**THE LIFE OF ALFRÉD
RÉNYI **

(1921 - 1970)

The explosive development of all the sciences has made our age one of specialized research. Fewer and fewer scientists take an active interest in the progress of knowledge outside their own delimited field, and fewer still would ever attempt any kind of interdisciplinary synthesis. Hungary's Alfréd Rényi was one of these very few, a scholar eager and able to use his specialist's knowledge of mathematics to solve problems in altogether different disciplines.

A man of catholic interests, Rényi’s life was one of intense and creative involvement in the exchange of ideas and in public affairs. When death claimed him at 49 he was in his prime.

Alfréd Rényi was born in Budapest on March 20, 1921, the only child of Artur Rényi , a mechanical engineer, and Barbara Alexander a daughter of the philosopher and literary critic Bernát Alexander. One might thus, say that Rényi’s love of literature and his strong devotion to Greek philosophy were his maternal heritage. In 1939, he finished secondary school in Budapest with top marks, but the newly passed racist laws debarred him from the university where his grandfather had once been professor. The autumn of 1939 he won honourable mention in the annual competition of the Mathematical Society, and in a Greek competition. After spending half a year as a labourer in the Ganz Shipyard in Budapest, he was admitted to the university the autumn 1940 to study mathematics and physics. I first met him in October or November of 1941 when he, with N. Schweitzer and G. Freud, started regularly to attend a lecture series I held to June of 1942. The main topic of discussion was number theory; at that time, Schweitzer seemed to be the one more interested in this subject.

Rényi finished his university studies in May of 1944; in June he was called up for forced-labour service. Fortunately, his company was not taken from Hungary immediately. When the order to evacuate to the West did come, Rényi escaped, and lived in Budapest using false documents. Whenever I met him during those days, I was amazed at his level-headedness and courage. In March, 1945, he got his Ph. D. at Szeged under F. Riesz. Returning to Budapest, he held various jobs as a statistician. In 1946 he married Katalin Schulhof, a noted mathematician. In October 1946, he went to Leningrad to work with Linnik; there he stayed till the next June. His progress during these few months - the first time in his life that he could concentrate fully on studying mathematics - was truly amazing. Previously, as appears from his publications, his interest centred mainly on series theory, although, as I mentioned, he also had some experience in number theory. His knowledge of probability theory, however, was unlikely to be more than rudimentary and his command of Russian was but elementary. Yet these few months were enough fur him to acquire a creative understanding of the works of the Soviet number theorists, mainly of the works of I. M. Vinogradov and Linnik; to write and defend his famous thesis; to publish two other papers; and to become thoroughly familiar with the theory of probability which: was to become his main mathematical interest. His development. during those months was nothing short of phenomenal. By an effort of the will, he had effaced his memories of the war years and of the forced-labour camp, to centre now on his work all the fiery energy of his youth and of his exceptional gifts of understanding and concentration.

On returning to Budapest, he was appointed University Privatdocent and Assistant Professor in October 1947. In 1949, he was appointed Professor Extraordinary in Debrecen and held this position till September 1950, when he became director of the Academy’s newly established Institute of Applied Mathematics. He became a corresponding member of the Hungarian Academy of Sciences in 1949, and was elected ordinary member in 1956. From 1952 until his untimely death, he was a professor of the Department of Probability and Statistics of Eötvös Loránd University.

Eloquently as the fruits of Rényi’s Leningrad sojourn testify to the extra- ordinary quickness and perceptiveness of his mind, one can hardly help feeling - on considering how very much he produced in so short a life - that only a man devoted exclusively to his own scientific work could leave behind such an opus. This was, in fact, very far from being the case. His teaching, as much as his administrative duties he fulfilled with great skill and enthusiasm. Indeed within a short time he made of his Institute (later renamed the Mathematical Research Institute of the Hungarian Academy of Sciences) a mathematical centre of international repute, while as a professor, he laid the foundations of the first school of probability in Hungary. From 1949 to 1953, he was secretary of the Mathematical Section of the reorganized Hungarian Academy of Sciences - the first to hold that office-and took a very active part in the work of several of its committees after that. time. From 1949 to 1955, he was secretary of the Bolyai János Mathematical Society, and played a leading role in organizing the Ist and IInd Mathematical Congresses held in 1950 and 1960 respectively. He was on the editorial board of all Hungarian mathematical journals: of Zeitschrift für Wahrscheinlichkeitstheorie; of the Journal of Combinatorial Theory; of the Journal of Applied Probability; of Information and Control and of the International Journal of Computer Mathematics. Over and above all this, he was active as a reviewer in Referativnii Zhurnal, Mathematical Reviews and the Statistical Theory and Method Abstracts.

Open to public duties, Rény' was at all times open also to mathematical discussion and cooperation. In fact, he produced joint papers with 36 co-authors on a variety of subjects. If one draws a graph taking all mathematicians of the world as the vertices and connects two veracity by an edge iff the corresponding mathematicians have a joint paper then - as Erdõs remarked - he, Rényi, Szekeres and Turán form a complete subgraph of order 4 in this graph.

In a short autobiography written in his last years. Rényi gave the following as the subjects of his papers: probability theory, statistics, information theory, combinatorics, graph theory. number theory and analysis. The order of listing - not an alphabetical one - in itself indicates that his interest in probabilitv theory prevailed over all his other scholarly interests. Practically all his mathematical works were, in fact,. interwoven implicitly- though sometimes implicitly - with probabilistic ideas. This is seen most, clearly in two papers he wrote in Hungarian, the ones entitled "Probabilistic Methods in Analysis". In these, he surveys various parts of the analysis, picks out some interesting results, and points out their probabilistic core. There is some indication in these papers that he had intended to continue these investigations. His skill in the application of probability was simply amazing. As even a cursory glance at the complete list of Rényi’s papers (sometimes written with co-authors) will show, he applied probability theory to solve concrete problems ranging from industry chemistry and biology to traffic and price control. The main difficulty in all these undertakings was to find the suitable model, which "approximated" reality and was "computable". His ability to understand the essence of a situation and his skill in finding for it an abstract mathematical model -- an abstraction that we might think of as analogous to the Brechtian Verfremdungseffekt - was really remarkable.

For Rényi, however, abstract models had a charm of their own quite in- dependently of their usefulness in the solution of any concrete problem. That this was indeed so appears from the first lines of the paper (No. 201) he wrote with Erdõs where the starting point is a problem of the "pseudo-application" type: Let there be given a country with n cities, n large, so that a direct air connection between any two cities would require two busy airports. Considering the capacity limits of the airports, what is the minimum number of flights that would get a passenger from any one city- to another so that he need change planes not more than once? This is a question that can be nicely reformulated and treated as an extremal graph problem. This airport problem is rather unlikely ever to occur in reality and its solution was in all probability never meant for application. But in a person as imbued with mathematics as Rényi was speculation as to how to overcome the difficulties of not getting a direct flight to some city almost automatically led to the formulation of a mathematical solution to his dilemma. The desire to find the optimal means of reaching his destination found expression in speculation as to how to devise a schedule so that a single change of planes would always suffice. At this point, the fascination of the immediately resulting graph problem tends to make one forget all the impractical features of the model, as one becomes more interested in the exciting mathematical problem that. is its result.

A singular part of Rényi’s oeuvre is the essays collected in his Ars Mathematica. I have mentioned Rényi’s literary heritage; ever since his childhood, he had been on friendly terms with outstanding literary figures - Gábor Devecseri, Ferenc Karinthy, György Somlyó and many others. All this however, would probably not have been sufficient to impell him to write these essays. It was rather a series of debates on the applications of mathematics which prompted him to do so. These debates sparked by a paper he had written on commission from an Academy Committee (No. 202) turned into vehement and open personal attacks on Rényi and went on for some years - as some articles from Magyar Tudomány (see e.g. No. 219) will show. They were debates that consumed much of his energy. The first three essays, in particular "Dialogue on Applications of Mathematics” and the one on Galileo grew directly out of these debates, and bear witness to a highly cultured and sophisticated mind.

Of course, Rényi’s activities also met with appreciation from many quarters.. In 1949, he was awarded the second, in 1954, the first grade of the Kossuth Prize for his scientific work. In 1951, he received the fourth grade of the "Medal nf the People's Republic" for his organizational work. He was invited to lecture at the International Mathematical Congress of Edinburgh in 1958, and was Rouse Ball lecturer in Cambridge in 1966. The summer of 1961 he spent one semester at the Michigan State University; in 1964, one semester at the University of Michigan; and in 1969 one semester at. the Universitv of North Carolina as visiting professor. Between 1965 and 1969, he was a member, and then vice president of the International Statistical Institute, and was elected honorary member of Churchill College in Cambridge.

Rényi's zest for life was by no means exhausted in his many-sided intellectual activities and involvement in public affairs. He was fond of rowing and swimming in the Danube in summer and of skiing in winter. With his wife and daughter Zsuzsa (born in 1948) he frequented concerts and theatres; at the parties they gave in their home, Rényi entertained his friends with witty anecdotes and with playing the piano. Those entering his study were welcomed by bookshelves jammed to the ceiling. The books, manuscripts and notes scattered on his desk made the visitor feel that he had entered tho scene of creative, productive activity, an activity that Alfréd Rényi carried on unabated to the last day of his life.

PÁL TURÁN