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| {{Infobox scientist
| | I am Jayne from Seiring. I love to play Post horn. Other hobbies are Petal collecting and pressing.<br><br>My web-site: [http://childsearchandrescue.org/node/34551 Reviews On Bookbyte Buyback] |
| |name = Alfréd Rényi
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| |image =
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| |birth_date = {{birth date|1921|03|20|df=y}}
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| |birth_place = [[Budapest]], [[Kingdom of Hungary|Hungary]]
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| |death_date = {{death date and age|1970|02|01|1921|03|20|df=y}}
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| |death_place = Budapest, [[People's Republic of Hungary|Hungary]]
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| |residence =
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| |nationality = [[Hungary|Hungarian]]
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| |fields = [[Mathematics]]
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| |workplaces = [[Eötvös Loránd University]]
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| |alma_mater = [[University of Szeged]]
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| |doctoral_advisor = [[Frigyes Riesz]]<ref>{{MathGenealogy |id=51155}}</ref>
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| |doctoral_students = [[Imre Csiszár]]<br>[[Bonifac Donat]]<br>[[Gyula O. H. Katona]]<br>[[János Komlós (mathematician)|János Komlós]]<br>[[András Prékopa]]<br>[[Gábor Székely]]
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| |known_for =
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| }}
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| {{eastern name order|Rényi Alfréd}}
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| '''Alfréd Rényi''' (20 March 1921 – 1 February 1970) was a [[Hungary|Hungarian]] [[mathematician]] who made contributions in [[combinatorics]], [[graph theory]], [[number theory]] but mostly in [[probability theory]].<ref>{{citation|title=Obituary: Alfred Renyi|first=David|last=Kendall|journal=Journal of Applied Probability|volume=7|issue=2|year=1970|pages=508–522|jstor=3211992}}.</ref><ref>{{citation|title=Alfred Renyi, 1921-1970|first1=P.|last1=Revesz|first2=I.|last2=Vincze|journal=The Annals of Mathematical Statistics|volume=43|issue=6|year=1972|jstor= 2240189|pages=i–xvi|doi=10.1214/aoms/1177690849}}.</ref>
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| ==Life==
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| Rényi was born in [[Budapest]] to Artur Rényi and Barbara Alexander; his father was a mechanical engineer while his mother was the daughter of a philosopher and literary critic, Bernát Alexander.
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| He was prevented from enrolling in university in 1939 due to the anti-Jewish laws then in force, but enrolled at the [[Eötvös Loránd University|University of Budapest]] in 1940 and finished his studies in 1944. At this point he was drafted to [[Labour service (Hungary)|forced labour service]], escaped, and completed his [[Ph.D.]] in 1947 at the [[University of Szeged]], under the advisement of [[Frigyes Riesz]]. He married Katalin Schulhof (who used Kató Rényi as her married name), herself a mathematician, in 1946; their daughter Zsuzsanna was born in 1948. After a brief assistant professorship at Budapest, he was appointed Professor Extraordinary at the [[University of Debrecen]] in 1949. In 1950, he founded the [[Alfréd Rényi Institute of Mathematics|Mathematics Research Institute]] of the [[Hungarian Academy of Sciences]], now bearing his name, and directed it until his early death. He also headed the Department of Probability and Mathematical Statistics of the [[Eötvös Loránd University]], from 1952. He was elected a corresponding member (1949), full member (1956) of the [[Hungarian Academy of Sciences]]
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| ==Work==
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| Rényi proved, using the [[large sieve]], that there is a number <math>K</math> such that every even number is the sum of a prime number and a number that can be written as the product of at most <math>K</math> primes. [[Chen's theorem]], a strengthening of this result, shows that the theorem is true for ''K'' = 2, for all sufficiently large even numbers. The case ''K'' = 1 is the still-unproven [[Goldbach conjecture]].
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| In [[information theory]], he introduced the spectrum of [[Rényi entropy|Rényi entropies]] of order α, giving an important generalisation of the [[Shannon entropy]] and the [[Kullback-Leibler divergence]]. The Rényi entropies give a spectrum of useful [[diversity indices]], and lead to a spectrum of [[fractal dimension]]s. The [[Rényi–Ulam game]] is a guessing game where some of the answers may be wrong.
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| In probability theory, he is also known for his [[Rényi's parking constants|parking constants]], which characterize the solution to the following problem: given a street of given length and cars of constant length parking on a random free position on the street, what is the density of cars when there are no more free positions? The solution to that problem is approximately equal to 74.75979% {{OEIS|A050996}}.<ref>[http://mathworld.wolfram.com/RenyisParkingConstants.html] Wolfram Mathworld on Rényi's parking constants</ref>
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| He wrote 32 joint papers with [[Paul Erdős]],<ref>{{cite web|url=http://www.oakland.edu/upload/docs/Erdos%20Number%20Project/erdtrib.pdf| title= Paul Erdős: The Master of Collaboration, Jerrold W. Grossman, March 8, 1996 |accessdate=16 June 2012}} {{wayback| url=http://web.archive.org/web/20060709195148/http://www.oakland.edu/enp/erdtrib.pdf}}</ref> the most well-known of which are his papers introducing the [[Erdős–Rényi model]] of [[random graph]]s.<ref>"On random graphs", Publ. Math. Debrecen, 1959, and "On the evolution of random graphs", Publ. Math. Inst. Hung. Acad. Sci, 1960.</ref>
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| ==Quotations==
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| Rényi, who was addicted to coffee, invented<ref>Jeff Suzuki (2002).''A History of Mathematics'', p. 731. "The first main result was by the Hungarian mathematician Alfred Renyi (March 20, 1921-February 1, 1970), who is best known for a saying of his: a mathematician is a machine for turning coffee into theorems."</ref><ref>[[Gyula O. H. Katona]]: Preface to ''Ars Mathematica'', Collected writings of Alfréd Rényi, TypoTeX, Budapest, 2005, p. 8.</ref> the quote: "''A mathematician is a device for turning coffee into theorems.''", which is generally ascribed to [[Paul Erdős|Erdős]]. It has been suggested that this sentence was originally formulated in [[German language|German]] (''Number Theory'', Springer 1995), where it can be interpreted as a wordplay on the double meaning of the word ''Satz'' (theorem or coffee residue), but it is more likely that the original formulation was in [[Hungarian language|Hungarian]].<ref>{{citation|url=http://pachjanos.wordpress.com/2010/12/16/anastasatos-conjecture/|title=Anastasatos’ Conjecture|first=János|last=Pach|authorlink=János Pach|date=December 16, 2010}}.</ref>
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| He is also famous for having said, "If I feel unhappy, I do mathematics to become happy. If I am happy, I do mathematics to keep happy."<ref>Quoted in [[Pál Turán]], "The Work of Alfréd Rényi", Matematikai Lapok 21 (1970) 199 - 210.</ref>
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| ==Remembrance==
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| The [[Alfréd Rényi Prize]], awarded by the [[Hungarian Academy of Science]], was established in his honor.<ref>{{cite web|url=http://www.omikk.bme.hu/archivum/angol/htm/renyi_a.htm|title=Rényi, Alfréd|accessdate=8 March 2010}}</ref>
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| ==Books==
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| * A. Rényi: ''Dialogues on Mathematics'', Holden-Day, 1967.
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| * A. Rényi: ''A diary on information theory'', Akadémiai Kiadó
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| * A. Rényi, ''Foundations of Probability'', Holden-Day, Inc., San Francisco, California, 1970, xvi + 366 pp
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| * A. Rényi, ''Probability Theory''. American Elsevier Publishing Company, Inc., New York, 1970, 666 pp.
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| * A. Rényi, ''Letters on Probability," Wayne State University Press, Detroit, 1972, 86pp.
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| ==References==
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| {{reflist}}
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| ==External links==
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| *[http://www.math.elte.hu/probability/renyi/racv.html The life of Alfréd Rényi], by [[Pál Turán]]
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| *{{MacTutor Biography|id=Renyi}}
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| {{Authority control|VIAF=36956448}}
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| {{Persondata <!-- Metadata: see [[Wikipedia:Persondata]]. -->
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| | NAME = Renyi, Alfred
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| | ALTERNATIVE NAMES =
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| | SHORT DESCRIPTION =Mathematician
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| | DATE OF BIRTH =20 March 1921
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| | PLACE OF BIRTH =Budhapest
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| | DATE OF DEATH =1 February 1970
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| | PLACE OF DEATH = Budapest, [[People's Republic of Hungary|Hungary]]
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| }}
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| {{DEFAULTSORT:Renyi, Alfred}}
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| [[Category:Hungarian Jews]]
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| [[Category:1921 births]]
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| [[Category:1970 deaths]]
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| [[Category:20th-century mathematicians]]
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| [[Category:Number theorists]]
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| [[Category:Combinatorialists]]
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| [[Category:Graph theorists]]
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| [[Category:Probability theorists]]
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| [[Category:Hungarian mathematicians]]
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| [[Category:Members of the Hungarian Academy of Sciences]]
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| [[Category:People from Budapest]]
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| [[Category:University of Debrecen faculty]]
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