Terry Tao has a specific objection on his web page. http://terrytao.wordpress.com/2008/02/07/ structure-and-randomness-in-the-prime-numbers/#comment-30714
2 July, 2008 at 6:28 pm Terence Tao It unfortunately seems that the decomposition claimed in equation (6.9) on page 20 of that paper is, in fact, impossible; it would endow the function h (which is holding the arithmetical information about the primes) with an extremely strong dilation symmetry which it does not actually obey. It seems that the author was relying on this symmetry to make the adelic Fourier transform far more powerful than it really ought to be for this problem.
Li has fixed this problem, and is up to version 4 of his paper. The discussion on the Tao blog has continued, raising another problem. At least one correspondent says "this kind of proof can't work because of xxx". I guess we'll have to wait a few more days for the dust to settle. One thing consipicuously missing from the discussion is any kudos to Mr Li, or suggestion that he's developed any valuable ideas, or a new approach. Rich ---- Quoting Jason <jason@lunkwill.org>:
I had lunch with Sarnak today -- he looked at the paper and said that there are many problems with the proof.
Ah yes, proof by personal communication[1]:
proof by eminent authority: 'I saw Karp in the elevator and he said it was probably NP- complete.'
proof by personal communication: 'Eight-dimensional colored cycle stripping is NP-complete [Karp, personal communication].'
1: http://www.princeton.edu/~sacm/humor/proof.html
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