Elected For.Mem.R.S. 1989
In the first part of the twentieth century, Hungary produced an unusually large number of world-class mathematicians. They included, most notably, L. Fejér, A. Haar, F. and M. Riesz, J. von Neumann, G. Pólya, G. SzegÕ , P. Turán and perhaps, above all, the subject of this memoir, Pál (Paul) ErdÕs. As Ernst Straus put it, ErdÕs was ‘the crown prince of problem solvers and the undisputed monarch of problem posers’. ErdÕs was born in Hungary but left his native land when he was 21; from then on he lived in England, the USA, Canada, Israel and many other countries but frequently visited Hungary and had many Hungarian friends. Although he never had a ‘proper’ academic job, through his prodigious output, his host of co-authors, his constant travels and his amazing body of unsolved problems, he has greatly influenced mathematics today. He proved fundamental results in number theory, combinatorics, probability and approximation theory, as well as in set theory, elementary geometry and topology, and real and complex analysis. He was instrumental in the birth of probabilistic number theory and was the main advocate of the use of probabilistic methods in mathematics in general. He was also one of the originators of modern graph theory. He had an exceptional ability for joint work and many of his best results were obtained in collaboration; he wrote altogether about 1500 papers, perhaps five times as many as other prolific mathematicians, and he had about 500 collaborators.