Đuro Kurepa (

Serbian Cyrillic The Serbian Cyrillic alphabet ( sr, / , ) is a variation of the Cyrillic script used to write the Serbian language, updated in 1818 by Serbian linguist Vuk Karadžić. It is one of the two alphabets used to write standard modern Serbian, t ...

: Ђуро Курепа, ; 16 August 1907 – 2 November 1993) was a Yugoslav

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, structure, space, models, and change. History On ...

. Throughout his life, Kurepa published over 700 articles, books, papers, and reviews and over 1,000 scientific reviews. He lectured at universities across Europe, as well as those in Canada, Cuba, Iraq, Israel, and the United States, and was quoted saying "I lectured at almost each of henineteen universities of he former

Yugoslavia Yugoslavia (; sh-Latn-Cyrl, separator=" / ", Jugoslavija, Југославија ; sl, Jugoslavija ; mk, Југославија ;; rup, Iugoslavia; hu, Jugoszlávia; rue, label=Pannonian Rusyn, Югославия, translit=Juhoslavija ...

..." His nephew was the noted mathematician Svetozar Kurepa. In English, his name was transliterated as Djuro Kurepa while in French he is often attributed as Georges Kurepa.

Early life

Born in

Majske Poljane Majske Poljane is a village in central Croatia, in the municipality/town of Glina, Sisak-Moslavina County. The village's geographic coordinates are , the altitude is 162 meters above sea level. The village was severely affected by the 2020 Petrin ...

, Kingdom of Croatia-Slavonia,

Austria-Hungary Austria-Hungary, often referred to as the Austro-Hungarian Empire,, the Dual Monarchy, or Austria, was a constitutional monarchy and great power in Central Europe between 1867 and 1918. It was formed with the Austro-Hungarian Compromise of ...

to a

Serb The Serbs ( sr-Cyr, Срби, Srbi, ) are the most numerous South Slavic ethnic group native to the Balkans in Southeastern Europe, who share a common Serbian ancestry, culture, history and language. The majority of Serbs live in their na ...

family, Kurepa was the youngest of Rade and Anđelija Kurepa's fourteen children. He began his schooling in Majske Poljane, continued his education in Glina, and graduated from high school in

Križevci Križevci (; la, Crisium; hu, Kőrös ; german: Kreutz ) is a city in central Croatia with a total population of 21,122 and with 11,231 in the city itself (2011), the oldest city in its county, the Koprivnica-Križevci County. History The f ...

. He received a diploma in theoretical mathematics and physics from the

University of Zagreb The University of Zagreb ( hr, Sveučilište u Zagrebu, ; la, Universitas Studiorum Zagrabiensis) is the largest Croatian university and the oldest continuously operating university in the area covering Central Europe south of Vienna and all of ...

in 1931, and began work as an assistant in the teaching of mathematics the same year. Kurepa then went to the

Collège de France The Collège de France (), formerly known as the ''Collège Royal'' or as the ''Collège impérial'' founded in 1530 by François I, is a higher education and research establishment ('' grand établissement'') in France. It is located in Paris n ...

and the

University of Paris , image_name = Coat of arms of the University of Paris.svg , image_size = 150px , caption = Coat of Arms , latin_name = Universitas magistrorum et scholarium Parisiensis , motto = ''Hic et ubique terrarum'' (Latin) , mottoeng = Here and a ...

, where he received his doctoral diploma in 1935; his advisor was French mathematician

Maurice René Fréchet Maurice may refer to: People *Saint Maurice (died 287), Roman legionary and Christian martyr *Maurice (emperor) or Flavius Mauricius Tiberius Augustus (539–602), Byzantine emperor *Maurice (bishop of London) (died 1107), Lord Chancellor and Lo ...

, and his thesis was titled ''Ensembles ordonnés et ramifiés''.

Middle years

Kurepa continued to receive post-doctoral education at

Warsaw University The University of Warsaw ( pl, Uniwersytet Warszawski, la, Universitas Varsoviensis) is a public university in Warsaw, Poland. Established in 1816, it is the largest institution of higher learning in the country offering 37 different fields of ...

Poland Poland, officially the Republic of Poland, is a country in Central Europe. It is divided into 16 administrative provinces called voivodeships, covering an area of . Poland has a population of over 38 million and is the fifth-most populou ...

and the University of Paris. He became an assistant professor at the University of Zagreb in 1937, associate professor the next year, and assumed the position of full professor in 1948. After the end of

World War II World War II or the Second World War, often abbreviated as WWII or WW2, was a world war that lasted from 1939 to 1945. It involved the vast majority of the world's countries—including all of the great powers—forming two opposing ...

and the formation of the

Socialist Federal Republic of Yugoslavia The Socialist Federal Republic of Yugoslavia, commonly referred to as SFR Yugoslavia or simply as Yugoslavia, was a country in Central and Southeast Europe. It emerged in 1945, following World War II, and lasted until 1992, with the breakup of Yu ...

, he traveled to five universities in the United States:

Harvard University Harvard University is a private Ivy League research university in Cambridge, Massachusetts. Founded in 1636 as Harvard College and named for its first benefactor, the Puritan clergyman John Harvard, it is the oldest institution of high ...

Cambridge Cambridge ( ) is a College town, university city and the county town in Cambridgeshire, England. It is located on the River Cam approximately north of London. As of the 2021 United Kingdom census, the population of Cambridge was 145,700. Cam ...

Massachusetts Massachusetts (Massachusett: ''Muhsachuweesut Massachusett_writing_systems.html" ;"title="nowiki/> məhswatʃəwiːsət.html" ;"title="Massachusett writing systems">məhswatʃəwiːsət">Massachusett writing systems">məhswatʃəwiːsət'' En ...

, the

University of Chicago The University of Chicago (UChicago, Chicago, U of C, or UChi) is a private university, private research university in Chicago, Illinois. Its main campus is located in Chicago's Hyde Park, Chicago, Hyde Park neighborhood. The University of Chic ...

Chicago (''City in a Garden''); I Will , image_map = , map_caption = Interactive Map of Chicago , coordinates = , coordinates_footnotes = , subdivision_type = Country , subdivision_name ...

Illinois Illinois ( ) is a state in the Midwestern United States. Its largest metropolitan areas include the Chicago metropolitan area, and the Metro East section, of Greater St. Louis. Other smaller metropolitan areas include, Peoria and Rockf ...

, the branch of the

University of California The University of California (UC) is a public land-grant research university system in the U.S. state of California. The system is composed of the campuses at Berkeley, Davis, Irvine, Los Angeles, Merced, Riverside, San Diego, San Franci ...

at Berkeley and the branch at

Los Angeles Los Angeles ( ; es, Los Ángeles, link=no , ), often referred to by its initials L.A., is the List of municipalities in California, largest city in the U.S. state, state of California and the List of United States cities by population, sec ...

California California is a state in the Western United States, located along the Pacific Coast. With nearly 39.2million residents across a total area of approximately , it is the most populous U.S. state and the 3rd largest by area. It is also the m ...

the

Institute for Advanced Study The Institute for Advanced Study (IAS), located in Princeton, New Jersey, in the United States, is an independent center for theoretical research and intellectual inquiry. It has served as the academic home of internationally preeminent schola ...

Princeton Princeton University is a private research university in Princeton, New Jersey. Founded in 1746 in Elizabeth as the College of New Jersey, Princeton is the fourth-oldest institution of higher education in the United States and one of the ni ...

New Jersey New Jersey is a state in the Mid-Atlantic and Northeastern regions of the United States. It is bordered on the north and east by the state of New York; on the east, southeast, and south by the Atlantic Ocean; on the west by the Delaware ...

and

Columbia University Columbia University (also known as Columbia, and officially as Columbia University in the City of New York) is a private research university in New York City. Established in 1754 as King's College on the grounds of Trinity Church in Manhatt ...

New York City New York, often called New York City or NYC, is the most populous city in the United States. With a 2020 population of 8,804,190 distributed over , New York City is also the most densely populated major city in the Un ...

, New York. Kurepa was ICM Plenary Speaker in 1954 and 1958.

Later life

In 1965, Kurepa shifted to the

University of Belgrade The University of Belgrade ( sr, / ) is a public university in Serbia. It is the oldest and largest modern university in Serbia. Founded in 1808 as the Belgrade Higher School in revolutionary Serbia, by 1838 it merged with the Kragujevac-ba ...

, where he focused on the fields of

logic Logic is the study of correct reasoning. It includes both formal and informal logic. Formal logic is the science of deductively valid inferences or of logical truths. It is a formal science investigating how conclusions follow from premise ...

and

set theory Set theory is the branch of mathematical logic that studies 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 mathematics, is mostly conce ...

mathematics. Kurepa was a member of several organizations, including the

Serbian Academy of Sciences and Arts The Serbian Academy of Sciences and Arts ( la, Academia Scientiarum et Artium Serbica, sr-Cyr, Српска академија наука и уметности, САНУ, Srpska akademija nauka i umetnosti, SANU) is a national academy and the ...

and the

Yugoslav Academy of Sciences and Arts The Croatian Academy of Sciences and Arts ( la, Academia Scientiarum et Artium Croatica, hr, Hrvatska akademija znanosti i umjetnosti, abbrev. HAZU) is the national academy of Croatia. HAZU was founded under patronage of the Croatian bishop Jo ...

He was also the founder and president of the Society of Mathematicians and Physicists of Croatia, the founder and chief editor of the journal ''Mathematica Balkanica'', and the president of the Yugoslav National Committee for Mathematics, the Balkan Mathematical Society, and the Union of Yugoslav Societies of Mathematicians, Physicisists and Astronomers. He received the AVNOJ Award in 1976, and retired from the University of Belgrade in 1977. He died after being beaten by thugs and hidden from view under stairs.

Legacy

Kurepa influenced set theory mathematics in several ways, including lending his name to the

Kurepa tree In set theory, a Kurepa tree is a tree (''T'', <) of height ω₁, each of whose levels is at most countable, and has at ...

. According to Kajetan Šeper, Kurepa's colleague from the University of Zagreb:

Professor Kurepa was not only the professional mathematician and teacher, but he was a scientist, philosopher, and humanist as well, in the true sense of these words. He was the founder and pioneer in mathematical logic and the foundations of mathematics in Croatia, and modern mathematical theories in Croatia and Yugoslavia. Generally speaking, he was the catalyzer, the initiator, and the bearer of mathematical science.

According to the Mathematics Genealogy Project, Kurepa supervised 27 students, including set theorist Stevo Todorčević and topologist Ljubisa D.R. Kocinac.

Publications

References

External links

* (thesis in Paris)
Biography of Kurepa

Dimitrić, Radoslav. Academician, Professor Ðuro Kurepa (1907--1993). The Review of Modern Logic 1994. 4:401-403
{{DEFAULTSORT:Kurepa, Djuro 1907 births 1993 deaths 1993 murders in Europe 1990s murders in Serbia 20th-century mathematicians People from Glina, Croatia Serbs of Croatia Set theorists Serbian mathematicians University of Warsaw alumni University of Paris alumni Faculty of Science, University of Zagreb alumni University of Zagreb faculty University of Belgrade faculty Members of the Serbian Academy of Sciences and Arts Yugoslav mathematicians People murdered in Serbia Serbian murder victims Deaths by beating in Europe Unsolved murders in Serbia Burials at Belgrade New Cemetery