Alfréd Rényi (20 March 1921 – 1 February 1970) 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, structure, space, models, and change.
History
On ...
known for his work in
probability theory
Probability theory is the branch of mathematics concerned with probability. Although there are several different probability interpretations, probability theory treats the concept in a rigorous mathematical manner by expressing it through a set ...
, though he also made contributions in
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 a ...
,
graph theory
In mathematics, graph theory is the study of '' graphs'', which are mathematical structures used to model pairwise relations between objects. A graph in this context is made up of '' vertices'' (also called ''nodes'' or ''points'') which are conn ...
, and
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 integer-valued functions. German mathematician Carl Friedrich Gauss (1777–1855) said, "Ma ...
.
Life
Rényi was born in
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 o ...
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.
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 escaped. He then completed his
PhD PHD or PhD may refer to:
* Doctor of Philosophy (PhD), an academic qualification
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* '' PhD: Phantasy Degree'', a Korean comic series
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** Ph.D. (Ph.D. al ...
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
ThUniversity of Debrecen( hu, Debreceni Egyetem) is a university located in Debrecen, Hungary. It is the oldest continuously operating institution of higher education in Hungary ever since its establishment in 1538 by Suleiman the Magnificent f ...
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.
Work
Rényi proved, using the
large sieve, that there is a number
such that every even number is the sum of a
prime number
A prime number (or a prime) is a natural number greater than 1 that is not a Product (mathematics), product of two smaller natural numbers. A natural number greater than 1 that is not prime is called a composite number. For example, 5 is prime ...
and a number that can be written as the product of at most
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.
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 . Thus, random parking is 25.2% less efficient than optimal packing.
He wrote 32 joint papers with
Paul Erdős, the most well-known of which are his papers introducing the
Erdős–Rényi model of
random graphs.
The corpus of his bibliography was compiled by the mathematician
Pál Medgyessy.
Quotations
Rényi, who was addicted to coffee, is the source of the quote: "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
A double entendre (plural double entendres) is a figure of speech or a particular way of wording that is devised to have a double meaning, of which one is typically obvious, whereas the other often conveys a message that would be too socially ...
on the meaning of the word ''Satz'' (theorem or coffee residue), but it is more likely that the original formulation was in Hungarian.
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."
Remembrance
The
Alfréd Rényi Prize The Alfréd Rényi Prize is awarded biennially by the Alfréd Rényi Institute of Mathematics of the Hungarian Academy of Science in honor of founder Alfréd Rényi
Alfréd Rényi (20 March 1921 – 1 February 1970) was a Hungarian mathematician ...
, awarded by the
Hungarian Academy of Science, was established in his honor.
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
Dover Publications, also known as Dover Books, is an American book publisher founded in 1941 by Hayward and Blanche Cirker. It primarily reissues books that are out of print from their original publishers. These are often, but not always, books ...
.
References
External links
The life of Alfréd Rényi by
Pál Turán
*
* .
{{DEFAULTSORT:Renyi, Alfred
1921 births
1970 deaths
20th-century Hungarian mathematicians
Number theorists
Graph theorists
Probability theorists
Members of the Hungarian Academy of Sciences
Mathematicians from Budapest
University of Debrecen faculty
Hungarian World War II forced labourers
Hungarian escapees
Escapees from Nazi concentration camps
Network scientists