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# Rényi, Alfréd

(1921–1970), mathematician. Alfréd Rényi was born in Budapest. His father, Artúr, was a mechanical engineer and translator; his mother, Barbara (Borka), was a photographer and the daughter of philosopher Bernát Alexander (1850–1927). It was from his mother’s side that Rényi acquired a love of literature and Greek philosophy; in secondary school his studies focused more on humanities than on sciences.

Anti-Jewish legislation impeded Rényi’s attempts to continue his education. Nevertheless, he persisted in pursuing a university degree, and after winning a national competition in Greek and a commendation in the annual mathematics competition of the Eötvös Loránd Mathematics and Physics Society, he was admitted in the fall of 1940 into a mathematics and physics program at Pázmány Péter University in Budapest. There he studied under Lipót Fejér, receiving a mathematics and physics teaching diploma in May 1944. The following month he was taken into the forced labor service, but he escaped and hid in Budapest with false papers. He also rescued his parents from the Pest ghetto.

From 1945 on, Rényi actively promoted left-wing views, traveling through the country as an activist for the National Coalition of New Landowners (UFOSZ). He received his doctorate, written under the supervision of Frigyes Riesz, in 1945 from the University of Szeged; his topic was the Cauchy-Fourier series. After marrying Katalin Schulhof, who later also became a prominent mathematician, Rényi studied with J. V. Linnyik and I. M. Vinogradov in Leningrad; in his Ph.D. thesis he solved the so-called quasi-Goldbach Conjecture in June 1947. In 1947, he became a full professor at the University of Budapest and, in 1949, taught at the Kossuth Lajos University in Debrecen. In 1950, he was appointed director of the Institute of Applied Mathematics of the Hungarian Academy of Sciences (later the Mathematical Research Institute) and in 1952 took the chair of the faculty of probability theory at Budapest ELTE University. He held both positions until his death.

Rényi was a member of the Hungarian Academy of Sciences (correspondent member from 1949 and full member from 1956), and secretary of the Third Section (1949–1953). He received the Kossuth Prize twice, in 1949 and 1954. Rényi (known as Buba) made contributions of lasting value in almost every branch of mathematics. He founded the Hungarian Probability Theory School, and his research led him to measures of the dependency of random variables. He introduced other measures, as well, to replace the correlation coefficients used in statistics. Additionally, he developed an axiomatic foundation for probability; several problems related to physics, particularly quantum mechanics, were solved using his results.

Rényi was also interested in the philosophy of mathematics, and he initiated Hungarian research into ancient mathematics. He published frequently on recreational mathematics, and tried to find practical applications for his theoretical findings. He was one of the initiators of the reform of mathematics teaching in schools. A brilliant lecturer, he actively participated in scholarly public life, serving as editor and on the editorial boards of numerous journals. He was the secretary of the Bolyai János Mathematical Society from 1949 to 1955 and its president from 1955 to 1970. Rényi was a visiting professor at several British and American universities and visited China. In 1972, the Mathematical Research Institute of the Hungarian Academy of Sciences established the Alfréd Rényi Prize in his memory, awarded each year to a young researcher at the institute.

## Suggested Reading

N. H. Bingham, “The Work of Alfréd Rényi: Some Aspects in Probability and Number Theory,” *Studia sicentiarum mathematicarum Hungarica* 26 (1991): 165–183; D. G. Kendall, “Obituary: Alfréd Rényi,” *Journal of Applied Probability* 7 (1970): 509–522; Leopold Schmetterer, “Alfréd Rényi, in Memoriam,” *Proceedings of the Sixth Berkeley Symposium on Mathematical Statistics and Probability,* vol. 2, pp. xxv–l (Berkeley, 1972); Pál Turán, “Rényi Alfréd,” *Magyar Tudomány* 15.7–8 (1970): 579–580.

## Author

## Translation

Translated from Hungarian by Veronika Szabó