Number Variance of Zeros of the Riemann Zeta Function

Berry has proposed a remarkable formula for the variance of the number of zeros of the Riemann zeta function in intervals of a given length. Berry's derivation is heuristic, and is based on the assumption that the zeta function corresponds to a chaotic dynamical system without time reversal symmetry. The possible significance of the formula and standard number-theoretic approaches to proving it will be discussed.