mathematics

Vera T. Sós

Vera T. Sós is a mathematics topic covered in the lgStudy science library. This page brings together a partial reference excerpt, illustrations, worked examples, real-world applications and a short study plan, so you can understand Vera T. Sós rather than just read about it. In short: Vera Turán Sós (11 September 1930 – 22 March 2023) was a Hungarian mathematician who specialized in number theory and combinatorics. She was a student and close collaborator of both Paul Erdős and Alfréd Rényi.

Key takeaways

Vera T. Sós belongs to mathematics; place it in that map before memorising details.
Learn the definition first, then one example that makes the definition concrete.
Connect Vera T. Sós to a quantity you can measure, compute or draw — that is where exam questions come from.
Reproduce the core statement of Vera T. Sós from memory before moving on to harder problems.

Reference excerpt

Vera Turán Sós (11 September 1930 – 22 March 2023) was a Hungarian mathematician who specialized in number theory and combinatorics. She was a student and close collaborator of both Paul Erdős and Alfréd Rényi. She also collaborated frequently with her husband Pál Turán, an analyst, number theorist, and combinatorist. Until 1987, she worked at the Department of Analysis at the Eötvös Loránd University, Budapest. Afterwards, she was employed by the Alfréd Rényi Institute of Mathematics. She was elected a corresponding member (1985) and member (1990) of the Hungarian Academy of Sciences. In 1997, Sós was awarded the Széchenyi Prize. One of her contributions is the Kővári–Sós–Turán theorem concerning the maximum possible number of edges in a bipartite graph that does not contain certain complete subgraphs. Another is the following so-called friendship theorem proved with Paul Erdős and Alfréd Rényi: 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, conjectured by Hugo Steinhaus 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 Alfréd Rényi and Paul Erdős, with whom she later collaborated, by her teacher Tibor Gallai. (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 Eötvös Loránd University. There, she studied as a mathematics and physics 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 Széchenyi Prize, 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, 2013 Széchenyi Prize, 1997 Academic Award, 1983 Cross of the Hungarian Order of Merit, 2002 Tibor Szele Medal, 1974 Honorary Doctorate from Eötvös Loránd University, Budapest Honorary Doctorate from the Hebrew University of Jerusalem in 2018.

Selected publications ——— (1958). "On the distribution mod 1 of the sequence nα". Ann. Univ. Sci. Budapest. Eötvös Sect. Math. 1: 127–134. ———; Kövari, T.; Turán, P. (1954). "On a problem of K. Zarankiewicz". Colloq. Math. 3: 50–57. doi:10.4064/cm-3-1-50-57. MR 0065617.

Notes

References MTI Ki Kicsoda [Who's Who] 2009, Magyar Távirati Iroda Zrt., Budapest, 2008, pp. 1130., ISSN 1787-288X A Magyar Tudományos Akadémia tagjai 1825–2002 III. (R–ZS). [Members 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. <https://www.youtube.com/watch?v=c39uLbMGNEo>. "Magyar Tudományos Akadémia (Hungarian Academy of Sciences)." MTA. N.p., n.d. Web. 20 April 2013. <http://mta.hu/koztestuleti_tagok?PersonId=19476>. "A Matematikus T. Sós Vera 75 éves (The Mathematician Vera Sos 75 Years Old)." http://www.nol.hu. N.p., n.d. Web. <http://www.nol.hu/archivum/archiv-376708>. Babai, László (2001). "In and Out of Hungary: Paul Erdős, His Friends, and Times" (PostScript). University of Chicago. Retrieved 2008-06-22.<https://web.archive.org/web/20070207131035/http://www.cs.uchicago.edu/files/tr_authentic/TR-2001-03.ps> Sos, Vera T. "A Matematika Professzor Asszonya." Interview. A Matematika Professzor Asszonya. N.p., n.d. Web. 20 April 2013. <http://www.termeszetvilaga.hu/tv2000/tv0009/matematika.html>.

External links Order and Disorder on YouTube (in Hungarian), lecture given by Sós on 6 November 2010 Vera T. Sós at the Mathematics Genealogy Project O'Connor, John J.; Robertson, Edmund F., "Vera Turán Sós", MacTutor History of Mathematics Archive, University of St Andrews

Illustrations

Worked examples

Example 1 — a first encounter with Vera T. Sós

Start with the simplest possible case. Write down what Vera T. Sós claims or describes in one sentence, then invent the smallest concrete situation in which that sentence is true. In mathematics, the smallest case is usually a single object, a single equation or a single measurement. Check that every symbol or term in your sentence has a meaning in that case.

Example 2 — changing one variable

Take the situation from Example 1 and change exactly one quantity: double it, halve it, or set it to zero. Predict what should happen to Vera T. Sós before you calculate. Comparing your prediction with the result is the fastest way to find out whether you understand the idea or only the words.

Example 3 — an exam-style question

Typical questions about Vera T. Sós ask you to (a) state it precisely, (b) apply it to given data, and (c) explain a limitation. Practise writing all three answers in under five minutes; the third part is what separates a full-mark answer from an average one.

Applications of Vera T. Sós

In research: Vera T. Sós appears in mathematics research whenever the underlying quantities have to be modelled precisely. Papers usually cite it as a starting assumption and then explore where it breaks down.
In technology and industry: Engineering practice reuses Vera T. Sós in design rules, simulations and safety margins. Knowing the idea lets you read a specification sheet and understand why the numbers look the way they do.
In the classroom: Vera T. Sós is common in secondary-school and first-year university syllabi. It links to neighbouring topics 1930 births, 2023 deaths, 20th-century Hungarian mathematicians, so understanding it makes those chapters shorter.
In everyday life: Look for Vera T. Sós outside the textbook — in sport, cooking, traffic, electronics or the sky above you. An example you found yourself is remembered far longer than one you were given.

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How to study Vera T. Sós in 20 minutes

Read the reference excerpt below once, without taking notes.
Close the page and write down what Vera T. Sós means in your own words.
Compare your version with the excerpt and mark what you missed.
Work through the three examples above with pen and paper.
Explain Vera T. Sós out loud to somebody else — or to Teacher Smith in the lgStudy chat.

Frequently asked questions

What is Vera T. Sós in simple terms?

Why does Vera T. Sós matter?

Because it connects several mathematics ideas at once: it gives you a definition you can apply, a quantity you can calculate, and a way to check whether a result is plausible.

How should I study Vera T. Sós?

Read the excerpt, restate it from memory, then work through the examples and applications listed on this page. The five-step study plan above takes about twenty minutes.

What does this page cover?

It gives you a compact reference excerpt plus original lgStudy explanations, examples, applications and study material on Vera T. Sós.