# Alfréd Rényi

The native form of this personal name is Rényi Alfréd. This article uses the Western name order.
Alfréd Rényi
Born 20 March 1921
Budapest, Hungary
Died 1 February 1970 (aged 48)
Budapest, Hungary
Nationality Hungarian
Fields Mathematics
Institutions Eötvös Loránd University
Alma mater University of Szeged
Doctoral students Imre Csiszár
Bonifac Donat
Gyula O. H. Katona
János Komlós
András Prékopa
Gábor Székely

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.[2][3]

## 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 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

## 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. 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 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% (sequence A050996 in OEIS).[4]

He wrote 32 joint papers with Paul Erdős,[5] the most well-known of which are his papers introducing the Erdős–Rényi model of random graphs.[6]

## Quotations

Rényi, who was addicted to coffee, invented[7][8] the quote: "A mathematician is a device for turning coffee into theorems.", which is generally ascribed to Erdős. It has been suggested that this sentence was originally formulated in 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.[9]

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."[10]

## Remembrance

The Alfréd Rényi Prize, awarded by the Hungarian Academy of Science, was established in his honor.[11]

## Books

• A. Rényi: Dialogues on Mathematics, Holden-Day, 1967.
• 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.

## References

1. ^
2. ^ Kendall, David (1970), "Obituary: Alfred Renyi", Journal of Applied Probability 7 (2): 508–522, 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.
4. ^ [1] Wolfram Mathworld on Rényi's parking constants
5. ^ "Paul Erdős: The Master of Collaboration, Jerrold W. Grossman, March 8, 1996". Retrieved 16 June 2012. Archive copy at the Wayback Machine
6. ^ "On random graphs", Publ. Math. Debrecen, 1959, and "On the evolution of random graphs", Publ. Math. Inst. Hung. Acad. Sci, 1960.
7. ^ 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."
8. ^ Gyula O. H. Katona: Preface to Ars Mathematica, Collected writings of Alfréd Rényi, TypoTeX, Budapest, 2005, p. 8.
9. ^ Pach, János (December 16, 2010), Anastasatos’ Conjecture.
10. ^ Quoted in Pál Turán, "The Work of Alfréd Rényi", Matematikai Lapok 21 (1970) 199–210.
11. ^ "Rényi, Alfréd". Retrieved 8 March 2010.