Vera Turán Sós (11 September 1930 – 22 March 2023) was a Hungarian

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 ...

who specialized in

number theory Number theory is a branch of pure mathematics devoted primarily to the study of the integers and arithmetic functions. Number theorists study prime numbers as well as the properties of mathematical objects constructed from integers (for example ...

and

combinatorics Combinatorics is an area of mathematics primarily concerned with counting, both as a means and as an end to obtaining results, and certain properties of finite structures. It is closely related to many other areas of mathematics and has many ...

. She was a student and close collaborator of both

Paul Erdős Paul Erdős ( ; 26March 191320September 1996) was a Hungarian mathematician. He was one of the most prolific mathematicians and producers of mathematical conjectures of the 20th century. pursued and proposed problems in discrete mathematics, g ...

and

Alfréd Rényi Alfréd Rényi (20 March 1921 – 1 February 1970) was a Hungarian mathematician known for his work in probability theory, though he also made contributions in combinatorics, graph theory, and number theory. Life Rényi was born in Budapest to A ...

. She also collaborated frequently with her husband

Pál Turán Pál Turán (; 18 August 1910 – 26 September 1976) also known as Paul Turán, was a Hungarian mathematician who worked primarily in extremal combinatorics. In 1940, because of his Jewish origins, he was arrested by History of the Jews in Hun ...

, an analyst, number theorist, and combinatorist. Until 1987, she worked at the Department of Analysis at the

Eötvös Loránd University Eötvös Loránd University (, ELTE, also known as ''University of Budapest'') is a Hungarian public research university based in Budapest. Founded in 1635, ELTE is one of the largest and most prestigious public higher education institutions in ...

Budapest Budapest is the Capital city, capital and List of cities and towns of Hungary, most populous city of Hungary. It is the List of cities in the European Union by population within city limits, tenth-largest city in the European Union by popul ...

. Afterwards, she was employed by the

Alfréd Rényi Institute of Mathematics The Alfréd Rényi Institute of Mathematics () is the research institute in mathematics of the Hungarian Academy of Sciences. It was created in 1950 by Alfréd Rényi, who directed it until his death. Since its creation, the institute has been th ...

. She was elected a corresponding member (1985) and member (1990) of the

Hungarian Academy of Sciences The Hungarian Academy of Sciences ( , MTA) is Hungary’s foremost and most prestigious learned society. Its headquarters are located along the banks of the Danube in Budapest, between Széchenyi rakpart and Akadémia utca. The Academy's primar ...

. In 1997, Sós was awarded the

Széchenyi Prize The Széchenyi Prize (), named after István Széchenyi, is a prize given in Hungary by the state, replacing the former State Prize in 1990 in recognition of those who have made an outstanding contribution to academic life in Hungary. Recipients ...

. One of her contributions is the Kővári–Sós–Turán theorem concerning the maximum possible number of edges in a

bipartite graph In the mathematics, mathematical field of graph theory, a bipartite graph (or bigraph) is a Graph (discrete mathematics), graph whose vertex (graph theory), vertices can be divided into two disjoint sets, disjoint and Independent set (graph theo ...

that does not contain certain

complete Complete may refer to: Logic * Completeness (logic) * Completeness of a theory, the property of a theory that every formula in the theory's language or its negation is provable Mathematics * The completeness of the real numbers, which implies t ...

subgraphs. Another is the following so-called friendship theorem proved with

and

: if, in a

finite graph In discrete mathematics, particularly in graph theory, a graph is a structure consisting of a set of objects where some pairs of the objects are in some sense "related". The objects are represented by abstractions called '' vertices'' (also call ...

, any two vertices have exactly one common neighbor, then some vertex is joined to all others. In number theory, Sós proved the

three-gap theorem In mathematics, the three-gap theorem, three-distance theorem, or Steinhaus conjecture states that if one places points on a circle, at angles of , , , ... from the starting point, then there will be at most three distinct distances between pairs ...

, conjectured by

Hugo Steinhaus Hugo Dyonizy Steinhaus ( , ; 14 January 1887 – 25 February 1972) was a Polish mathematician and educator. Steinhaus obtained his PhD under David Hilbert at Göttingen University in 1911 and later became a professor at the Jan Kazimierz Univers ...

and proved independently by Stanisław Świerczkowski.

Life and career

Vera Sós was the daughter of a school teacher. As an adolescent, Sós attended the Abonyi Street Jewish high school in Budapest and graduated in 1948. She was later introduced to

and

, with whom she later collaborated,Erdős, P.; Rényi, A.; Sós, V. T. On the problem of graph theory. Studia Sci. Math. Hungar. 1 (1966), 215–235 by her teacher

Tibor Gallai Tibor Gallai (born Tibor Grünwald, 15 July 1912 – 2 January 1992) was a Hungarian mathematician. He worked in combinatorics, especially in graph theory, and was a lifelong friend and collaborator of Paul Erdős. He was a student of Dénes K� ...

. (Together, she and Erdős wrote thirty papers.) Sós considered Gallai to be the person who discovered her gift for mathematics. Sós was also one of three girls in Gallai's class to become mathematicians. Sós later attended

. There, she studied as a mathematics and

physics Physics is the scientific study of matter, its Elementary particle, fundamental constituents, its motion and behavior through space and time, and the related entities of energy and force. "Physical science is that department of knowledge whi ...

major and graduated in 1952. Although she was still a student, Sós taught at Eötvös University in 1950. At the age of twenty, Sós attended a Mathematical Congress in Budapest, Hungary and attended a summer internship. Sós met her husband and collaborator Paul Turán in college. They married in 1952. The two had two children, in 1953 and 1960, György and Thomas Turán. Pál Turán died in September 1976. In 1965, Sós began the weekly Hajnal–Sós seminar at the Mathematical Institute of the Hungarian Academy for Science with András Hajnal. The seminar is considered to be a "forum for new results in combinatorics." This weekly seminar continues to this day. Throughout her years working in mathematics, Sós was honored with many awards as a result of her work. One of the many awards includes the

, which she received in 1997. The Széchenyi Prize is an award given to those who have greatly contributed to the academic life of Hungary.

Awards

* Member of

Academia Europaea The Academia Europaea is a pan-European Academy of humanities, letters, law, and sciences. The Academia was founded in 1988 as a functioning Europe-wide Academy that encompasses all fields of scholarly inquiry. It acts as co-ordinator of Europe ...

, 2013 *

, 1997 * Academic Award, 1983 * Cross of the Hungarian Order of Merit, 2002 * Tibor Szele Medal, 1974 * Honorary Doctorate from

, Budapest * Honorary Doctorate from the

Hebrew University of Jerusalem The Hebrew University of Jerusalem (HUJI; ) is an Israeli public university, public research university based in Jerusalem. Co-founded by Albert Einstein and Chaim Weizmann in July 1918, the public university officially opened on 1 April 1925. ...

in 2018.

Selected publications

* *

Notes

References

* MTI Ki Kicsoda ho's Who2009, Magyar Távirati Iroda Zrt., Budapest, 2008, pp. 1130., * A Magyar Tudományos Akadémia tagjai 1825–2002 III. (R–ZS). embers of the Hungarian Academy of Sciences 1825–2002, volume III. Ed. Ferenc Glatz. Budapest: MTA Társadalomkutató Központ, 2003, pp. 1155–1156. * "T. Sós Vera: Rend, Rendezetlenség és Ami a Kettő Között Van." Lecture. 6 November 2010. YouTube. YouTube, 24 January 2012. Web. 20 April 2013. . * "Magyar Tudományos Akadémia (Hungarian Academy of Sciences)." MTA. N.p., n.d. Web. 20 April 2013. . * "A Matematikus T. Sós Vera 75 éves (The Mathematician Vera Sos 75 Years Old)." http://www.nol.hu. N.p., n.d. Web. . *Babai, László (2001). "In and Out of Hungary: Paul Erdős, His Friends, and Times" (PostScript). University of Chicago. Retrieved 2008-06-22. * Sos, Vera T. "A Matematika Professzor Asszonya." Interview. A Matematika Professzor Asszonya. N.p., n.d. Web. 20 April 2013. .

External links

* (in Hungarian), lecture given by Sós on 6 November 2010 * * {{DEFAULTSORT:Sos, Vera T. 1930 births 2023 deaths 20th-century Hungarian mathematicians 20th-century women mathematicians Number theorists Combinatorialists Scientists from Budapest Eötvös Loránd University alumni Academic staff of Eötvös Loránd University Members of Academia Europaea Members of the Hungarian Academy of Sciences Corresponding Members of the Austrian Academy of Sciences Commander's Crosses with Star of the Order of Merit of the Republic of Hungary (military)