The Riemann hypothesis is often presented as the most important unsolved problem in mathematics.  Why is that?

In this talk the Riemann hypothesis will be described, including the context that led to it. Then examples will be given that illustrate a range of problems where the Riemann hypothesis can be applied once it gets solved and where the problems themselves don’t sound related to the Riemann hypothesis at all.  

It will be assumed that the audience is familiar with basic complex analysis.