Maxim Gerspach: Currently there are no reasons to doubt the Riemann Hypothesis

Abstract.

We discuss a recent preprint of David Farmer outlining and summarising various heuristics around the Riemann zeta function and the Riemann hypothesis, many of which have their origins in Random Matrix Theory. We try to explain some of these heuristics in a hands-on manner using a fair amount of graphs and numerics. We then go on to explain some of the doubts that have been cast on the Riemann Hypothesis in the past and try to explain why the observed phenomena do in fact fit into our heuristic framework. In particular it should be pointed out that the numerics, to the point that we are able to observe them, can be quite deceiving.