Jovan Karamata ( sr-Cyrl, Јован Карамата; February 1, 1902 – August 14, 1967) was a

Serbia , image_flag = Flag of Serbia.svg , national_motto = , image_coat = Coat of arms of Serbia.svg , national_anthem = () , image_map = , map_caption = Location of Serbia (gree ...

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 ...

and university professor. He is remembered for contributions to

analysis Analysis (: analyses) is the process of breaking a complex topic or substance into smaller parts in order to gain a better understanding of it. The technique has been applied in the study of mathematics and logic since before Aristotle (38 ...

, in particular, the Tauberian theory and the theory of slowly varying functions. Considered to be among the most influential Serbian mathematicians of the 20th century, Karamata was one of the founders of the Mathematical Institute of the

Serbian Academy of Sciences and Arts The Serbian Academy of Sciences and Arts (; , SANU) is a national academy and the most prominent academic institution in Serbia, founded in 1841 as Society of Serbian Letters (, DSS). The Academy's membership has included Nobel Prize, Nobel la ...

, established in 1946.

Life

Jovan Karamata was born in

Zagreb Zagreb ( ) is the capital (political), capital and List of cities and towns in Croatia#List of cities and towns, largest city of Croatia. It is in the Northern Croatia, north of the country, along the Sava river, at the southern slopes of the ...

on February 1, 1902, into a family descended from merchants based in the city of

Zemun Zemun ( sr-cyrl, Земун, ; ) is a Subdivisions of Belgrade, municipality in the city of Belgrade, Serbia. Zemun was a separate town that was absorbed into Belgrade in 1934. It lies on the right bank of the Danube river, upstream from downtown ...

, which was then in

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, and now in

Serbia , image_flag = Flag of Serbia.svg , national_motto = , image_coat = Coat of arms of Serbia.svg , national_anthem = () , image_map = , map_caption = Location of Serbia (gree ...

. Being of Aromanian origin, the family traced its roots back to

Pyrgoi Pyrgoi (, before 1927: Κατράνιτσα – ''Katranitsa'') is a village and a Communities and Municipalities of Greece, community of the Eordaia, Eordaia municipality. It is located in Northern Greece, in the region of Western Macedonia. Bef ...

Eordaia Eordaia () is a municipality in the Kozani regional unit, Western Macedonia, Greece. The seat of the municipality is the town Ptolemaida. The municipality has an area of 708.807 km2. The population was 42,515 in 2021. Municipality The munici ...

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''(his father Ioannis Karamatas was the president of the "Greek Community of Zemun")''; Aromanians mainly lived and still live in the area of modern

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.The Greek Communities in former Yugoslavia (17th - 20th century) republication of article of ''Kathimerini'' newspaper, from 12th of July 1998
/ref> Its business affairs on the borders of the

Austro-Hungarian Austria-Hungary, also referred to as the Austro-Hungarian Empire, the Dual Monarchy or the Habsburg Monarchy, was a multi-national constitutional monarchy in Central Europe between 1867 and 1918. A military and diplomatic alliance, it consist ...

and Ottoman empires were very well known. In 1914, he finished most of his primary school in Zemun but because of constant warfare on the borderlands, Karamata's father sent him, together with his brothers and his sister, to

Switzerland Switzerland, officially the Swiss Confederation, is a landlocked country located in west-central Europe. It is bordered by Italy to the south, France to the west, Germany to the north, and Austria and Liechtenstein to the east. Switzerland ...

for their own safety. In

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, 1920, he finished primary school oriented towards mathematics and sciences. In the same year he enrolled at the Engineering faculty of

Belgrade University The University of Belgrade () is a public research university in Belgrade, 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 Krag ...

and, after several years moved to the Philosophy and Mathematicians sector, where he graduated in 1925. He spent the years 1927–1928 in

Paris Paris () is the Capital city, capital and List of communes in France with over 20,000 inhabitants, largest city of France. With an estimated population of 2,048,472 residents in January 2025 in an area of more than , Paris is the List of ci ...

, as a fellow of the

Rockefeller Foundation The Rockefeller Foundation is an American private foundation and philanthropic medical research and arts funding organization based at 420 Fifth Avenue, New York City. The foundation was created by Standard Oil magnate John D. Rockefeller (" ...

, and in 1928 he became Assistant for Mathematics at the Faculty of Philosophy of Belgrade University. In 1930 he became Assistant Professor, in 1937 Associate Professor and, after the end of

World War II World War II or the Second World War (1 September 1939 – 2 September 1945) was a World war, global conflict between two coalitions: the Allies of World War II, Allies and the Axis powers. World War II by country, Nearly all of the wo ...

, in 1950 he became Full Professor. In 1951 he was elected Full Professor at the

University of Geneva The University of Geneva (French: ''Université de Genève'') is a public university, public research university located in Geneva, Switzerland. It was founded in 1559 by French theologian John Calvin as a Theology, theological seminary. It rema ...

. In 1933 he became a member of

Yugoslav Academy of Sciences and Arts The Croatian Academy of Sciences and Arts (; , HAZU) is the national academy of Croatia. HAZU was founded under the patronage of the Croatian bishop Josip Juraj Strossmayer under the name Yugoslav Academy of Sciences and Arts (, JAZU) since its ...

, Czech Royal Society in 1936, and Serbian Royal Academy in 1939 as well as a fellow of Serbian Academy of Sciences in 1948. He was one of the founders of the ''Mathematical Institute'' of the

in 1946. Karamata was member of the

Swiss Swiss most commonly refers to: * the adjectival form of Switzerland * Swiss people Swiss may also refer to: Places * Swiss, Missouri * Swiss, North Carolina * Swiss, West Virginia * Swiss, Wisconsin Other uses * Swiss Café, an old café located ...

, French and

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mathematical societies, the French Association for the Development of Science, and the primary editor of the journal ''L’Enseignement Mathématique'' in

Geneva Geneva ( , ; ) ; ; . is the List of cities in Switzerland, second-most populous city in Switzerland and the most populous in French-speaking Romandy. Situated in the southwest of the country, where the Rhône exits Lake Geneva, it is the ca ...

. He also taught at the

University of Novi Sad The University of Novi Sad ( sr-Cyrl-Latn, Универзитет у Новом Саду, Univerzitet u Novom Sadu; ) is a public university in Novi Sad, Serbia. Alongside nationally prestigious University of Belgrade, University of Novi Sad is ...

. In 1931 he married Emilija Nikolajevic, who gave birth to their two sons and two twin daughters. His wife died in 1959. After a long illness, Karamata died on August 14, 1967, in Geneva. His ashes rest in his native town of Zemun.

Legacy

Karamata published 122 scientific papers, 15 monographs and text-books as well as 7 professional-pedagogical papers. Karamata is best known for his work on

mathematical analysis Analysis is the branch of mathematics dealing with continuous functions, limit (mathematics), limits, and related theories, such as Derivative, differentiation, Integral, integration, measure (mathematics), measure, infinite sequences, series ( ...

. He introduced the notion of regularly varying function, and discovered a new class of theorems of Tauberian type, today known as Karamata's tauberian theorems. He also worked on

Mercer's theorem In mathematics, specifically functional analysis, Mercer's theorem is a representation of a symmetric positive-definite function on a square as a sum of a convergent sequence of product functions. This theorem, presented in , is one of the most ...

Frullani integral In mathematics, Frullani integrals are a specific type of improper integral named after the Italian mathematician Giuliano Frullani. The integrals are of the form :\int _^\,x where f is a function defined for all non-negative real numbers that has ...

, and other topics in analysis. In 1935 he introduced the brackets and braces notation for Stirling numbers (analogous to the

binomial coefficients In mathematics, the binomial coefficients are the positive integers that occur as coefficients in the binomial theorem. Commonly, a binomial coefficient is indexed by a pair of integers and is written \tbinom. It is the coefficient of the te ...

notation), which is now known as Karamata notation. He is also cited for Karamata's inequality. In Serbia, Karamata founded the "Karamata's (Yugoslav) school of mathematics”. Today, Karamata is the most cited Serbian mathematician. He is the developer and co-developer of dozens of mathematical theorems and has had a lasting influence in 20th-century mathematics.

References

External links

Tổng quát về Bất đẳng thức Karamata
(tiếng Việt) {{DEFAULTSORT:Karamata, Jovan 1902 births 1967 deaths Scientists from Zagreb Serbs of Croatia Serbian mathematicians University of Belgrade Faculty of Philosophy alumni Academic staff of the University of Geneva Mathematical analysts Yugoslav mathematicians Serbian people of Aromanian descent

Life

Legacy

See also

References

Further reading

External links