Alfréd Rényi: Difference between revisions

Alfréd Rényi
Alfréd Rényi
Born	20 March 1921; Budapest, Hungary
Died	1 February 1970 (aged 48); Budapest, Hungary
Alma mater	University of Szeged
	Scientific career
Fields	Mathematics
Institutions	Eötvös Loránd University
Doctoral advisor	Frigyes Riesz
Doctoral students	Imre Csiszár; Gyula O. H. Katona; János Komlós; András Prékopa; Gábor Székely; Janos Galambos

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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.^[2]^[3]

Life

Rényi was born in Budapest to Artúr Rényi and Borbála Alexander; his father was a mechanical engineer, while his mother was the daughter of philosopher and literary critic Bernhard Alexander; his uncle was Franz Alexander, a Hungarian-American psychoanalyst and physician.^[4]

He was prevented from enrolling in university in 1939 due to the anti-Jewish laws then in force, but enrolled at the University of Budapest in 1940 and finished his studies in 1944. At this point, he was drafted to forced labour service, from which he managed to escape during transportation of his company. He was in hiding with false documents for six months. Biographers tell an incredible story about Rényi: after half of a year in hiding, he managed to get hold of a soldier's uniform and march his parents out of the Budapest Ghetto, where they were captive. That mission required enormous courage and planning skills.^[4]

Rényi then completed his PhD in 1947 at the University of Szeged, under the advisement of Frigyes Riesz. He did his postgraduate in Moscow and Leningrad, where he collaborated with a prominent Soviet mathematician Yuri Linnik.^[4]

Rényi 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 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), then full member (1956), of the Hungarian Academy of Sciences.^[4]

Work

Rényi proved, using the large sieve, that there is a number $K$ 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 $K$ primes.^[5] 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.

In information theory, he introduced the spectrum of 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 dimensions. The Rényi–Ulam game is a guessing game where some of the answers may be wrong.

In probability theory, he is also known for his parking constants, which characterize the solution to the following problem: given a street of some length and cars of unit length parking on a random free position on the street, what is the mean density of cars when there are no more free positions? The solution to that problem is asymptotically equal to 0.7475979 (sequence A050996 in the OEIS).^[6] Thus, random parking is 25.2% less efficient than optimal packing.

He wrote 32 joint papers with Paul Erdős,^[7] the most well-known of which are his papers introducing the Erdős–Rényi model of random graphs.^[8]

The corpus of his bibliography was compiled by the mathematician Pál Medgyessy.^[9]

Quotations

Rényi, who was addicted to coffee, is the source of the quote:^[10]^[11] "A mathematician is a device for turning coffee into theorems", which is often ascribed to Erdős. It has been suggested that this sentence was originally formulated in German, where it can be interpreted as a double entendre on the meaning of the word Satz (theorem or coffee residue), but it is more likely that the original formulation was in Hungarian.^[12]

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."^[13]

Remembrance

The Alfréd Rényi Prize, awarded by the Hungarian Academy of Science, was established in his honor.^[14]

In 1950 Rényi founded the Mathematics Research Institute of the Hungarian Academy of Sciences. It was renamed the Alfréd Rényi Institute of Mathematics in July 1999.

Books

A. Rényi: Dialogues on Mathematics, Holden-Day, 1967.
A. Rényi: A diary on information theory, Akadémiai Kiadó
A. Rényi, Foundations of Probability, Holden-Day, Inc., San Francisco, 1970, xvi + 366 pp
A. Rényi, Probability Theory. American Elsevier Publishing Company, New York, 1970, 666 pp.
A. Rényi, Letters on Probability, Wayne State University Press, Detroit, 1972, 86pp.

Foundations of Probability and Probability Theory have both been reprinted by Dover Publications.

References

^ Alfréd Rényi at the Mathematics Genealogy Project
^ Kendall, David (1970), "Obituary: Alfred Renyi", Journal of Applied Probability, 7 (2): 508–522, doi:10.1017/S0021900200035154, JSTOR 3211992.
^ Revesz, P.; Vincze, I. (1972), "Alfred Renyi, 1921-1970", The Annals of Mathematical Statistics, 43 (6): i–xvi, doi:10.1214/aoms/1177690849, JSTOR 2240189.
^ ^a ^b ^c ^d Hersch 1993.
^ Rényi, A. A. (1948). "On the representation of an even number as the sum of a prime and an almost prime". Izvestiya Akademii Nauk SSSR Seriya Matematicheskaya (in Russian). 12: 57–78.
^ Weisstein, Eric W. "Rényi's Parking Constants". MathWorld. Retrieved 2017-01-21.
^ Grossman, Jerrold W. (1996-03-08). "Paul Erdős: The Master of Collaboration" (PDF). Retrieved 2017-01-21.
^ "On random graphs", Publ. Math. Debrecen, 1959, and "On the evolution of random graphs", Publ. Math. Inst. Hung. Acad. Sci, 1960.
^ Pál Medgyessy's entry in Tudósnaptár ("Calendar of Scientists")
^ Suzuki, Jeff (2002). A History of Mathematics. Prentice Hall. p. 731. ISBN 9780130190741. 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.
^ Gyula O. H. Katona (2005). Preface to Ars Mathematica, Collected writings of Alfréd Rényi. Budapest: TypoTeX. p. 8.
^ Pach, János (2010-12-16), Anastasatos' Conjecture, retrieved 2017-01-21.
^ Pál Turán (1970). "The Work of Alfréd Rényi". Matematikai Lapok 21: 199–210.
^ "Rényi, Alfréd". 2013-07-17. Retrieved 2017-01-21.

Sources

Hersch, Reuben (1993). "A Visit to Hungarian Mathematics". The Mathematical Intelligencer. 15 (2): 13–26. doi:10.1007/BF03024187. S2CID 122827181.

External links

The life of Alfréd Rényi, by Pál Turán
O'Connor, John J.; Robertson, Edmund F., "Alfréd Rényi", MacTutor History of Mathematics Archive, University of St Andrews
Alfréd Rényi at the Mathematics Genealogy Project.

[1] Alfréd Rényi at the Mathematics Genealogy Project

[2] Kendall, David (1970), "Obituary: Alfred Renyi", Journal of Applied Probability, 7 (2): 508–522, doi:10.1017/S0021900200035154, JSTOR 3211992.

[3] Revesz, P.; Vincze, I. (1972), "Alfred Renyi, 1921-1970", The Annals of Mathematical Statistics, 43 (6): i–xvi, doi:10.1214/aoms/1177690849, JSTOR 2240189.

[FOOTNOTEHersch1993-4] Hersch 1993.

[Alfréd_Rényi_1948-5] Rényi, A. A. (1948). "On the representation of an even number as the sum of a prime and an almost prime". Izvestiya Akademii Nauk SSSR Seriya Matematicheskaya (in Russian). 12: 57–78.

[6] Weisstein, Eric W. "Rényi's Parking Constants". MathWorld. Retrieved 2017-01-21.

[7] Grossman, Jerrold W. (1996-03-08). "Paul Erdős: The Master of Collaboration" (PDF). Retrieved 2017-01-21.

[8] "On random graphs", Publ. Math. Debrecen, 1959, and "On the evolution of random graphs", Publ. Math. Inst. Hung. Acad. Sci, 1960.

[9] Pál Medgyessy's entry in Tudósnaptár ("Calendar of Scientists")

[10] Suzuki, Jeff (2002). A History of Mathematics. Prentice Hall. p. 731. ISBN 9780130190741. 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.

[11] Gyula O. H. Katona (2005). Preface to Ars Mathematica, Collected writings of Alfréd Rényi. Budapest: TypoTeX. p. 8.

[12] Pach, János (2010-12-16), Anastasatos' Conjecture, retrieved 2017-01-21.

[13] Pál Turán (1970). "The Work of Alfréd Rényi". Matematikai Lapok 21: 199–210.

[14] "Rényi, Alfréd". 2013-07-17. Retrieved 2017-01-21.

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@@ Line 1: / Line 1: @@
-{{Short description|Hungarian mathematician}}
+{{Short description|Hungarian mathematician (1921–1970)}}
 {{eastern name order|Rényi Alfréd}}
 {{Infobox scientist
-|name              = Alfréd Rényi
+|name          	= Alfréd Rényi
-|image             =
+|image         	= Alfred Kato Renyi.jpg
-|birth_date        = {{birth date|1921|03|20|df=y}}
+|birth_date    	= {{birth date|1921|03|20|df=y}}
-|birth_place       = [[Budapest]], [[Kingdom of Hungary|Hungary]]
+|birth_place   	= Budapest, Hungary
-|death_date        = {{death date and age|1970|02|01|1921|03|20|df=y}}
+|death_date    	= {{death date and age|1970|02|01|1921|03|20|df=y}}
-|death_place       = Budapest, [[People's Republic of Hungary|Hungary]]
+|death_place   	= Budapest, Hungary
-|residence         =
+|fields        	= [[Mathematics]]
-|nationality       = [[Hungary|Hungarian]]
+|workplaces    	= [[Eötvös Loránd University]]
-|fields            = [[Mathematics]]
+|alma_mater    	= [[University of Szeged]]
-|workplaces        = [[Eötvös Loránd University]]
-|alma_mater        = [[University of Szeged]]
 |doctoral_advisor  = [[Frigyes Riesz]]<ref>{{MathGenealogy |id=51155}}</ref>
-|doctoral_students = [[Imre Csiszár]]<br>[[Gyula O. H. Katona]]<br>[[János Komlós (mathematician)|János Komlós]]<br>[[András Prékopa]]<br>[[Gábor Székely]]
+|doctoral_students = [[Imre Csiszár]]<br>[[Gyula O. H. Katona]]<br>[[János Komlós (mathematician)|János Komlós]]<br>[[András Prékopa]]<br>[[Gábor Székely]]<br>[[Janos Galambos]]
-|known_for         =
+|known_for     	=
 }}
-'''Alfréd Rényi''' (20 March 1921 – 1 February 1970) was a Hungarian [[mathematician]] who made contributions in [[combinatorics]], [[graph theory]], [[number theory]] but mostly in [[probability theory]].<ref>{{citation
+'''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]].<ref>{{citation
 | title=Obituary: Alfred Renyi
 | first=David
@@ Line 26: / Line 24: @@
 | year=1970
 | pages=508–522
+| doi=10.1017/S0021900200035154
-| jstor=3211992}}.</ref><ref>{{citation
+| jstor=3211992| doi-access=free
+}}.</ref><ref>{{citation
 | title=Alfred Renyi, 1921-1970
 | first1=P.
@@ Line 42: / Line 42: @@
 ==Life==
-Rényi was born in [[Budapest]] to Artur Rényi and Barbara Alexander; his father was a mechanical engineer, while his mother was the daughter of philosopher and literary critic [[Bernhard Alexander]]; his uncle was [[Franz Alexander]], a Hungarian-American psychoanalyst and physician.
+Rényi was born in [[Budapest]] to Artúr Rényi and Borbála Alexander; his father was a mechanical engineer, while his mother was the daughter of philosopher and literary critic [[Bernhard Alexander]]; his uncle was [[Franz Alexander]], a Hungarian-American psychoanalyst and physician.{{sfn|Hersch|1993}}
-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]], from which he escaped. He then 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), then full member (1956), of the [[Hungarian Academy of Sciences]].
+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]], from which he managed to escape during transportation of his company. He was in hiding with false documents for six months. Biographers tell an incredible story about Rényi: after half of a year in hiding, he managed to get hold of a soldier's uniform and march his parents out of the [[Budapest Ghetto]], where they were captive. That mission required enormous courage and planning skills.{{sfn|Hersch|1993}}
+Rényi then completed his [[PhD]] in 1947 at the [[University of Szeged]], under the advisement of [[Frigyes Riesz]]. He did his postgraduate in [[Moscow]] and [[St Petersburg|Leningrad]], where he collaborated with a prominent Soviet mathematician [[Yuri Linnik]].{{sfn|Hersch|1993}}
+Rényi 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), then full member (1956), of the [[Hungarian Academy of Sciences]].{{sfn|Hersch|1993}}
 ==Work==
-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''&nbsp;=&nbsp;2, for all sufficiently large even numbers. The case ''K''&nbsp;=&nbsp;1 is the still-unproven [[Goldbach conjecture]].
+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.<ref name="Alfréd Rényi 1948">{{cite journal | last=Rényi | first=A. A. | language=Russian | title=On the representation of an even number as the sum of a prime and an almost prime | journal=Izvestiya Akademii Nauk SSSR Seriya Matematicheskaya | volume=12 | pages=57–78 | year=1948 }}</ref> [[Chen's theorem]], a strengthening of this result, shows that the theorem is true for ''K''&nbsp;=&nbsp;2, for all sufficiently large even numbers. The case ''K''&nbsp;=&nbsp;1 is the still-unproven [[Goldbach conjecture]].
-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.
+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.
-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 some length and cars of unit length parking on a random free position on the street, what is the mean density of cars when there are no more free positions? The solution to that problem is asymptomatically equal to 0.7475979 {{OEIS|A050996}}.<ref>{{cite web
+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 some length and cars of unit length parking on a random free position on the street, what is the mean density of cars when there are no more free positions? The solution to that problem is asymptotically equal to 0.7475979 {{OEIS|A050996}}.<ref>{{cite web
 | url=http://mathworld.wolfram.com/RenyisParkingConstants.html
 | title=Rényi's Parking Constants
@@ Line 56: / Line 61: @@
 | last=Weisstein
 | work=[[MathWorld]]
-| accessdate=2017-01-21}}</ref> Thus, random parking is 25.2% less efficient than optimal packing.
+| access-date=2017-01-21}}</ref> Thus, random parking is 25.2% less efficient than optimal packing.
 He wrote 32 joint papers with [[Paul Erdős]],<ref>{{cite web
@@ Line 64: / Line 69: @@
 | last=Grossman
 | date=1996-03-08
-| accessdate=2017-01-21}}</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>
+| access-date=2017-01-21}}</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>
+The corpus of his bibliography was compiled by the mathematician [[Pál Medgyessy]].<ref>[https://tudosnaptar.kfki.hu/historia/egyen.php?namenev=medgyessy Pál Medgyessy's entry] in ''Tudósnaptár'' ("Calendar of Scientists")</ref>
 ==Quotations==
@@ Line 73: / Line 80: @@
 | year=2002
 | pages=731
+| publisher=Prentice Hall
 | quote=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.
 | isbn=9780130190741}}</ref><ref>{{cite book
 | title=Preface to ''Ars Mathematica'', Collected writings of Alfréd Rényi
-| work=TypoTeX
+| publisher=TypoTeX
 | location=Budapest
 | author=Gyula O. H. Katona
 | author-link=Gyula O. H. Katona
 | page=8
-| year=2005}}</ref> "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, 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.<ref>{{citation
+| year=2005}}</ref> "A mathematician is a device for turning coffee into theorems", which is often ascribed to Erdős. It has been suggested that this sentence was originally formulated in German, where it can be interpreted as a [[double entendre]] on the meaning of the word ''Satz'' (theorem or coffee residue), but it is more likely that the original formulation was in Hungarian.<ref>{{citation
 | url=https://pachjanos.wordpress.com/2010/12/16/anastasatos-conjecture/
-| title=Anastasatos’ Conjecture
+| title=Anastasatos' Conjecture
 | first=János
 | last=Pach
 | author-link=János Pach
 | date=2010-12-16
-| accessdate=2017-01-21}}.</ref>
+| access-date=2017-01-21}}.</ref>
 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>{{cite journal
@@ Line 94: / Line 102: @@
 | author=Pál Turán
 | author-link=Pál Turán
-| work=Matematikai Lapok 21
+| journal=Matematikai Lapok 21
 | year=1970
 | pages=199–210}}</ref>
@@ Line 103: / Line 111: @@
 | title=Rényi, Alfréd
 | date=2013-07-17
-| accessdate=2017-01-21}}</ref>
+| access-date=2017-01-21}}</ref>
+In 1950 Rényi founded the [[Alfréd Rényi Institute of Mathematics|Mathematics Research Institute]] of the [[Hungarian Academy of Sciences]]. It was renamed the [[Alfréd Rényi Institute of Mathematics]] in July 1999.
 ==Books==
@@ Line 116: / Line 126: @@
 ==References==
 {{Reflist|30em}}
+== Sources ==
+* {{cite journal
+| last1 	 = Hersch
+| first1     = Reuben
+| date  	 = 1993
+| title 	 = A Visit to Hungarian Mathematics
+| url   	 = https://www.academia.edu/11078641
+| journal    = The Mathematical Intelligencer
+| volume     = 15
+| issue 	 = 2
+| pages 	 = 13–26
+| doi   	 =10.1007/BF03024187
+| s2cid = 122827181
+}}
 ==External links==
@@ Line 128: / Line 153: @@
 [[Category:1970 deaths]]
 [[Category:20th-century Hungarian mathematicians]]
-[[Category:Jewish Hungarian mathematicians]]
 [[Category:Number theorists]]
 [[Category:Graph theorists]]
@@ Line 134: / Line 158: @@
 [[Category:Members of the Hungarian Academy of Sciences]]
 [[Category:Mathematicians from Budapest]]
-[[Category:University of Debrecen faculty]]
+[[Category:Academic staff of the University of Debrecen]]
+[[Category:Hungarian World War II forced labourers]]
+[[Category:Hungarian escapees]]
+[[Category:Escapees from Nazi concentration camps]]
+[[Category:Network scientists]]

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