Colloquium

The Duffin-Schaeffer conjecture was first proposed in 1941. Since that time it has been one of the most important open problems in metric number theory. It has triggered about a dozen papers with partial results in support of the conjecture. In the summer of 2019 a proof was announced by Dimitris Koukoulopoulos and James Maynard. Their proof appears to be very complicated and exploits a remarkable new idea. Happily, it also appears to be correct. The proof could be presented in a one semester course on metric number theory. In this more modest colloquium I will describe the basic problem, review some of its history and briefly indicate the main technical difficulty that has now been overcome by Koukoulopoulos and Maynard.