A proof of the Riemann Hypothesis?


Has anybody else heard about this? Some dudes claim to have proved the Riemann Hypothesis. I heard about it yesterday. It looks like it’s been around for a few months, though. Also, the Riemann Hypothesis entry at mathworld.wolfram.com (http://mathworld.wolfram.com/RiemannHypothesis.html) doesn’t say anything about it. Unfortunately, I lack the degree of mathematical sophistication required to parse (let alone understand) the paper.

So, who has the Straight Dope?

I don’t know, but Slashdot mentioned it a few days ago.

This comment (and the followups) suggests that the proof is poorly written. Hopefully one of the Maths geeks on the board will show up and comment.

Well, it is very poorly written, but it might have the basic idea right. I can’t be sure, cause I’m not really familiar with the type of math they’re using.

Based on the fact that mathworld has nothing to say about it, I’d guess that no one is taking it seriously. That doesn’t mean it’s wrong, just that it’s not a good paper.

It seems suspicious that it has been around since early November and this is the first I have heard of it. When Wiles announced the FLT, word flashed around the mathematical world within minutes. And Wiles’ original argument was flawed. But Wiles had a track record. And eventually it was completed. I have just emailed a colleague who is a number theorist, but I am not holding my breath on this.

On the other hand, there is are two cases I know of in which people who didn’t have track records actually did extraordinary things that were at first ignored. One was the proof of something called the Biberbach conjecture and the other was Apery’s proof that zeta(3) was irrational. So anything is possible. When I hear from my colleague, I will let you all know. He was one of the four people in theworld whom Wiles sent his final paper on the FLT to be checked.

I wouldn’t be so hasty about that decision. In my experience, it can take years for MathWorld to update something. The most recent listing under MathWorld Headline News is January 13th.

Mercifully, I’m not a slave to hep-th abstracts these days, so this is also the first I’ve heard of it. Again, if this were a real breakthrough, I’d be surprised by that.
But I don’t agree with the Slashdot post: no, it’s not referreed, but hep-th is not just some dumping ground. Indeed, it’s the very heart of the Los Alamos server and the original basis that the whole scheme was founded on. So they can’t be dismissed as cranks on that basis. And for theoretical physics, it’s actually not badly written. Not knowing the background, I can’t follow the details, but there are no obvious alarm bells.
Even so, the pure mathematicians are surely right. They are writing as sloppy physicists and the likely mistakes are just those that will probably slip through their fingers. (And also those readers who’re not able to check every step in the argument.)