I first met him in October or November of 1941 when he ... started regularly to attend a lecture series I held to June of 1942. The main topic of discussion was number theory ...

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.

Alfréd got hold of a soldier's uniform, walked into the ghetto, and marched his parents out. ... It requires familiarity with the circumstances to appreciate the skill and courage needed to perform these feats.

Whenever I met him during those days, I was amazed at his level-headedness and courage.

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.

... at present one of the strongest methods of analytical number theory.

A set of integers $S$, with the property that there exists an absolute constant $K$ such that each $x$ in $S$ has at most $K$ distinct prime factors, is called an almost-prime set. Each $x$ in $S$ is called an almost-prime number. The author indicates the proof, to be given in detail elsewhere, that each even integer is the sum of an almost-prime number (taken from a fixed set $S$) and a prime number. He also states that he can prove that there exist infinitely many primes $p$ such that $p + 2$ is almost-prime (being in a fixed set $S^{*}$). The first result, regarding the representation of an even number, is an approximation to the unproved Goldbach conjecture and supersedes an earlier proof of the same proposition by Estermann (1932) which made use of an unproved generalized Riemann hypothesis for all Dirichlet $L$-series. The second result is an approximation to the conjecture of the existence of infinitely many twin primes and is apparently a new result.

In the hands of writers like Linnik, Erdős and Rényi, the theory of numbers is not clearly distinguished from the theory of probability. Each lends techniques to the other, and important problems lie along their common frontier. Thus, when Rényi is referred to as a great applied probabilist, this is partly because of his interests in probability applied to other parts of mathematics.

Probability theory and its applications had been neglected in the curriculum of Hungarian universities until very recently when the author started to lecture regularly on these topics. He had therefore to prepare mimeographed notes for his students which lead, after repeated revisions, to the publication of the present book. It is thus the first modern Hungarian text book on probability theory and offers an excellent introduction into this field. ... It is regrettable that this book is useful only to Hungarian students; it would deserve to be added to the foreign language publications of the Hungarian Academy of Sciences.

... a mathematician is a machine for converting coffee into theorems

Mathematics is like your daughter Helena, who suspects every time a suitor appears that he is not really in love with her, but is interested in her only because he wants to be the son-in-law of the king. She wants a husband who loves her for her own beauty, her wit and charm, and not for the wealth and power he can get by marrying her. Similarly, mathematics reveals its secrets only to those who approach it with pure love, for its own beauty. Those who do this are, of course, also rewarded with results of practical importance. But if somebody asks at each step "What can I profit by this?" he will not get far.

... a pure mathematician of massive achievements and towering stature in the classical fields of number theory and analysis. Rényi possessed also an inquisitive and dogged interest in all the phenomena of the world about him, and in all the scholarly activities of his colleagues, whether scientific or humane, and this unique combination of powers and interests enabled him to build up a research institute in which the criterion for acceptability of a subject for investigation was 'does there exits at least one mathematician with a genuine interest in this topic'? Once accepted as appropriate, however, the topic would be pursued in a thoroughly professional way; the argument would be followed wherever it led, and buttressed by whatever mathematical means seemed appropriate, however exotic or sophisticated.

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 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 the scene of creative, productive activity, an activity that Alfréd Rényi carried on unabated to the last day of his life.