The Mathematics of Paul Erdos

P aul Erdős died September 20, 1996, and a memorial article appears elsewhere in this issue. This feature article gives a cross section of his monumental oeuvre. Most of Erdős’s work falls roughly into the following categories: • number theory • finite combinatorics (including graph theory) • combinatorial geometry • set theory, set-theoretical topology • constructive theory of functions (approximation theory) • other areas of classical analysis (polynomials, theory of series, functions of a complex variable) • probability theory, ergodic theory The first two areas are represented in Erdős’s work by more than 600 articles each, the next three by more than 100 articles each. There are some overlaps in this rough count. A large number of articles fall into a “miscellaneous” category. In what follows, Pomerance gives a glimpse into the variety of topics Erdős worked on in number theory. Babai discusses (infinite) set theory, finite combinatorics, combinatorial geometry, combinatorial number theory, and probability theory. Vértesi treats approximation theory, with a hint of related work on polynomials. Paul Erdős, Number Theorist Extraordinaire