Alfréd Rényi
Encyclopedia
Alfréd Rényi was a Hungarian
mathematician
who made contributions in combinatorics
, graph theory
, number theory
but mostly in probability theory
.
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.
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
, 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 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
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 
primes. See also 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 dimension
s. The Rényi–Ulam game is a guessing game where some of the answers may be wrong.
He wrote 32 joint papers with Paul Erdős
, the most well-known of which are his papers introducing the Erdős–Rényi model
of random graph
s. Rényi, who was addicted to coffee, invented the quote: "A mathematician is a device for turning coffee into theorems.", which is generally ascribed to Erdős
. The sentence was originally in German, being a wordplay on the double meaning of the word Satz (theorem or residue of coffee).
The Alfréd Rényi Prize
, awarded by the Hungarian Academy of Science, was established in his honor.
Hungary
Hungary , officially the Republic of Hungary , is a landlocked country in Central Europe. It is situated in the Carpathian Basin and is bordered by Slovakia to the north, Ukraine and Romania to the east, Serbia and Croatia to the south, Slovenia to the southwest and Austria to the west. The...
mathematician
Mathematician
A mathematician is a person whose primary area of study is the field of mathematics. Mathematicians are concerned with quantity, structure, space, and change....
who made contributions in combinatorics
Combinatorics
Combinatorics is a branch of mathematics concerning the study of finite or countable discrete structures. Aspects of combinatorics include counting the structures of a given kind and size , deciding when certain criteria can be met, and constructing and analyzing objects meeting the criteria ,...
, graph theory
Graph theory
In mathematics and computer science, graph theory is the study of graphs, mathematical structures used to model pairwise relations between objects from a certain collection. A "graph" in this context refers to a collection of vertices or 'nodes' and a collection of edges that connect pairs of...
, number theory
Number theory
Number theory is a branch of pure mathematics devoted primarily to the study of the integers. Number theorists study prime numbers as well...
but mostly in probability theory
Probability theory
Probability theory is the branch of mathematics concerned with analysis of random phenomena. The central objects of probability theory are random variables, stochastic processes, and events: mathematical abstractions of non-deterministic events or measured quantities that may either be single...
.
Life
Rényi was born in BudapestBudapest
Budapest is the capital of Hungary. As the largest city of Hungary, it is the country's principal political, cultural, commercial, industrial, and transportation centre. In 2011, Budapest had 1,733,685 inhabitants, down from its 1989 peak of 2,113,645 due to suburbanization. The Budapest Commuter...
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.
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
Labour service (Hungary)
Labour service arose in Hungary during World War II as the required military substitution for Jewish men, who were no longer permitted to serve in the regular armed forces since the passing of the Hungarian anti-Jewish laws...
, escaped, and completed his Ph.D.
Ph.D.
A Ph.D. is a Doctor of Philosophy, an academic degree.Ph.D. may also refer to:* Ph.D. , a 1980s British group*Piled Higher and Deeper, a web comic strip*PhD: Phantasy Degree, a Korean comic series* PhD Docbook renderer, an XML renderer...
in 1947 at the University of Szeged
University of Szeged
The University of Szeged is one of Hungary's most distinguished universities, and is among the most prominent higher education institutions in Central Europe...
, under the advisement of Frigyes Riesz
Frigyes Riesz
Frigyes Riesz was a mathematician who was born in Győr, Hungary and died in Budapest, Hungary. He was rector and professor at University of Szeged...
. 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
University of Debrecen
The University of Debrecen is a university located in Debrecen, Hungary. It is the oldest continuously operating institution of higher education in Hungary .-History:...
in 1949. In 1950, he founded the Mathematics Research Institute
Alfréd Rényi Institute of Mathematics
The Alfréd Rényi Institute of Mathematics is the research institute in mathematics of the Hungarian Academy of Sciences. It was created in 1950 by Alfréd Rényi, who directed it until his death. Since its creation, the institute has been the center of mathematical research in Hungary. It received...
of the Hungarian Academy of Sciences
Hungarian Academy of Sciences
The Hungarian Academy of Sciences is the most important and prestigious learned society of Hungary. Its seat is at the bank of the Danube in Budapest.-History:...
, 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
Hungarian Academy of Sciences
The Hungarian Academy of Sciences is the most important and prestigious learned society of Hungary. Its seat is at the bank of the Danube in Budapest.-History:...
Work
He proved, using the large sieve, that there is a number 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 primes. See also Goldbach conjecture.In information theory
Information theory
Information theory is a branch of applied mathematics and electrical engineering involving the quantification of information. Information theory was developed by Claude E. Shannon to find fundamental limits on signal processing operations such as compressing data and on reliably storing and...
, he introduced the spectrum of Rényi entropies
Rényi entropy
In information theory, the Rényi entropy, a generalisation of Shannon entropy, is one of a family of functionals for quantifying the diversity, uncertainty or randomness of a system...
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
Fractal dimension
In fractal geometry, the fractal dimension, D, is a statistical quantity that gives an indication of how completely a fractal appears to fill space, as one zooms down to finer and finer scales. There are many specific definitions of fractal dimension. The most important theoretical fractal...
s. The Rényi–Ulam game is a guessing game where some of the answers may be wrong.
He wrote 32 joint papers with Paul Erdős
Paul Erdos
Paul Erdős was a Hungarian mathematician. Erdős published more papers than any other mathematician in history, working with hundreds of collaborators. He worked on problems in combinatorics, graph theory, number theory, classical analysis, approximation theory, set theory, and probability theory...
, the most well-known of which are his papers introducing the Erdős–Rényi model
Erdos–Rényi model
In graph theory, the Erdős–Rényi model, named for Paul Erdős and Alfréd Rényi, is either of two models for generating random graphs, including one that sets an edge between each pair of nodes with equal probability, independently of the other edges...
of random graph
Random graph
In mathematics, a random graph is a graph that is generated by some random process. The theory of random graphs lies at the intersection between graph theory and probability theory, and studies the properties of typical random graphs.-Random graph models:...
s. Rényi, who was addicted to coffee, invented the quote: "A mathematician is a device for turning coffee into theorems.", which is generally ascribed to Erdős
Paul Erdos
Paul Erdős was a Hungarian mathematician. Erdős published more papers than any other mathematician in history, working with hundreds of collaborators. He worked on problems in combinatorics, graph theory, number theory, classical analysis, approximation theory, set theory, and probability theory...
. The sentence was originally in German, being a wordplay on the double meaning of the word Satz (theorem or residue of coffee).
Remembrance
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."The Alfréd Rényi Prize
Alfréd Rényi Prize
The Alfréd Rényi Prize is awarded biannually by the Alfréd Rényi Institute of Mathematics of the Hungarian Academy of Science in honor of founder Alfréd Rényi. By the current rules it is given to one or two fellows of the Institute in recognition of their outstanding performance in mathematics...
, 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, California, 1970, xvi + 366 pp
- A. Rényi, Probability Theory. American Elsevier Publishing Company, Inc., New York, 1970, 666 pp.
External links
- The life of Alfréd Rényi, by Pál TuránPál TuránPaul Turán was a Hungarian mathematician who worked primarily in number theory. He had a long collaboration with fellow Hungarian mathematician Paul Erdős, lasting 46 years and resulting in 28 joint papers.- Life and education :...