If you peruse the Number Theory papers on the arXiv, you'll see that there is a purported proof of the Riemann hypothesis every few weeks. So far, none of them have been vetted by a professional journal. I'd be very surprised (but happy) if this turned out to contain a correct proof.
A more interesting question would be "Why is this particular proof by this otherwise unknown author getting so much attention?"
2) I believe some theorists have already looked at it and I haven't heard anything negative [disclaimer: I'm far from an expert and wouldn't be able to even agree or disagree with their analyses].
Re:A proof of the Riemann hypothesis
by cperciva on Wednesday July 02, 2008 @04:57PM
(#234539)
This isn't my area, but I know enough to say that he speaks the right language and builds on existing results in the field.
So I'd classify this as a serious contender... in the same sense as other serious contenders have been put forward every 1-2 years for the past 50 years, only to be withdrawn after someone points out mistakes. I'd say that it's almost certain that there are mistakes somewhere in this paper -- the only question is whether they're serious flaws or just minor errors which can be worked around.
http://terrytao.wordpress.com/2008/02/07/structure-and-rando...
If you peruse the Number Theory papers on the arXiv, you'll see that there is a purported proof of the Riemann hypothesis every few weeks. So far, none of them have been vetted by a professional journal. I'd be very surprised (but happy) if this turned out to contain a correct proof.
A more interesting question would be "Why is this particular proof by this otherwise unknown author getting so much attention?"
1) He authored http://en.wikipedia.org/wiki/Li%27s_criterion
2) I believe some theorists have already looked at it and I haven't heard anything negative [disclaimer: I'm far from an expert and wouldn't be able to even agree or disagree with their analyses].
So I'd classify this as a serious contender... in the same sense as other serious contenders have been put forward every 1-2 years for the past 50 years, only to be withdrawn after someone points out mistakes. I'd say that it's almost certain that there are mistakes somewhere in this paper -- the only question is whether they're serious flaws or just minor errors which can be worked around.