There's quite a lot of interest in the proof by some key experts despite their general impression that the proof is wrong and unfixable.

Maybe experts are using this proof as an opportunity to promote theoretical computer science? It's a way to get more grad students and funding?

I think there's some meta-worry that if all attempts to prove P=NP are treated as kookery, nobody serious will dare circulate any work on it, and so nobody will actually end up proving it. So there seems to be some going out of their way to treat a serious good-faith effort with respect.

My impression is that while the proof may have issues that are unfixable that the approach taken in the proof is one that's novel and could still have interesting implications in the theory of computational complexity.

Or, more likely, there are lots of good ideas that can be applied to other difficult problems.

But this is not a sure point; the ideas may be fresh, but it's too early to tell whether it's useful for other problems in computer science.

Doesn’t really matter because if they never care to look they will never find out.

People are interested because there is still hope that the proof is not unfixable.

No, these people are not "smart enough" to think of marketing strategies of this kind for TOC :-)

I think the proof either has some elements that might be helpful in settling the whole issue, or is so complicated that has become an interesting target for researchers.

Regardless of how this plays out, this needs to be at the top of Top Science Stories of 2010 lists. If it is a good proof, Top News Stories of 2010 (or whatever year it is confirmed).

If this indeed proves P!=NP then i would think it would make a bit more top lists than just Top Science Stories 2010.

I think you're overestimating the value most people place on math theorems. I doubt this story will be given more importance than "robot who can do the laundry" or some similarly "soft" science stories by the mainstream press, as important as it may be.

OTOH, Wiles work on Fermat's Last Theorem was major news in 1993 and 1994.

Ask 10 random pedestrians if they remember what the first name was of 'Wiles' and what he did.

People are far more likely to remember things such as the world trade center bombing as 'major news'.

I'm happy enough it rated a mention on the 1993 wikipedia page:

http://en.wikipedia.org/wiki/1993

  > The sad part is that “Vinay Deolalikar is
  > standing by his P!=NP claim and proof.”

Why is this sad? He is effectively saying that as things stand, he, who has worked on this proof for years, knows and understands it better than the people who've had a day or two to look at it. Further, it's plausible, even likely, that most of the early objections are simple misunderstandings, or finding things that haven't been explained fully.

There's nothing wrong with standing by the proof at this stage - it's entirely appropriate. What have been found so far are a few holes and a meta-concern over the potentially overly broad applicability to known false results.

It's all normal.

Part of the problem of this process happening in the full glare of publicity like this is that entirely normal things are mis-interpreted and then blown out of proportion. No wonder Wiles spent so long hiding, and then only confided in exactly one person to start with, without writing it all down in a widely disseminatable form.

There is a huge difference between being a crank and being incorrect. The death of subtly is depressing.

This line by Lipton is a response to the questions that were raised when the preprint was removed Deolalikar’s personal HP page on Monday. Many were wondering if it was a retraction, and this is denying that.

But as so far as I have seen in Toa's wiki or Lipton's forums, there has not yet been a specific object to any lemma or claim in the paper. The author has no more reason to believe there is a flaw in his argument than he did on August 6.

OK, I am unqualified to comment on this proof because the math is over my head, but what is wrong about Deolalikar's response that is posted in the article? The author copies the comment, does not point out where it is wrong, and goes on to talk about how the methods behind the proof may be useful even though it is still probably unfixable. Does a more mathematically sophisticated person really read Deolalikar's comment and immediately recognize it as invalid and/or desparate? To the point where we're now saying that to engage and respond to critiques is to "behave like a crank rather than a scientist"?

I have more sympathy. The guy has worked on this for a few years. I'd stick to my guns too (for a while atleast) :)

He also didn't intend for it to be published!

I am not surprised by OP's response though. A number of people on Lipton's page, including some people with strong credentials, were of the opinion that the researchers were wasting their time.