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here is the deal, it is extremely difficult to prove P ?= NP. However it is comparatively easier to have a wrong proof. The only thing that you can say is that

here is the deal, it is extremely difficult to prove P ?= NP. However it is comparatively easier to have a wrong proof. The only thing that you can say is that this approach was one of the trickier ones to do it in a wrong way. Yet it does not "necessarily" means that this approach is actually a starting point. Just it seems to be more complex than the other approaches.

JadeNB 16y ago
> The only thing that you can say is that this approach was one of the trickier ones to do it in a wrong way. Or, rather, that someone (well qualified) thinks it was. I am very sceptical of a refutation based on the assumption that the proof founders on a beginner's mistake; it's not impossible, but, if Deolalikar is a beginner in the relevant field (I have no idea!), then it seems very likely that he would have consulted with someone who wasn't to avoid such trip-ups. > Yet it does not "necessarily" means that this approach is actually a starting point. I am a mathematician, not a computer scientist; but I think it's safe to say that any approach to a well known problem that is not (1) immediately dismissible (by experts) as crackpottery or (2) a laborious advance an inch down a familiar road of reasoning is likely to represent a promising starting point for something (future research in general, if not the answer to the specific question). If it is (3) described by experts as a novel and/or unexpected approach, as I think that this paper was, then that likelihood becomes a near-certainty.
- akshayubhat 16y ago
  I am not at all discounting efforts by vinay deolalikar. Nor passing a judgmental remark about his proof. My only comment to the parent commenter was that: 1: Falsifiability principal suggests that we assume any proof to be wrong until proved otherwise. 2: Its job of Mathematicians and other researchers to be skeptical and not to accept any proof unless rigorously proven otherwise, irrespective of the status of person proving. And researchers are doing exactly that. 3: Just because a proof is convoluted or uses methods from different field is not a valid criteria for acceptability of a proof or deniability or even novelty. Now talking about this case in particular: His proof relies on connection between Complexity and Statistical Physics. This connection isn't routinely used to prove results in CS Theory, also it is difficult to find experts in both areas. Thus it is difficult for even experts in one of the two areas to correctly gauge importance of his methods. Finally my only point is that other researchers have been doing right job, by not passing a direct hasty judgement.

JadeNB 16y ago

> The only thing that you can say is that this approach was one of the trickier ones to do it in a wrong way. Or, rather, that someone (well qualified) thinks it was. I am very sceptical of a refutation based on the assumption that the proof founders on a beginner's mistake; it's not impossible, but, if Deolalikar is a beginner in the relevant field (I have no idea!), then it seems very likely that he would have consulted with someone who wasn't to avoid such trip-ups. > Yet it does not "necessarily" means that this approach is actually a starting point. I am a mathematician, not a computer scientist; but I think it's safe to say that any approach to a well known problem that is not (1) immediately dismissible (by experts) as crackpottery or (2) a laborious advance an inch down a familiar road of reasoning is likely to represent a promising starting point for something (future research in general, if not the answer to the specific question). If it is (3) described by experts as a novel and/or unexpected approach, as I think that this paper was, then that likelihood becomes a near-certainty.

akshayubhat 16y ago
I am not at all discounting efforts by vinay deolalikar. Nor passing a judgmental remark about his proof. My only comment to the parent commenter was that: 1: Falsifiability principal suggests that we assume any proof to be wrong until proved otherwise. 2: Its job of Mathematicians and other researchers to be skeptical and not to accept any proof unless rigorously proven otherwise, irrespective of the status of person proving. And researchers are doing exactly that. 3: Just because a proof is convoluted or uses methods from different field is not a valid criteria for acceptability of a proof or deniability or even novelty. Now talking about this case in particular: His proof relies on connection between Complexity and Statistical Physics. This connection isn't routinely used to prove results in CS Theory, also it is difficult to find experts in both areas. Thus it is difficult for even experts in one of the two areas to correctly gauge importance of his methods. Finally my only point is that other researchers have been doing right job, by not passing a direct hasty judgement.