Gyula Kőnig was a Hungarian mathematician

Mathematician

A mathematician is a person whose primary area of study is the field of mathematics. Mathematicians are concerned with quantity, structure, space, and change....

. He was born in Győr

Gyor

-Climate:-Main sights:The ancient core of the city is Káptalan Hill at the confluence of three rivers: the Danube, Rába and Rábca. Püspökvár, the residence of Győr’s bishops can be easily recognised by its incomplete tower. Győr’s oldest buildings are the 13th-century dwelling tower and the...

, Hungary

Hungary

Hungary , officially the Republic of Hungary , is a landlocked country in Central Europe. It is situated in the Carpathian Basin and is bordered by Slovakia to the north, Ukraine and Romania to the east, Serbia and Croatia to the south, Slovenia to the southwest and Austria to the west. The...

 and died in Budapest

Budapest

Budapest is the capital of Hungary. As the largest city of Hungary, it is the country's principal political, cultural, commercial, industrial, and transportation centre. In 2011, Budapest had 1,733,685 inhabitants, down from its 1989 peak of 2,113,645 due to suburbanization. The Budapest Commuter...

. His mathematical publications in foreign languages appeared under the name Julius König. His son Denes Konig

Dénes König

Dénes Kőnig was a Jewish Hungarian mathematician who worked in and wrote the first textbook on the field of graph theory....

 is the famous graph theorist.

Biography

Kőnig's name in Hungarian was Kőnig Gyula or in the more common European name order Gyula Kőnig, but when Kőnig contributed to German mathematical journals he called himself "Julius König."

Gyula Kőnig was highly gifted literarily and mathematically. He studied medicine in Vienna

Vienna

Vienna is the capital and largest city of the Republic of Austria and one of the nine states of Austria. Vienna is Austria's primary city, with a population of about 1.723 million , and is by far the largest city in Austria, as well as its cultural, economic, and political centre...

 and, from 1868 on, in Heidelberg

Heidelberg

-Early history:Between 600,000 and 200,000 years ago, "Heidelberg Man" died at nearby Mauer. His jaw bone was discovered in 1907; with scientific dating, his remains were determined to be the earliest evidence of human life in Europe. In the 5th century BC, a Celtic fortress of refuge and place of...

. After having worked, instructed by Hermann von Helmholtz

Hermann von Helmholtz

Hermann Ludwig Ferdinand von Helmholtz was a German physician and physicist who made significant contributions to several widely varied areas of modern science...

, on electrical stimulation of nerves, he switched to mathematics and obtained his doctorate under the supervision of Leo Königsberger

Leo Königsberger

Leo Königsberger 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.-Biography:...

, a very famous mathematician at that time. His thesis Zur Theorie der Modulargleichungen der elliptischen Functionen covers 24 pages. As a post-doc he completed his mathematical studies in Berlin

Berlin

Berlin is the capital city of Germany and is one of the 16 states of Germany. With a population of 3.45 million people, Berlin is Germany's largest city. It is the second most populous city proper and the seventh most populous urban area in the European Union...

 attending lessons by Leopold Kronecker

Leopold Kronecker

Leopold Kronecker was a German mathematician who worked on number theory and algebra.He criticized Cantor's work on set theory, and was quoted by as having said, "God made integers; all else is the work of man"...

 and Karl Weierstraß. He then returned to Budapest where he was appointed as a dozent 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. In 1905 he retired but continued to give lessons on topics of his interest. His son Dénes

Dénes König

Dénes Kőnig was a Jewish Hungarian mathematician who worked in and wrote the first textbook on the field of graph theory....

 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

Leopold Kronecker was a German mathematician who worked on number theory and algebra.He criticized Cantor's work on set theory, and was quoted by as having said, "God made integers; all else is the work of man"...

 and David Hilbert

David Hilbert

David Hilbert was a German mathematician. He is recognized as one of the most influential and universal mathematicians of the 19th and early 20th centuries. Hilbert discovered and developed a broad range of fundamental ideas in many areas, including invariant theory and the axiomatization of...

 as well as Emmy Noether

Emmy Noether

Amalie Emmy Noether was an influential German mathematician known for her groundbreaking contributions to abstract algebra and theoretical physics. Described by David Hilbert, Albert Einstein and others as the most important woman in the history of mathematics, she revolutionized the theories of...

. 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

Set theory is the branch of mathematics that studies sets, which are collections of objects. Although any type of object can be collected into a set, set theory is applied most often to objects that are relevant to mathematics...

.

Kőnig and set theory

One of the greatest achievements of Georg Cantor 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

Continued fraction

In mathematics, a continued fraction is an expression obtained through an iterative process of representing a number as the sum of its integer part and the reciprocal of another number, then writing this other number as the sum of its integer part and another reciprocal, and so on...

s. Kőnig found a simple method involving decimal numbers which had escaped Cantor.

1904, on the III. international mathematical congress at Heidelberg Kőnig gave a talk to disprove Cantor's continuum hypothesis

Continuum hypothesis

In mathematics, the continuum hypothesis is a hypothesis, advanced by Georg Cantor in 1874, about the possible sizes of infinite sets. It states:Establishing the truth or falsehood of the continuum hypothesis is the first of Hilbert's 23 problems presented in the year 1900...

. 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 Felix Bernstein; this theorem, however, was not as generally valid as Bernstein had claimed. Ernst Zermelo

Ernst Zermelo

Ernst Friedrich Ferdinand Zermelo was a German mathematician, whose work has major implications for the foundations of mathematics and hence on philosophy. He is known for his role in developing Zermelo–Fraenkel axiomatic set theory and his proof of the well-ordering theorem.-Life:He graduated...

, 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 proving that not all sets could be well-ordered.
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 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

Richard's paradox

In logic, Richard's paradox is a semantical antinomy in set theory and natural language first described by the French mathematician Jules Richard in 1905. Today, the paradox is ordinarily used in order to motivate the importance of carefully distinguishing between mathematics and metamathematics...

.

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 Jourdain

Philip Edward Bertrand Jourdain was a British logician and follower of Bertrand Russell.He was born in Ashbourne in Derbyshire one of a large family belonging to Emily Clay and his father Francis Jourdain . He was partly disabled by Friedreich's ataxia...

 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 60 (1905) 177-180.
• Über die Grundlagen der Mengenlehre und das Kontinuumproblem, Mathematische Annalen 61 (1905) 156-160.
• Über die Grundlagen der Mengenlehre und das Kontinuumproblem (Zweite Mitteilung), Mathematische Annalen 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.
• J. J. O'Connor, E. F. Robertson: The MacTutor History of Mathematics archive
• including two portraits of Gyula Kőnig
• Niedersächsische Staats- und Universitätsbibliothek Göttingen, Digitalisierungszentrum,
• Universitätsbibliothek Heidelberg
• The Mathematics Genealogy Project