Question

I'm not sure if you were aware, but yesterday (18th November 2009) was the Riemann Hypothesis Day, the 150th birthday of the famous unsolved mathematical problem. To celebrate it, a series of lectures, directly or indirectly related to RH, was held all over the world. I had the honour to be present at a superb one held by prof. Boris Širola here in Zagreb, Croatia.

So, my impression is that we're still far from understanding zeroes of the Riemann zeta function. There are many deep and important results in that direction, but the goal still seems out of reach. How many mathematicians are actually actively working on solving the RH? I mean, is there a lot of effort being put into it at this very moment? How many "directions of attack" are being explored?

I was wondering about that because a friend pointed out a few days ago that RH is probably going to be resolved much sooner than P vs NP, due to the mere power of accumulated knowledge and understanding, and the fact that not so many researchers are working on P vs NP. What do you think?

Answer 1

Here is a url to a site devoted to the P vs NP problem among its contents are 54 attempts to prove P vs NP. I think that there are a lot of people working on P vs NP. Among other incentives are a million dollar prize for its solution. Here is the url:

http://www.win.tue.nl/~gwoegi/P-versus-NP.htm

I don't think either P vs NP or the Rienmann hypothesis are close to solution and I have no idea which will be solved first.

Answer 2

I don't think there's any feeling on when the RH will be solved. Unlike some other famous problems, there is no proposed program "which would solve RH if we could eliminate some technical obstacles." We understand a lot more about the statistical properties of zeros of L-functions than we did 50 years ago, but even still they remain by and large mysterious. Conrey's article in the Notices of the AMS gives a very lucid discussion of RH and its history, including some attempts at solving it and some speculations as to what tools may eventually be involved in its resolution.