Louis de Branges is a mathematician at Purdue who has had a long history of claiming proofs of the Riemann hypothesis. His latest claim has lead to a press release from Purdue. The press release points to what seems to be an older
The actual purported proof is here. One mystifying thing about it is that in the abstract and introductory paragraph it repeatedly refers to relations to quantum mechanics, but there seems to be nothing about this in the body of the paper. Weyl’s book on quantum mechanics and group theory appears in the references, but nothing in the text seems to refer to this.
de Branges has a checkered history as a mathematician, with several of his claimed proofs of the Riemann hypothesis and other problems turning out to be incorrect. On the other hand, he did produce a correct proof of one well-known problem, the Bieberbach Conjecture. In that case his initial manuscript was pretty impenetrable, but after he explained his ideas to a group of Russian mathematicians, they gave a more understandable version of the proof and it became clear that de Branges really did have a proof. It looks like this one may also take some major effort to see what he really has.
For more about de Branges and the Riemann hypothesis, see the recent popular book “The Riemann Hypothesis: the Greatest Unsolved Problem of Mathematics” by Karl Sabbagh. A review of this book has some interesting comments about de Branges and his NSF funding.
A couple weeks ago a preprint appeared on the arXiv by R. A. Arenstorf, a mathematician at Vanderbilt University, claiming a proof of the twin prime conjecture. I asked one of my colleagues who is an expert on the subject about it and he said he didn’t believe it and would bet $100 it was wrong. Today I see that Arenstorf has withdrawn the preprint, saying that a serious error has been found.