Re:Preprint, not a reviewed paper (Score 3, Interesting)

The comments made by Tao and Connes are the sort of comments one would make if the paper was irrevocably flawed. For instance, Tao notes that "the decomposition claimed in equation (6.9) ... is, in fact, impossible; it would endow the function h ... with an extremely strong dilation symmetry which it does not actually obey. It seems that the author was relying on this symmetry ..."

In more simple terms: Partway into the paper the author proved something that is definitely false; he then relied on this false theorem to complete the proof.

It's possible that Tao is wrong in his analysis or that the rest of the proof is actually independent of the false theorem that it appears to depend on. However, it's reasonably likely that this proof cannot be repaired.