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, mathematical structure, structure, space, Mathematica ...
known for his work in
probability theory
Probability theory or probability calculus 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 expre ...
, though he also made contributions in
combinatorics
Combinatorics is an area of mathematics primarily concerned with counting, both as a means and as an end to obtaining results, and certain properties of finite structures. It is closely related to many other areas of mathematics and has many ...
,
graph theory
In mathematics and computer science, graph theory is the study of ''graph (discrete mathematics), graphs'', which are mathematical structures used to model pairwise relations between objects. A graph in this context is made up of ''Vertex (graph ...
, and
number theory
Number theory is a branch of pure mathematics devoted primarily to the study of the integers and arithmetic functions. Number theorists study prime numbers as well as the properties of mathematical objects constructed from integers (for example ...
.
Life
Rényi was born in
Budapest
Budapest is the Capital city, capital and List of cities and towns of Hungary, most populous city of Hungary. It is the List of cities in the European Union by population within city limits, tenth-largest city in the European Union by popul ...
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 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.
Rényi then completed his
PhD in 1947 at the
University of Szeged, under the advisement of
Frigyes Riesz. He did his postgraduate in
Moscow
Moscow is the Capital city, capital and List of cities and towns in Russia by population, largest city of Russia, standing on the Moskva (river), Moskva River in Central Russia. It has a population estimated at over 13 million residents with ...
and
Leningrad
Saint Petersburg, formerly known as Petrograd and later Leningrad, is the List of cities and towns in Russia by population, second-largest city in Russia after Moscow. It is situated on the Neva, River Neva, at the head of the Gulf of Finland ...
, where he collaborated with a prominent Soviet mathematician
Yuri Linnik.
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.
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
In number theory, Chen's theorem states that every sufficiently large parity (mathematics), even number can be written as the sum of either two prime number, primes, or a prime and a semiprime (the product of two primes).
It is a weakened form o ...
, 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
Information theory is the mathematical study of the quantification (science), quantification, Data storage, storage, and telecommunications, communication of information. The field was established and formalized by Claude Shannon in the 1940s, ...
, 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 dimension
In mathematics, a fractal dimension is a term invoked in the science of geometry to provide a rational statistical index of complexity detail in a pattern. A fractal pattern changes with the Scaling (geometry), scale at which it is measured.
It ...
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
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, one of which is typically obvious, and the other often conveys a message that would be too socially unacc ...
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, awarded by the
Hungarian Academy of Science, was established in his honor.
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
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, book ...
.
References
Sources
*
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
Academic staff of the University of Debrecen
Hungarian World War II forced labourers
Hungarian escapees
Escapees from Nazi concentration camps
Network scientists