Translation, presentation and annotation of

Alfred Rényi's "A Socratic Dialogue on Mathematics''

by Josep Maria Font (University of Barcelona)

Butlletí de la Societat Catalana de Matemàtiques 17 (2002) 51--67

Alfréd Rényi (Budapest, 1921--1970) was one of the greatest Hungarian mathematicians of the XXth century. After a secondary school period equally inclined (under the influence of his mother) towards mathematics and towards humanities he studied mathematics with Féjer in Budapest and in 1945 he earned his Ph. D. at Szeged with Riesz. He studied number theory and probability theory in Leningrad, with Linnik and Vinogradov. Back to Hungary, in 1950 he was appointed the first director of the Institute of Applied Mathematics newly created in the Hungarian Academy of Sciences, and in a few years he made it an internationally renowned research center (recently this institute was renamed as "Institute of Mathematics Alfréd Rényi"). In 1952 he was appointed professor of Probability Theory and Statistics at Budapest's University Eötvös Loránd, where he created a whole Department, which he chaired together with the Institute until his untimely death. Rényi was a very active member of the mathematical community both at a local and at an international level. He served in the editorial board of several journals, published around three hundred papers and books (some of these translated into several languages), visited universities in Germany, England, America, earned prizes, etc.

His mathematical interests, ordered as he himself once ranked them, were: probability theory, statistics, information theory, combinatorics, graph theory, number theory, analysis. He developed deep probabilistic methods in number theory, where he proved the so-called Goldbach's quasi-conjecture: every even number is the sum of a prime number and an almost prime number (a number having exactly two prime factors). He also applied probabilistic techniques to quantum mechanicsc, industrial chemistry, biology, traffic regulation and price control. Together with his strong interest in the applications of mathematics, he was also very interested in recreational mathematics, the philosophy of mathematics, old mathematics and elementary school teaching of mathematics. He was a very creative mathematician of a high level and broad interests, he had an inexhaustible organizational energy and a charming personality.

His view on the relations between mathematics and its applications originated an important debate in his country during several years, which lead him to write, among other papers, three essays addressed to the general public where he exposed his ideas in the form of a fictitious dialogue, featuring Socrates, Archimedes and Galileo respectively. These three small gems of the mathematical literature were collected in the book "Dialogues on Mathematics" published in Hungarian in 1965 and translated into six languages.

In this issue of the Butlletí de la Societat Catalana de Matemàtiques we offer the translation into catalan of the first of these dialogues, A socratic dialogue on mathematics, which first appeared in Hungarian in 1962. Here Rényi exposes his ideas on the nature of mathematics, also throwing in some thoughts on the teaching and the applications of mathematics, and even some political reflections. Rényi shows his knowledge of the greek world, his mastering of the socratic method, and his literary skills. This piece is a particularly bright example of the virtues of dialogues as an expository method, and should be ranked together with the classical dialogues of Plato and Galileo and with more recent ones, such as those of Lewis Carroll, Lakatos, Heyting, Hofstadter, and Knuth (the latter author acknowledges Rényi's influence on his choosing the dialogue form).

We wish you enjoy it.