Montgomery's pair correlation conjecture

In mathematics, Montgomery's pair correlation conjecture is a conjecture made by Hugh Montgomery (1973) that the pair correlation between pairs of zeros of the Riemann zeta function (normalized to have unit average spacing) is

${\displaystyle 1-\left({\frac {\sin(\pi u)}{\pi u}}\right)^{\!2},}$

which, as Freeman Dyson pointed out to him, is the same as the pair correlation function of random Hermitian matrices.