They keep cranking them out, don’t they?
Of course, there is the minutest possibility that this time its for real, but just going by history, I am prepared to bet all my savings against it.
Update: I apologize if my post seems to suggest that Xian-Jin Li, the author of the purported proof, is a crank. In fact, he is a competent mathematician who has done good work in the past. Nonetheless, I think that the chances of this proof being correct are extremely low; in fact Terry Tao claims to have already found a mistake.
Update 2: Xian-Jin Li has posted a new version (actually
two three new versions!) of his preprint on the Arxiv. Most pertinently, the definition of the function h on page 20 has changed; so perhaps this addresses Tao’s objection above.
The reason I will be very surprised if this proof turns out to be correct is that it involves mostly functional analysis on the adeles. It has been generally believed that such techniques are not sufficient to prove Riemann. It would be a stunning achievement if Riemann is solved using only such elementary tools; will be following this news closely over the next few days.