
P ≠ NP - zacs
http://www.scribd.com/doc/35539144/pnp12pt
======
randomwalker
Several points on the question of whether the proof is likely to be correct:

* As far as I know this paper wasn't circulated for informal peer review before being made public; I heard no talk on the grapevine. (Edit: apparently it _was_ circulated and someone other than the author made it public.)

* Therefore a proper assessment is going to take a while. Until then we can only speculate :-)

* While the crank attempts at P =? NP are statistically much more common (<http://news.ycombinator.com/item?id=347295>), this isn't one of them. The author is a legit computer scientist: <http://www.hpl.hp.com/personal/Vinay_Deolalikar/>

* On the other hand he hasn't published much on complexity theory and isn't known in that community. Which is weird but not necessarily a red flag.

* Looking at his papers, it's possible he's been working on this for about 5+ years -- he has two threads of research, basic and industrial, and the former line of publications dried up around 2004.

* On the other hand I don't think anyone knew he was working on this. The only known serious effort was by Ketan Mulmuley at U Chicago.

* It has been known that the straightforward combinatorial approaches to P =? NP aren't going to work, and therefore something out of left field was required (<http://web.cs.wpi.edu/~gsarkozy/3133/p78-fortnow.pdf>). Mulmuley's plan of attack involved algebraic geometry.

* This paper uses statistical physics. This approach doesn't seem to have been talked about much in the community; I found only one blog comment [http://rjlipton.wordpress.com/2009/04/27/how-to-solve-pnp/#c...](http://rjlipton.wordpress.com/2009/04/27/how-to-solve-pnp/#comment-1260) which mentions the survey propagation algorithm. (Deolalikar's paper also talks about it tangentially.)

* If the statistical physics method used here is powerful enough to resolve P != NP, then there's a good chance it is powerful enough to have led to many smaller results before the author was able to nail the big one. It's a little weird we haven't heard anything about that earlier.

* Finally, since the author is using physics-based methods, there's the possibility that he is using something that's a "theorem" in physics even though it is technically only a conjecture and hasn't actually been proven. Physicists are notorious for brushing technicalities under the rug. It would be very unlikely that the author didn't realize that, but still worth mentioning.

* If that is indeed what happened here, but the rest of the proof holds up, then we would be left with a reduction from P != NP to a physics conjecture, which could be very interesting but not ground breaking.

Conclusion: overall, it certainly looks superficially legit. But in non peer
reviewed solutions of open problems there's always a high chance that there's
a bug, which might or might not be fixable. Even Andrew Wiles's first attempt
at FLT had one. So I wouldn't get too excited yet.

~~~
Confusion

      * If the statistical physics method used here is powerful
      enough to resolve P != NP, then there's a good chance it
      is powerful enough to have led to many smaller results
      before the author was able to nail the big one. It's a
      little weird we haven't heard anything about that earlier.
    

Well, Wiles didn't publish intermediate results either, partly because someone
might have beat him to the final result with those intermediate results. It
would also give away what he was working on. Deolalikar was aiming for the
grand prize as well, so skipping the publishing of intermediate results
doesn't seem strange to me.

~~~
Vivtek
The conclusion might seem to be that prizes harm science.

Which sucks, but intermediate results are important for science as a whole; if
there's significant financial reason to withhold them, we're no better than
the alchemists.

~~~
pmiller2
But, there was no prize for solving FLT other than being able to list on one's
CV "Proved FLT."

~~~
shadowfox
You wouldnt actually need to put that in your CV

~~~
bonafidehan
You actually won't need a CV.

~~~
shadowfox
That is a more precise statement :)

------
zacs
The paper's origin was that the author mailed a copy for review to some very
high-level folks in the field (Cook, Mazirani, Sipser, etc). Here's the mail:

Date: Fri, 6 Aug 2010 21:28:39 +0000 Subject: Proof announcement: P is not
equal to NP

Dear Fellow Researchers,

I am pleased to announce a proof that P is not equal to NP, which is attached
in 10pt and 12pt fonts.

The proof required the piecing together of principles from multiple areas
within mathematics. The major effort in constructing this proof was uncovering
a chain of conceptual links between various fields and viewing them through a
common lens. Second to this were the technical hurdles faced at each stage in
the proof.

This work builds upon fundamental contributions many esteemed researchers have
made to their fields. In the presentation of this paper, it was my intention
to provide the reader with an understanding of the global framework for this
proof. Technical and computational details within chapters were minimized as
much as possible.

This work was pursued independently of my duties as a HP Labs researcher, and
without the knowledge of others. I made several unsuccessful attempts these
past two years trying other combinations of ideas before I began this work.

Comments and suggestions for improvements to the paper are highly welcomed.

Sincerely,

Vinay Deolalikar Principal Research Scientist HP Labs

<http://www.hpl.hp.com/personal/Vinay_Deolalikar/>

~~~
leif
Somewhere, deep in a dark corner of my heart, I hope and pray that this paper
is correct, just so we can keep and revere the immortal words "I am pleased to
announce a proof that P is not equal to NP, _which is attached in 10pt and
12pt fonts_."

~~~
pclark
I'm not academic - can you explain why he mentioned the font sizes? Why are
they relevant?

~~~
xsmasher
I find the sentence comical in its humility and practicality; I assume leif
did too. Acangiano puts it in the same league as Fermat's famous note in the
margin of his copy of Arithmetica.

I assume he included the paper in two font sizes to suit the reader's
preference; no deeper meaning.

~~~
leif
Yeah, basically I found it funny juxtaposing the announcement of such a
magnificent result (should it end up proving true) with such a mundane,
utilitarian comment.

------
tzs
102 pages via one of the most annoying PDF readers on the planet? No thanks.

There are good, free, PDF readers for every major operating system and for
every major mobile device. I wish people would just link directly to PDFs.

~~~
emmett
Have you tried Scribd since they've transitioned to HTML 5? I now find it
quite usable.

~~~
amvp
I got their flash viewer for this. I do sometimes get the html5 viewer, and I
assumed the selection was based on a preference set by the uploader. Isn't it?

~~~
alextgordon
It seems they're A/B testing it. I got the html5 viewer all but one time
viewing this.

------
Eliezer
Scott Aaronson expresses his confidence that the proof is wrong by offering to
supplement the million-dollar Clay prize with $200,000 of his own money if
it's correct:

<http://scottaaronson.com/blog/?p=456>

~~~
Confusion
I find it strange that he doesn't explain his confidence with at least a
general description of the way in which he thinks the proof will fail.

I suppose he could have safely claimed this with Wiles's original proof as
well, since it did have at least one non-trivial flaw that required amending.
It's quite possible that the proof contains flaws, but will still hold up in
the end, because the flaws can be corrected. But I feel that's a bit of a lame
gamble.

~~~
albertzeyer
Sometimes there are also flaws which can not be corrected.

But I cannot make a qualified guess if this might be the case here.

~~~
Confusion
Of course, but that's an even larger gamble, if you don't have at least a very
specific hunch about the way in which a proof will fail. All in all, this
announcement by Aaronson seems rather rash. I don't understand why he would do
such a thing.

~~~
eru
I am OK with it. He put his money where his mouth is, instead of just putting
his mouth somewhere.

------
lkozma
I skimmed through the synopsis but this philosophical statement baffles me
(although obviously it is unrelated to the validity or invalidity of the
proof):

"The implications of [P ?= NP] on the general philosophical question of [..]
whether human creativity can be automated, would be profound."

How so? If P!=NP, that is obeyed by the brain as much as by computers and
whatever trick our brains does to be creative despite of this, will be
available to computers as well, regardless of P?=NP. What am I missing?

~~~
dasht
You must read it in context.

What it says is that if P == NP then the implications are profound for
applications such as cryptography and on the general question of whether human
creativity can be automated.

You can see why P == NP would have profound implications for crypto: many of
our widely used techniques would turn out to, um, be easy to crack.

I believe the intent regarding human creativity is that humans often end up
with a practical need to deal with some real-world instance of a size-able NP-
complete problem. We don't know any way to efficiently find the optimal
solution so we creatively deal with what we can figure out (the traveling
salesman's optimization problem, placed into the real world, might count). Are
our creative guessworks and heuristic discoveries essential? Or can automation
based on P == NP eliminate the need for them - and do better than we do on
these problems.

~~~
fmora
Lets assume that P==NP, why assume that we would be able to find algorithms to
easily crack crypto?

Let me put it another way, lets say that we finally discover that it is
possible to time travel to the past. However, the energy needed to travel back
int time is the equivalent of a million Suns because that is the amount of
energy needed to warp space enough so that time will reverse itself. And we
found proof of this when we observed the black holes of two galaxies
colliding. So, even if it were possible it would still not matter. Practically
speaking, it would still not be possible to travel back in time.

My gut feeling is that if it were to turn out that P==NP that would not
necessarily mean that all of a sudden we would be able to find the exact
algorithms that make it easy to crack cryptography algorithms easily.

~~~
varjag
We would know from the proof that such algorithms would exist, and possibly
get a method from the proof as to how formulate them.

Also, gut feeling doesn't work in math. I mean, not at all.

------
johnswamps
Here's a list of many other proofs for the P vs NP problem:
<http://www.win.tue.nl/~gwoegi/P-versus-NP.htm>

~~~
faragon
I hope this become wrong as well.

------
jackfoxy
Very interesting approach! How cool if this is the real deal. The last 30
years has seen a lot of theoretical work on computation as a physical process.
If the greatest conjecture in CS is proved using tools from physics it really
brings together math, physics, and CS.

Edit: As someone else pointed out a few minutes ago
<http://www.hpl.hp.com/personal/Vinay_Deolalikar/> confirmations began
arriving today. How soon before Vinay has a Wikipedia entry? For those who are
qualified to evaluate this, I suspect a consensus as to validity will develop
within weeks if not days. If thumbs up, he must be worthy of one of the
outstanding large-cash-value math prizes. Perhaps even the Nobel?

~~~
mzl
Wrong area for a Nobel prize, the prize areas are physics, chemistry,
physiology/medicine, literature, and peace. There is also a prize in economics
given at the same time.

~~~
eru
Perhaps he could steal the Economics "Nobel" prize, like lots of other
mathematicians have done.

There was a paper about how recognizing bad securities is a NP hard problem a
while ago. So this is applicable. (Tongue-in-cheek.)

~~~
linhares
[http://scholar.google.com.br/scholar?q=%2B%22np+complete%22+...](http://scholar.google.com.br/scholar?q=%2B%22np+complete%22+%2Bfinance&hl=pt-
BR&btnG=Pesquisar&lr=)

------
sidww2
His personal home page <http://www.hpl.hp.com/personal/Vinay_Deolalikar/>
seems to have been updated.

"Manuscript sent on 6th August to several leading researchers in various
areas. Confirmations began arriving 8th August early morning. Final version of
the paper to be posted here shortly. Stay tuned. "

~~~
studer
It's been updated again, with a revised version of the draft ("minor updates")
dated August 9, 2010.

------
tshtf
I've not seen any discussion of his paper yet, but the author has an
impressive CV:

<http://www.hpl.hp.com/personal/Vinay_Deolalikar/>

------
mmaunder
Bummer! It's like proving conclusively that the tooth fairy, Santa and the
Easter bunny definitely don't exist.

------
bramcohen
While the author of this paper does not appear to be a crank, nowhere in the
entire paper does it discuss why the fundamental barriers of naturalization,
algebrization, and relativization don't apply to the work, making it seem
unlikely that those barriers have actually been overcome.

~~~
long
From what little I understand, those barriers prevent only certain proof
strategies from working. So for instance, the Razborov-Rudich barrier concerns
a class of combinatorial proofs (the so-called natural proofs); this paper
uses two techniques - statistical mechanics and model theory - which I gather
are out of the province of RR.

~~~
cdavidcash
"only certain proof strategies" is technically correct, but its closer to
"essentially every proof strategy we can conceive of".

And besides, the question is over the entire proof strategy and not the
specific techniques involved. It seems plausible that one could give a
relativizing proof using some method of calculation from statistical
mechanics, for example.

~~~
long
Again, I'm no expert, but relativization and algebrization are properties of
proofs that invoke oracles, which this paper doesn't appear to do.

~~~
cdavidcash
Ah, that is not how those "barriers" work. Roughly, the relativization barrier
goes like this: Say you have a proof that P!=NP. Does it also prove that P^A
!= NP^A for any oracle A? If it does, then the proof is flawed, because there
<i>does</i> exist an oracle A such that P^A = NP^A!

Such proofs are said to relativize -- i.e., they are still valid relative to
any oracle.

~~~
long
Ah, thanks for explaining!

------
simonista
I'd like to say congratulations to Vinay Deolalikar for getting to this point
and putting the paper out there. As randomwalker and others have said, this
appears to at least be a legitimate attempt. It must take some seriously thick
skin to work on a paper that a) is in an area so full of failed attempts and
error filled proofs; and b) that EVERYONE is going to read and try to tear
apart.

------
vide0star
We created a prediction market for the next winner of the Clay Prize here
<http://smarkets.com/current-affairs/clay-prize/next-winner>

------
dalton
WOW.

Assuming this isn't a hoax, and the proof holds up, this is front-page news
kind of big deal.

As I recall, this has way more real-world practical usage than the Fermats
Last Theorem proof.

Read the "Consequences of Proof" section in the Wikipedia article here:
<http://en.wikipedia.org/wiki/P_versus_NP_problem>

[edit] The responses below are correct. Proving P=NP means the world gets
turned upside down. P != NP is already sort of assumed.

~~~
ynniv
a) Complicated academic proofs take (and _should_ take) months if not years to
verify, and will only be "front-page news" after verification. This is hardly
the first unverified proof of the [edit: possible (in)]equality of P and NP.

b) The practical consequences of P=NP are immense. The practical consequences
of P≠NP are that we can stop looking for computational unicorns and fairies.

We have for some time thought that P≠NP, but boy do people like those unicorns
and fairies.

~~~
Groxx
I doubt it'll impact the unicorns-and-fairies searches significantly. _Most_
people already work under the assumption that P≠NP.

Similarly, _most_ people believe the world is round, and we go around the Sun.
This hasn't prevented serious flat-Earthers nor geocentrists from existing.

~~~
tel
It has been something of a damper on their funding, however.

------
xtacy
At least for this, we should have a reddit like system for peer reviewing, so
that comments from all reviewers can be seen by everyone.

~~~
alextp
This is actually not a bad idea, and some scientific groups are pressuring to
move to this model. See Yann LeCun's proposal (
<http://www.lecun.com/ex/pamphlets/publishing-models.html> ) for an example.
ICML almost does this. The review is done privately (due to some well-
discussed elsewhere issues with double anonymity), but there's a public
discussion site for all papers <http://mldiscuss.appspot.com/> . And people do
use it, and for some papers you will find important information there.

------
uptown
Some background on the P ≠ NP problem:

<http://en.wikipedia.or/wiki/P_versus_NP_problem>

<http://www.claymath.org/millennium/P_vs_NP/>

~~~
hbt
Edit: Actual link is

<http://en.wikipedia.org/wiki/P_Versus_NP_Problem>

------
benhalllondon
Anyone got a link to any proper discussion?

~~~
kjrose
Yeah, I'd be curious to see what people who are still working in the field
have to say. My red flags went up as soon as I read "statistical" in the
abstract, since that could easily imply the common problem of assuming the
existence of a secure PRNG. However, I haven't read the entire paper in depth
(and likely won't have time to anytime soon), so I don't really know if that
common trap was fallen into.

~~~
hga
Statistical _mechanics_ : <http://en.wikipedia.org/wiki/Statistical_mechanics>

~~~
kjrose
"is the application of probability theory"

My comment still stands.

~~~
hga
I wonder, since you said your problem was that it " _could easily imply the
common problem of assuming the existence of a secure PRNG_ ". Statistical
mechanics involves real, true randomness, and the statistical comes in e.g.
where you use statistical _models_ of things at the micro scale to explain
macro scale behavior. I don't get the impression that it involves statistics
in the way you are using the word.

------
gill1109
I think that whether P is NP or not could turn out to be undecidable and in
fact one could add either equality or inequality as an independent axiom. The
theory of computational complexity is about asymptotic results as the size of
the instances goes to infinity and involves `there exists` statements whose
meaning when applied to infinite sets is typically ambiguous. For instance, it
turned out to be a matter of choice whether or not you want the set of all
subsets of real numbers between zero and one to equal or to be strictly larger
than the set of so called measurable sets. And whether or not a set is
measurable can be characterized in a very concrete way about the possibility
of approximating it by unions of intervals. So the question of whether or not
there exist non measurable sets turned out to depend on `what you mean by
set`in a way which people hadn´t thought about before. I suspect the question
whether or not P is NP will depend on what we mean by P and NP in ways which
so far no one thought about.

------
jarsj
I think this is getting unwanted publicity. The author never released the
proof in public or made any announcement. He only sent it to his expert
friends so that they can point out potential flaws. May be this needs more
research and putting him in spotlight is not helping anything.

~~~
philwelch
Actually I think a leak is more helpful than either the author himself
releasing the proof publicly or keeping everything under wraps.

Especially since the cold fusion thing[1], researchers have been loath to
publicly announce revolutionary findings lest the findings fail to pan out.
Researchers don't want to be known as publicity-seeking cranks, they want to
be known as earnest and honest academics, which I suspect entails playing to
the in-crowd and letting the system work[2]--the system being to talk to your
colleagues before hand, release everything through peer-reviewed journals, and
if everything passes muster, you've eliminated any risks to your reputation
while achieving renown as the guy who proved P != NP.

On the other hand, having the proof publicly available to anyone who can
understand it can massively parallelize the process of having it verified, or
having errors found and potentially corrected. Meanwhile, the researcher's
reputation is maintained, because he did the right thing, and if any errors
are found he'll be judged to have acted prudently and conservatively in
advance of having his findings reviewed.

[1] Fleischmann and Pons publicly claimed to have discovered a means to induce
nuclear fusion at room temperature in 1989, but their results couldn't be
replicated.

[2] And the system _does_ work--this is no criticism.

------
noahlt
Why isn't this in a peer-reviewed journal?

~~~
aswanson
Because it hasn't undergone the proper level of review in order to be
published in one. As it stands, there is no reason to take it seriously until
it has been. There have been several posts of such papers here before, and I
would highly advise the level of skepticism expressed by a fellow HNer with
submissions like this c.f. : <http://news.ycombinator.com/item?id=893877>

~~~
scott_s
Granted, but this author does not set off any crackpot flags: he's had plenty
of prior publications in areas relevant to the proof and works in an industry
research lab. Another poster points this out:
<http://news.ycombinator.com/item?id=1585999>

~~~
pmiller2
Also, the paper was written using LaTeX. I have a friend who spent a semester
helping to edit a small mathematics journal, and, with virtually 100%
accuracy, you could tell the crackpot papers from the serious ones based
simply on whether they used LaTeX or not.

~~~
shasta
Submissions in .doc format can also be immediately judged with near 100%
accuracy.

------
dasht
So: What publicly traded firms benefit from a confirmation that P!=NP and are
there any that lose (e.g., that were betting that P might == NP).

There's gotta be money in this news :-)

~~~
shrikant
There sure is: <http://www.claymath.org/millennium/P_vs_NP/>

~~~
dasht
Ah, yes. No, I meant for the outside investor with early news of the purported
proof who is willing to bet that it holds up.

For example, if there is some crypto company whose business is premised on
hedging that a "P == NP" proof is just around the corner - short them.
Alternatively, maybe buy the firm we think of as RSA. That kind of thing.

This paper hasn't yet got a lot of press attention and I'm only about 1/4
joking when I say I'm curious as to what effect it will have on various stocks
if it isn't quickly debunked.

~~~
euccastro
HP will get some prestige out of this, and not much else will happen short
term. Almost everyone was already assuming P != NP.

------
frevd
I think there might be a way to solve all n-SAT problems (if reformulated
using conjunctive normal form) in O(C) best up to worst O(C * N * N) time and
O(C * N) space (C = number of AND-clauses, N = number of distinct literals
from all clauses). would that still be polynomial and a valid proof or even
possible (not a mathematician I am)? on the other hand, proving P = NP would
not be wise, morally seen, would it?

------
todayortomorrow
Looking at the comments at [https://rjlipton.wordpress.com/2010/08/08/a-proof-
that-p-is-...](https://rjlipton.wordpress.com/2010/08/08/a-proof-that-p-is-
not-equal-to-np/) there are many points to clarify. Specially the intuition
from statistic physics is not true in other examples and the difference is not
clear. So ...

------
agbell
4 possible problems with the proof:
[http://rjlipton.wordpress.com/2010/08/09/issues-in-the-
proof...](http://rjlipton.wordpress.com/2010/08/09/issues-in-the-proof-
that-p%E2%89%A0np/)

------
Jun8
This is sad: This result, if correct, is the mathematical result of the
century; however, it still hasn't appeared in Google News or Google trends.

~~~
houseabsolute
It's a leaked PDF of an unverified proof which has yet to appear in any
mainstream news source and is relevant, probably, to no one but computer
scientists. So it's not even remotely surprising that it has not yet appeared
on Google News. I have no idea what part of this you think is sad.

~~~
Jun8
This result is _much_ more relevant than either Perelman's proof of the
Poincare Conjuncture or Wiles' proof or Fermat's Conjuncture, both of which
got huge coverage in the mainstream media. If you think this is relevant to
"no one but computer scientists" you are naive about the ramifications of the
result.

The proof is unverified but most qualified sources say it is one of the best
efforts in many years, it could even be _the_ proof. This was the #1 news in
most technical blogs yesterday.

~~~
xyzzyz
The thing is, we can't talk about any result yet. So far, we only have a paper
which didn't even underwent peer-review. I'm sure it will get enormous media
coverage, but not sooner than it gets published.

------
cakeface
* RSA and all our other current crypto algorithms breathe a collective sigh of relief _

------
alanh
Wow. 100% of zac’s 724 karma points come from this post & his comments on it.

------
farrero69
bñpg en el cual se puede jugar al mitico mario bros.

<http://blog-de-un-youtube-facebook-tuenti.blogspot.com/>

------
WildUtah
Everyone has been suspecting or assuming that P is a strict subset of NP for
decades. Still, every time someone proposes a serious attempt at proving it,
it's front page news and smart people will have to comb over the argument for
months to have confidence that it's right.

The opposite proposition -- that P is equal to NP -- is widely doubted. But if
there were a proof that P and NP were equal, anyone with a good data set could
verify the proof in a few minutes. Just run the proof on a hard 3-SAT or
whatever and observe the answer returning significantly before the heat death
of the universe.

So what we think is true is insanely hard to verify but what we think is false
is blazingly obvious to check. Chalk another one up for irony.

~~~
Ramfjord
P is a strict subset of NP. If you can solve the problem in polynomial time,
then you can verify a solution simply by generating it.

~~~
RiderOfGiraffes
That means it's a subset and is trivial. To claim it's a _strict_ subset means
there's something in NP that's not in P.

------
ilkhd2
See, all these monstrous old companies such as IBM and HP, they hire pure
scientists such as Chaitin and this guy, and every once in awhile it pays off.
I have feeling, yonger companies, with their own research departments, they
are still very down to earth, and look for immediate profit from R&D.

~~~
werrett
To quote the announcement email which zacs posted earlier:

    
    
      This work was pursued independently of my duties as 
      a HP Labs researcher, and without the knowledge of 
      others. I made several unsuccessful attempts these 
      past two years trying other combinations of ideas 
      before I began this work.
    

So based off this solitary data point, it seems that while they might hire the
brains it doesn't necessarily follow that they have free rein to work on
esoteric "non-profitable" projects.

------
crizCraig
The two main consequences that would follow are (from Wikipedia):

"A proof that showed that P ≠ NP, while lacking the practical computational
benefits of a proof that P = NP, would also represent a very significant
advance in computational complexity theory and provide guidance for future
research. It would allow one to show in a formal way that many common problems
cannot be solved efficiently, so that the attention of researchers can be
focused on partial solutions or solutions to other problems. Due to widespread
belief in P ≠ NP, much of this focusing of research has already taken place."

"Cryptography, for example, relies on certain problems being difficult. A
constructive and efficient solution to the NP-complete problem 3-SAT would
break many existing cryptosystems such as Public-key cryptography, used for
economic transactions over the internet, and Triple DES, used for transactions
between banks. These would need to be modified or replaced."

So basically we can focus on finding good approximations to NP problems and
feel safe that this proof won't immediately jeopardize all of our bank
accounts.

~~~
NateLawson
The above is false (par for Wikipedia). While RSA is based on the difficulty
of factoring, DES (and 3DES) are not. The DES cipher is based on
substitution/permutation and not number theory.

Also, factoring is known to be subexponential (e.g., GNFS). While there is no
known polynomial time factoring algorithm, this may give some evidence that
the integer factorization problem might be in P. Factoring is known to not be
NP-complete and we hope it is not in P. While a proof that P=NP would be
disastrous for RSA, a proof that P!=NP does not mean factorization is
guaranteed to be safe against future advances in algorithms.

In other words, proof that P!=NP would be an amazing result but someone could
still improve factoring algorithms.

------
ilkhd2
Hee is another PDF: <http://www.win.tue.nl/~gwoegi/P-versus-NP/Deolalikar.pdf>

------
binaryfinery
What to do? Read paper or hit next months deadline...

------
newacct
P = NP if and only if N = 1 or P = 0

~~~
petercooper
Beat you to it! <http://twitter.com/peterc/status/20667523417>

I didn't post it here because I realized it's a joke most people won't get and
those who do get it won't find it funny ;-) This joke could even be a Reddit
vs HN shibboleth as I just saw it made there too and it's being voted up.

~~~
linhares
P!=NP if and only if P=1 and N=1.

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LiteOn
That paper is written just a smidgen above my reading level.

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d0m
I always felt that it was logical that N != NP. However, I certainly couldn't
prove it.

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regexnow
Interesting

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ziadbc
Can someone call Knuth? If he gives it the thumbs up then I'll believe it.

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waqf
I'm not sure whether Knuth has the ergodic-theory background. Perhaps call
Terry Tao?

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studer
Tao comments on it (very briefly) here:

[http://terrytao.wordpress.com/2009/08/01/pnp-
relativisation-...](http://terrytao.wordpress.com/2009/08/01/pnp-
relativisation-and-multiple-choice-exams/#comment-46431)

~~~
ziadbc
Thanks for the info. I originally posted my request (half serious, half
jokingly) when not many explanations in the thread were there to respond to
the validity of the paper. Thanks for your insight.

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parfe
Proving P ≠ NP is like finding the Higgs Boson. It doesn't change anything and
a lot of people spent a lot of time showing that they have spent a lot of time
changing nothing.

