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 in the same sense as other serious contenders have been put forward every 1-2 years for the past 50 years, only to be withdrawn after someone points out mistakes.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.
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].
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[ 5.8 ms ] story [ 65.1 ms ] threadSo 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 in the same sense as other serious contenders have been put forward every 1-2 years for the past 50 years, only to be withdrawn after someone points out mistakes.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.
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].
http://terrytao.wordpress.com/2008/02/07/structure-and-rando...