"Prime Formula Weds Number Theory and Quantum Physics," by Barry Cipra. Science, 20 December 1996, pages 2014-2015.
Theoretical physicists and number theorists have come upon a mysterious link between quantum mechanics and a mathematical object known as the Riemann zeta function. The Riemann Hypothesis, which is a conjecture about the zeta function that was proposed in the mid-19th century, has deep consequences for number theory and is one of the outstanding problems of modern mathematics. What physicists and number theorists have observed is that the distribution of the zeros of the zeta function (that is, the values which, when plugged into the function, give the value 0) looks very much like certain energy levels observed in quantum mechanical models. According to the article, this connection may on the one hand provide a way of reconciling quantum mechanics and chaos theory, and on the other provide a route for proving the Riemann Hypothesis.