In 1972, Hugh Montgomery proposed a conjecture regarding the asymptotic behavior of the distribution of spacing between the zeros of the Riemann zeta function. A serendipitous encounter with Freeman Dyson at the Institute of Advanced Study resulted in an unexpected discovery about the profound connection between the pair correlation functions of the zeros of the Riemann zeta function and the eigenvalues of random matrices. This connection sparked extensive research at the crossroads of number theory and mathematical physics. In this talk, we will explore Montgomery's conjecture and its consequences.