Vera T. Sós (born September 11, 1930) is 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, structure, space, models, and change. History On ...

, specializing in

number theory Number theory (or arithmetic or higher arithmetic in older usage) is a branch of pure mathematics devoted primarily to the study of the integers and arithmetic function, integer-valued functions. German mathematician Carl Friedrich Gauss (1777� ...

and

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

. She was a student and close collaborator of both

Paul Erdős Paul Erdős ( hu, Erdős Pál ; 26 March 1913 – 20 September 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 ...

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 ...

. 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. He had a long collaboration with fellow Hungarian mathematician Paul Erdős, lasting 4 ...

, the analyst, number theorist, and combinatorist (the letter T in her name stands for Turán). Until 1987, she worked at the Department of Analysis at the

Eötvös Loránd University Eötvös Loránd University ( hu, Eötvös Loránd Tudományegyetem, ELTE) 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 Hung ...

Budapest Budapest (, ; ) is the capital and most populous city of Hungary. It is the ninth-largest city in the European Union by population within city limits and the second-largest city on the Danube river; the city has an estimated population ...

. Since then, she has been employed by the

Alfréd Rényi Institute of Mathematics The Alfréd Rényi Institute of Mathematics ( hu, Rényi Alfréd Matematikai Kutatóintézet) 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. ...

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

Hungarian Academy of Sciences The Hungarian Academy of Sciences ( hu, Magyar Tudományos Akadémia, MTA) is the most important and prestigious learned society of Hungary. Its seat is at the bank of the Danube in Budapest, between Széchenyi rakpart and Akadémia utca. Its ma ...

. In 1997, Sós was awarded the

Széchenyi Prize The Széchenyi Prize ( hu, Széchenyi-díj), 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 Hu ...

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

bipartite graph In the mathematical field of graph theory, a bipartite graph (or bigraph) is a graph whose vertices can be divided into two disjoint and independent sets U and V, that is every edge connects a vertex in U to one in V. Vertex sets U and V are ...

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 In the mathematical field of graph theory, the friendship graph (or Dutch windmill graph or -fan) is a planar, undirected graph with vertices and edges. The friendship graph can be constructed by joining copies of the cycle graph with a ...

proved with

and

: if, in a finite graph, 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 ( ; ; January 14, 1887 – February 25, 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 Unive ...

and proved independently by

Stanisław Świerczkowski Stanisław (Stash) Świerczkowski (16 July 1932 – 30 September 2015) was a Polish mathematician famous for his solutions to two iconic problems posed by Hugo Steinhaus: the three-gap theorem and the Non-Tetratorus Theorem. Early life and ed ...

Life and career

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

and

, who she later collaborated with,Erdős, P.; Rényi, A.; Sós, V. T. On a 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 have thirty joint papers.) Sós considered Gallai to be the person who discovered her gift for mathematics. Sós was also one of three girls out of all the girls in Gallai's class that became a mathematician. Sós later attended

. There, she studied as a mathematics and

physics Physics is the natural science that studies matter, its 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 which r ...

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 Paul may refer to: *Paul (given name), a given name (includes a list of people with that name) *Paul (surname), a list of people People Christianity * Paul the Apostle (AD c.5–c.64/65), also known as Saul of Tarsus or Saint Paul, early Chri ...

in college. They married in 1952. The two had two children in 1953 and 1960, Gyorgy and Thomas Turan. 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 András Hajnal (May 13, 1931 – July 30, 2016) was a professor of mathematics at Rutgers University and a member of the Hungarian Academy of Sciences known for his work in set theory and combinatorics. Biography Hajnal was born on 13 May 1931,

. 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 has been 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 Europea ...

: 2013 *

: 1997 * Academic Award: 1983 * Cross of the Hungarian Order of Merit: 2002 * Tibor Szele Medal: 1974List o
awards
given to Vera T. Sós

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 Nov. 2010. YouTube. YouTube, 24 Jan. 2012. Web. 20 Apr. 2013. . * "Magyar Tudományos Akadémia (Hungarian Academy of Sciences)." MTA. N.p., n.d. Web. 20 Apr. 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 Apr. 2013. .

External links

* (in Hungarian), lecture given by Sós on November 6, 2010 * * {{DEFAULTSORT:Sos, Vera T. 1930 births 20th-century Hungarian mathematicians Number theorists Combinatorialists Members of Academia Europaea Living people 20th-century women mathematicians