Number Theory is arguably one of the most fascinating subjects in mathematics, while theoretical physics has helped us to shape our understanding of the laws of Nature. Both are characterized by the standards of clarity, beauty and depth. Sometimes the two subjects converge in a miraculous way, providing one of those vital, wonderful and superb narratives that are occasionally found in science. Our story concerns the Riemann Hypothesis, certainly the most famous open problem in mathematics, but one that is not usually seen as being connected to physics. It states that the zeros of the Riemann zeta function lie on the critical line Re(s)=1/2. Professor Mussardo will interpret and lend support to this hypothesis from the point of view of statistical physics, which suggests that the truth of the Riemann Hypothesis being a kind of arithmetical analogue of Brownian motion. He will present the probabilistic arguments which lead to this conclusion, and also discuss a battery of highly non-trivial tests which support the validity of this result with an extremely high confidence.