The past few years have seen the emergence of compelling evidence for a connection between the zeros of the Riemann ζ-function and the eigenvalues of random matrices. This hints at a link between the distribution of the prime numbers, which is governed by the Riemann zeros, and properties of waves in complex systems (e.g. waves in random media, or in geometries where the ray dynamics is chaotic), which may be modelied using random matrix theory. These developments have led to a significant deepening of our understanding of some of the most important problems relating to the ζ-function and its kin, and have stimulated new avenues of research in random matrix theory. In particular, it would appear that several long-standing questions concerning the distribution of values taken by the ζ-function on the line where the Riemann Hypothesis places its zeros can be answered using techniques developed in the study of random matrices.
