ALL THE ROADS TAKEN BY PAUL ERDÓS

Abstract

The notion of Erdös number has floated around the mathematical research community for more than thirty years, as a way to quantify the common knowledge that mathematical and scientific research has become a very collaborative process in the twentieth century, not an activity engaged in solely by isolated individuals. In this paper we explore sorne (fairly short) collaboration paths that one can follow from Paul Erdös to researchers inside and outside of mathematics. In particular, we find that all the Fields Medalists up tbrough 1998 have Erdös numbers less than 6, and that over 60 Nobel prize winners in physics, chemistry, economics, and medicine have Erdös numbers less than 9.