Navigating Research on Riemann Hypothesis

[Newtime]

Let me start off by saying I have not yet had a formal course in Number Thoery and have only read briefly on the subject...hence the question:

How close (in terms that would be understood by someone in my position) is the math community to proving the Riemann Hypothesis? I'm assuming there are journal articles published on recent research but like I said these would be over my head and I wouldn't know the significance (or lack thereof) of what I was reading.

 

[mathman]

Look it up on Wikipedia. The article contains a thorough description of the subject as well as descriptions of various works attempting to solve it.

 

[CRGreathouse]

How close (in terms that would be understood by someone in my position) is the math community to proving the Riemann Hypothesis?

Extremely far. Several major results haver been proved, restricting the positions zeros can fall -- but not very far. As far as I know, the zeros violating the RH could be as common as the primes (but, like the primes, they are known to be of asymptotic density 0).

 

[gcsetma]

Let me start off by saying I have not yet had a formal course in Number Thoery and have only read briefly on the subject...hence the question:

How close (in terms that would be understood by someone in my position) is the math community to proving the Riemann Hypothesis? I'm assuming there are journal articles published on recent research but like I said these would be over my head and I wouldn't know the significance (or lack thereof) of what I was reading.

J. Brian Conrey wrote an excellent article a few years back on the Riemann Hypothesis (The Riemann Hypothesis, Notices of the AMS, March 2003) which provides an overview in relative layman's terms.