One thing many people don't understand is that sometimes it is easier to prove a stronger result than a particular result, which could be exactly this case. I don't know if this paper is correct, but the technique used seems plausible independent of the length of the paper.

The paper addresses that directly:

"Thus, while our proof of RH might look too short to be true, it really involves at least two rather long papers [6, 8], not to mention [9]."

Strange, that sentence has already been rewritten.

I am surprised that in 30 years since [8] no one took another step toward the result in this new paper.

Arxiv detracts from, does not add, to credibility. it's an open preprint platform after all. This is like saying "No way such an important project would be anywhere other than github." That's not much of an argument.

As for flaws, it's four pages. They can be written up in an afternoon, if the paper makes sense to its intended audience. Of course, that's not exactly HN.

EDIT: Very interesting replies. I'll leave this up, though apparently quite wrong.

There are vast areas of research where every credible paper gets posted to the arxiv. So even though being on the arxiv does not imply credibility, not being on the arxiv implies lack thereof.

I can vouch for this. Lots of theoretical physics on there (in fact, I would say the majority of it). Whether stuff is posted on arXiv highly depends on the field.

I'm incredulous of:

>There are vast areas of research where every credible paper gets posted to the arxiv

due to your word "every" which from context you mean literally; no exceptions. So, what would these vast areas of research be? The statement would not be true for any areas of research I know about.

EDIT: Thanks for the replies - fascinating. That in certain fields, no paper is worth reading if not on arxiv.

High-energy physics. Yes, literally every paper that's worth your time is on arxiv first. The only time anyone reads from an actual peer-reviewed journal is when something that was on arxiv eventually gets published (you know, a year later) and might have minor corrections. And I don't know a single person that picks up journals for those crucial papers that were never posted to arxiv.

What's the point of "formal peer-review", anyway? If you're in the community you talk to your colleagues about what's on arxiv and you know what's good and what isn't. You don't need a journal to tell you.

For the areas I used to work in for many years, high energy physics and quantum gravity, I can't think of a single exception.

Of course I don't have total knowledge of these fields, only my corner of them, and I'm sure you'll find a counterexample if you dig deep enough, but if counterexamples are remarkable and rare, then the heuristic: "Not on the arxiv, not likely to be credible" stands.

I will add that astrophysics is the same way. I'm not aware of a single paper I've come across from the last 15 years that isn't on the arxiv.

I would say that yes, if a project is on github (or any other openly accessible platform) it greatly adds to the credibility of said project. Just like papers that are early-released on arvix it allows me to form an opinion about it and more importantly allows more intelligent people than me to read the code and draw conclusions which I can then lean on.

So in other words...what's the downside of publishing on arvix? You can also send it to a peer reviewed journal.

Arxiv is not for all,it is only authors vouched by other members. It is a very weak form of peer review.

Arxiv is pretty much for all. What you call vouching is just endorsement, and it's not peer review at all.

what I got Googling 'pseudoscience arxiv' - http://arxiv.org/find/all/1/all:+AND+marvin+herndon/0/1/0/al...

These titles wouldn't even make it past HN's front page, they would be flagged - by lay people with no background.

Let me emphasize: arxiv is not peer-reviewed, it is an open publication platform.

Out of the above list, I only clicked through one - http://arxiv.org/abs/physics/0510090 reading "Teaching Earth Dynamics: What's Wrong with Plate Tectonics Theory?"

Quote:

"I review what is wrong with plate tectonics theory ... and describe my new Whole-Earth Decompression Dynamics Theory, which unifies the two previous, dominant theories in a self-consistent manner. Along the way, I disclose details of what real science is all about, details all too often absent in textbooks and classroom discussions."

This wouldn't make it past a HN reader. "I disclose details of what real science is all about." No peer would ever accept that, in any journal on any subject.

Any errors in the actual content of the paper shouldn't take long to turn up. There seems to be nothing more high-powered than calculus used in the proofs.