Hi all, I see that on 1 July 2008, analytic number theorist Xian-Jin Li (Math, Brigham Young University) announced a proof of RH. Interestingly enough, Li is a former Ph.D. student (Purdue, 1993) of Louis de Branges, who has been somewhat notorious of late for announcing his own "proof" of RH back in 2004, which as I understand it was never accepted by experts. See http://genealogy.math.ndsu.nodak.edu/id.php?id=16641 This initially gave me pause, but looking at Li's papers (via Google Scholar) I see that they have been published and cited by others. Most relevant, perhaps, is a paper by Bombieri and Lagarias which as I understand it generalizes an RH criterion due to Li. This isn't my field at all, but I have the initial impression that Li's work appears to fit into a community effort by many of the best mathematicians now working. Does anyone have information or comments? (I think I've seen Lagarias post here, so I'd be particularly interested comments from him.) How about some interesting consequences of RH?