and one of Federal states of Austria, nine federal states of Austria. It is Austria's primate city, with just over two million inhabitants. ...
and, from 1868 on, in
Heidelberg Heidelberg (; ; ) is the List of cities in Baden-Württemberg by population, fifth-largest city in the States of Germany, German state of Baden-Württemberg, and with a population of about 163,000, of which roughly a quarter consists of studen ...
. After having worked, instructed by
Hermann von Helmholtz Hermann Ludwig Ferdinand von Helmholtz (; ; 31 August 1821 – 8 September 1894; "von" since 1883) was a German physicist and physician who made significant contributions in several scientific fields, particularly hydrodynamic stability. The ...
, on electrical stimulation of nerves, he switched to mathematics. He obtained his doctorate under the supervision of the mathematician
Leo Königsberger Leo Königsberger (15 October 1837 – 15 December 1921) was a German mathematician, and historian of science. He is best known for his three-volume biography of Hermann von Helmholtz, which remains the standard reference on the subject. Biog ...
. His thesis ''Zur Theorie der Modulargleichungen der elliptischen Functionen'' covers 24 pages. As a post-doc he completed his mathematical studies in
Berlin Berlin ( ; ) is the Capital of Germany, capital and largest city of Germany, by both area and List of cities in Germany by population, population. With 3.7 million inhabitants, it has the List of cities in the European Union by population withi ...
attending lessons by
Leopold Kronecker Leopold Kronecker (; 7 December 1823 – 29 December 1891) was a German mathematician who worked on number theory, abstract algebra and logic, and criticized Georg Cantor's work on set theory. Heinrich Weber quoted Kronecker as having said, ...
and Karl Weierstraß. He then returned to Budapest, where he was appointed as a ''
dozent The term "docent" is derived from the Latin word , which is the third-person plural present active indicative of ('to teach, to lecture'). Becoming a docent is often referred to as habilitation or doctor of science and is an academic qualifica ...
'' at the university in 1871. He became a professor at the Teacher's College in Budapest in 1873 and, in the following year, was appointed professor at the Technical University of Budapest. He remained with the university for the rest of his life. He was on three occasions dean of the Engineering Faculty and also on three occasions was rector of the university. In 1889 he was elected a member of the Hungarian Academy of Sciences. Although of Jewish descent, Kőnig converted to Christianity soon after his election. In 1905 he retired but continued to give lessons on topics of his interest. His son Dénes also became a distinguished mathematician.


Works

Kőnig worked in many mathematical fields. His work on polynomial ideals, discriminants and elimination theory can be considered as a link between
Leopold Kronecker Leopold Kronecker (; 7 December 1823 – 29 December 1891) was a German mathematician who worked on number theory, abstract algebra and logic, and criticized Georg Cantor's work on set theory. Heinrich Weber quoted Kronecker as having said, ...
and
David Hilbert David Hilbert (; ; 23 January 1862 – 14 February 1943) was a German mathematician and philosopher of mathematics and one of the most influential mathematicians of his time. Hilbert discovered and developed a broad range of fundamental idea ...
as well as
Emmy Noether Amalie Emmy Noether (23 March 1882 – 14 April 1935) was a German mathematician who made many important contributions to abstract algebra. She also proved Noether's theorem, Noether's first and Noether's second theorem, second theorems, which ...
. Later on his ideas were simplified considerably, to the extent that today they are only of historical interest. Kőnig already considered material influences on scientific thinking and the mechanisms which stand behind thinking. But mainly he is remembered for his contributions to and his opposition against
set theory Set theory is the branch of mathematical logic that studies Set (mathematics), sets, which can be informally described as collections of objects. Although objects of any kind can be collected into a set, set theory – as a branch of mathema ...
.


Kőnig and set theory

One of the greatest achievements of
Georg Cantor Georg Ferdinand Ludwig Philipp Cantor ( ; ;  – 6 January 1918) was a mathematician who played a pivotal role in the creation of set theory, which has become a foundations of mathematics, fundamental theory in mathematics. Cantor establi ...
was the construction of a one-to-one correspondence between the points of a square and the points of one of its edges by means of
continued fraction A continued fraction is a mathematical expression that can be written as a fraction with a denominator that is a sum that contains another simple or continued fraction. Depending on whether this iteration terminates with a simple fraction or not, ...
s. Kőnig found a simple method involving decimal numbers which had escaped Cantor. In 1904, at the third
International Congress of Mathematicians The International Congress of Mathematicians (ICM) is the largest conference for the topic of mathematics. It meets once every four years, hosted by the International Mathematical Union (IMU). The Fields Medals, the IMU Abacus Medal (known before ...
at
Heidelberg Heidelberg (; ; ) is the List of cities in Baden-Württemberg by population, fifth-largest city in the States of Germany, German state of Baden-Württemberg, and with a population of about 163,000, of which roughly a quarter consists of studen ...
, Kőnig gave a talk to disprove Cantor's
continuum hypothesis In mathematics, specifically set theory, the continuum hypothesis (abbreviated CH) is a hypothesis about the possible sizes of infinite sets. It states: Or equivalently: In Zermelo–Fraenkel set theory with the axiom of choice (ZFC), this ...
. The announcement was a sensation and was widely reported by the press. All section meetings were cancelled so that everyone could hear his contribution. Kőnig applied a theorem proved in the thesis of
Hilbert David Hilbert (; ; 23 January 1862 – 14 February 1943) was a German mathematician and philosophy of mathematics, philosopher of mathematics and one of the most influential mathematicians of his time. Hilbert discovered and developed a broad ...
's student Felix Bernstein; this theorem, however, was not as generally valid as Bernstein had claimed.
Ernst Zermelo Ernst Friedrich Ferdinand Zermelo (; ; 27 July 187121 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 set theory, Z ...
, the later editor of Cantor's collected works, found the error already the next day. In 1905 there appeared short notes by Bernstein, correcting his theorem, and Kőnig, withdrawing his claim. Nevertheless, Kőnig continued his efforts to disprove parts of set theory. In 1905 he published a paper that claimed to prove that not all sets could be
well-ordered In mathematics, a well-order (or well-ordering or well-order relation) on a set is a total ordering on with the property that every non-empty subset of has a least element in this ordering. The set together with the ordering is then called a ...
. This statement was doubted by Cantor in a letter to Hilbert in 1906: Cantor was wrong. Today Kőnig's assumption is generally accepted. Contrary to Cantor, presently the majority of mathematicians considers
undefinable numbers Informally, a definable real number is a real number that can be uniquely specified by its description. The description may be expressed as a construction or as a formula of a formal language. For example, the positive square root of 2, \sqrt, c ...
not as absurdities. This assumption leads, according to Kőnig, Kőnig's conclusion is not stringent. His argument does not rule out the possibility that the continuum can be well-ordered; rather, it rules out the conjunction of "the continuum can be well-ordered by a definition in language L" and "the property of being definable in language L is itself definable in language L". The latter is no longer generally held to be true. For an explanation compare
Richard's paradox In logic, Richard's paradox is a semantical antinomy of set theory and natural language first described by the French mathematician Jules Richard in 1905. The paradox is ordinarily used to motivate the importance of distinguishing carefully betwe ...
. The last part of his life Kőnig spent working on his own approach to set theory, logic and arithmetic, which was published in 1914, one year after his death. When he died he had been working on the final chapter of the book.


About Kőnig

At first Georg Cantor highly esteemed Kőnig. In a letter to
Philip Jourdain Philip Edward Bertrand Jourdain (16 October 1879 – 1 October 1919) was a British mathematician, logician and follower of Bertrand Russell. Background He was born in Ashbourne in Derbyshire* one of a large family belonging to Emily Clay and ...
in 1905 he wrote: Later on Cantor changed his attitude:


Some papers and books by Kőnig

*''Zur Theorie der Modulargleichungen der elliptischen Functionen'', Thesis, Heidelberg 1870. *''Ueber eine reale Abbildung der s.g. Nicht-Euclidischen Geometrie'', Nachrichten von der Königl. Gesellschaft der Wissenschaften und der Georg-August-Universität zu Göttingen, No. 9 (1872) 157-164. *''Einleitung in die allgemeine Theorie der Algebraischen Groessen'', Leipzig 1903. *
Zum Kontinuum-Problem
'',
Mathematische Annalen ''Mathematische Annalen'' (abbreviated as ''Math. Ann.'' or, formerly, ''Math. Annal.'') is a German mathematical research journal founded in 1868 by Alfred Clebsch and Carl Neumann. Subsequent managing editors were Felix Klein, David Hilbert, ...
60 (1905) 177-180. *
Über die Grundlagen der Mengenlehre und das Kontinuumproblem
',
Mathematische Annalen ''Mathematische Annalen'' (abbreviated as ''Math. Ann.'' or, formerly, ''Math. Annal.'') is a German mathematical research journal founded in 1868 by Alfred Clebsch and Carl Neumann. Subsequent managing editors were Felix Klein, David Hilbert, ...
61 (1905) 156-160. *
Über die Grundlagen der Mengenlehre und das Kontinuumproblem
'' (Zweite Mitteilung),
Mathematische Annalen ''Mathematische Annalen'' (abbreviated as ''Math. Ann.'' or, formerly, ''Math. Annal.'') is a German mathematical research journal founded in 1868 by Alfred Clebsch and Carl Neumann. Subsequent managing editors were Felix Klein, David Hilbert, ...
63 (1907) 217-221. *''Neue Grundlagen der Logik, Arithmetik und Mengenlehre'', Leipzig 1914.


Literature and links

*Brockhaus: Die Enzyklopädie, 20th ed. vol. 12, Leipzig 1996, p. 148. *W. Burau: Dictionary of Scientific Biography vol. 7, New York 1973, p. 444. *H. Meschkowski, W. Nilson (eds.): Georg Cantor Briefe, Berlin 1991. *W. Mückenheim: Die Mathematik des Unendlichen, Aachen 2006. *B. Szénássy, History of Mathematics in Hungary until the 20th Century, Berlin 1992. * *Niedersächsische Staats- und Universitätsbibliothek Göttingen, Digitalisierungszentrum, *Universitätsbibliothek HeidelbergJulius Koenig
at www.ub.uni-heidelberg.de *


Notes

{{DEFAULTSORT:Konig, Gyula 1849 births 1913 deaths Members of the Hungarian Academy of Sciences 20th-century Hungarian mathematicians Mathematicians from Austria-Hungary Hungarian people of Jewish descent