Introduction

Abstract

We do not have much to add here. We only want to express our gratitude to Arthur Stone, Cedric Smith, William Tutte and Irving Kaplansky for their personal recollections of those days when many contemporary theories were being created. In those early days, Erdős’ interests were almost entirely devoted to number theory and, as seen from his own contribution, as well as from the other contributions to this chapter, number theory is an old love which does not fade. But so is an early combinatorial puzzle solved by four young Cambridge undergraduates (three of which are among authors of this chapter). C. Smith related this puzzle to P. Erdős while W. Tutte in his characteristic style connects his very recent research to his own early beginnings.