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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]}
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
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]}
Rényi, who was addicted to coffee, is the source^{[7]}^{[8]} of 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, 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]}
The Alfréd Rényi Prize, awarded by the Hungarian Academy of Science, was established in his honor.^{[11]}
Hungary, Buda Castle, Danube, European Union, Europe
Budapest, European Union, Slovakia, Pécs, Hungarian language
Budapest, Hungary, Utrecht Network, University of Tartu, University of Bergen
Szeged, Hungarian language, Computer science, Hungary, Cluj-Napoca
Logic, Set theory, Statistics, Number theory, Mathematical logic
Computer science, Mathematics, Topology, Combinatorics, Numerical analysis
Graph theory, Probability theory, Erdős–Rényi model, Statistics, Network science
Judith Q. Longyear, Paul Erdős, Péter Frankl, Adolph Winkler Goodman, Alan Tucker
Paul Erdős, Péter Frankl, Abraham Wald, Alfred Tauber, Alfréd Haar
Philadelphia, Hungarian language, Hungary, Temple University, Probability