What are the most promising approches for solving Riemann hypothesis?

Question

I'm not a mathematician but still I'm very interested in Riemann hypothesis. I discovered it with the Numberphile channel. I would like to know what are the current work done of this subject and if there are any promising method to solve it?

Answer 1

You might look at Peter Borwein's recent book "The Riemann Hypothesis: A Resource for the Afficionado and Virtuoso Alike".

Answer 2

This question has been partially addressed at mathoverflow. See the question https://mathoverflow.net/questions/34699/approaches-to-riemann-hypothesis-using-methods-outside-number-theory, which focuses on methods outside number theory, and also https://mathoverflow.net/questions/96642/current-status-of-the-riemann-hypothesis. It appears at present that there is no really promising approach, but I may be very wrong.