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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?

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

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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.

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    $\begingroup$ The book "[Prime Numbers and the Riemann Hypothesis][1]". may be of interest, since it is by mathematicians but is mainly intended (it seems to me) for non-mathematicians. While it does not address your question specifically, it has a wealth of information about r.h. and its implications. [1]: wstein.org/rh/rh.pdf Possibly this blog about a possible connection to quasicrystals would be of interest as well: golem.ph.utexas.edu/category/2013/06/… (I didn't intend this to be a comment on a comment). $\endgroup$ – jbuddenh Jul 17 '15 at 0:47

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