# Claimed Proof That P != NP

#### kdawson posted about 4 years ago | from the sufficiently-complex dept.

457
morsch writes *"Researcher Vinay Deolalikar from HP Labs claims proof that P != NP. The 100-page paper has apparently not been peer-reviewed yet, so feel free to dig in and find some flaws. However, the attempt seems to be quite genuine, and Deolalikar has published papers in the same field in the past. So this may be the real thing. Given that $1M from the Millennium Prize is involved, it will certainly get enough scrutiny. Greg Baker broke the story on his blog, including the email Deolalikar sent around."*

## Well, duh (5, Funny)

## Anonymous Coward | about 4 years ago | (#33183704)

I mean, NP has an N in front of the P. That's obviously not the same as P. Also, P != HP.

## Re:Well, duh (1, Interesting)

## hedwards (940851) | about 4 years ago | (#33183750)

## In other news, HP sex Scandal == Push other news (4, Funny)

## tomhudson (43916) | about 4 years ago | (#33184276)

It's funny how we don't hear anything from HP for ages, then as soon as there's a sex scandal involving the disgraced CEO [engadget.com] , out come all sorts of distractions.

I smell a rat. Okay, I smell 2 rats - Mark Hurd (ex-CEO) and HPs' spin department.

## Re:Well, duh (5, Funny)

## Anonymous Coward | about 4 years ago | (#33183766)

I mean, NP has an N in front of the P. That's obviously not the same as P. Also, P != HP.

If you knew really advanced mathematics you'd know that NP means N times P. So NP does equal P when N=1. But not the rest of the time. Oh and it does when P=0. How much was that prize again?

## Re:Well, duh (5, Informative)

## Peach Rings (1782482) | about 4 years ago | (#33183830)

Ohhhh my god, someone modded this insightful.

P is polynomial time.

NP is non-deterministic polynomial time.

They're algorithmic complexity classes.

## Re:Well, duh (4, Insightful)

## Anonymous Coward | about 4 years ago | (#33183884)

Ohhhh my god, someone modded this insightful.

Okay... sometimes when it's really

reallyobvious that something's a joke, it's okay to play along and make mock serious follow ups and even *gasp* non-serious moderations. This works on the basis that it's obvious that both the original poster and the modder are joking.really## Re:Well, duh (4, Funny)

## Peach Rings (1782482) | about 4 years ago | (#33184020)

I had an unshakable image of some web design "IT guy" who had one forgotten lecture on this subject back in trade school nodding sagely as he thinks he understands what everyone's talking about and reaching for the Insightful moderation.

I didn't have the benefit of the reassuring

Score:5, Funnythat you had.## Re:Well, duh (-1, Troll)

## Cylix (55374) | about 4 years ago | (#33183990)

I don't know if I trust that statement as it seems as if it was created from a techno babble generator.

If "non-deterministic polynomial time" is an actual "algorithmic complexity class' then so is my "anomalous quantum field" which generally intersects with a "temporal phase disturbance."

And now I will return to watching Idiocracy or as I like to call it... the future.

## Re:Well, duh (1)

## ioshhdflwuegfh (1067182) | about 4 years ago | (#33184036)

## Re:Well, duh (2, Funny)

## PopeRatzo (965947) | about 4 years ago | (#33184098)

Professor Corey? Is that you, Irwin?

## Re:Well, duh (0)

## Anonymous Coward | about 4 years ago | (#33184004)

Hook, line and sinker.

## Re:Well, duh (5, Funny)

## Draek (916851) | about 4 years ago | (#33184048)

Funny doesn't give karma, Insightful does.

At least that's what I tell myself so I can sleep at night.

## Funny can cost you karma (1, Insightful)

## davidwr (791652) | about 4 years ago | (#33184100)

+1 funny

-1 overated

+1 funny

+1 funny

-1 overated

+1 funny

+1 funny

-1 overated

+1 funny

+1 funny

-1 overated

+1 funny

+1 funny

-1 overated

+1 funny

repeat last 3 lines as many times as you like.

Net result: post is +5 funny but you take major karma hits.

Disclaimer: This was true in the early days of funny = no karma boost. They may have fixed it by now. Personally, I think karma should not contribute to karma except to offset overrated or some similar rating designed to indicate "not as funny as it's currently rated."

## Re:Funny can cost you karma (1)

## siride (974284) | about 4 years ago | (#33184186)

## Poly? Poly want a cracker? (0)

## Anonymous Coward | about 4 years ago | (#33184118)

Say who/wha/where? We are da linuxers, we don no no maths!!

## Re:Well, duh (0, Flamebait)

## icebike (68054) | about 4 years ago | (#33184114)

I mean, NP has an N in front of the P. That's obviously not the same as P. Also, P != HP.

If you knew really advanced mathematics you'd know that NP means N times P. So NP does equal P when N=1. But not the rest of the time. Oh and it does when P=0. How much was that prize again?

And if you didn't know any advanced mathematics You could read the wiki page about this problem:

http://en.wikipedia.org/wiki/P_versus_NP_problem [wikipedia.org]

However, it seems you could read that page, and still have not a single useable clue.

## Re:Well, duh (1)

## RabbitWho (1805112) | about 4 years ago | (#33184164)

I love you guys.

## Rats! (0)

## 5pp000 (873881) | about 4 years ago | (#33183720)

I was right on the edge of solving it myself.

Not :-)

## Well, Thank God... (5, Funny)

## jjohnson (62583) | about 4 years ago | (#33183730)

I was a afraid he might have left out an important step.

## Re:Well, Thank God... (3, Funny)

## ArsonSmith (13997) | about 4 years ago | (#33183804)

it was shortened the original proof he was working on was 10Pt !=(or Not) 12Pt font. The journalist shortened it to P!=NP. The rest of the text is meaningless other than to illustrate the difference.

## Re:Well, Thank God... (0, Offtopic)

## Twinbee (767046) | about 4 years ago | (#33183948)

Just gonna moan about your sig, sorry. If by definition, one language is simpler, more elegant, faster yet also slightly more high level, terser, yet more powerful than another programming language, that would make it 'better' than another language given all else equal. If we accept that a language could be slightly better than another language then it stands to reason that a language could be *much* better (or indeed, much worse).

I don't really currently like or hate any language (I use c/c++ mostly, if only for the speed) as they all have their glaring faults. But in theory, and maybe in practise within 100 years, a language will be so good that it deserves to be loved, and yes, loved more so than other languages.

## Re:Well, Thank God... (0)

## Anonymous Coward | about 4 years ago | (#33184152)

I'll give you this: you did prove his sig lacking. It should just say "anyone talking about any language, platform, or manufacturer doesn't know what they're talking about."

## this is going to create history (0)

## Anonymous Coward | about 4 years ago | (#33183740)

## Re:this is going to create history (1)

## Peach Rings (1782482) | about 4 years ago | (#33183860)

FLT took over

three hundred sixty yearsto prove, and so far P=NP appears to be even slipperier. The whole field of study is only 40 years old too.## Re:this is going to create history (1)

## icannotthinkofaname (1480543) | about 4 years ago | (#33183910)

It's only going to create history if there is no flaw in the proof. If Deolalikar missed something, then this is all hype.

## Simpletons! (0)

## hansamurai (907719) | about 4 years ago | (#33183752)

For values of N where N != 1

## Re:Simpletons! (1)

## hkz (1266066) | about 4 years ago | (#33183858)

And P is nonzero.

## I think this is going to take a while. (1)

## IgnitusBoyone (840214) | about 4 years ago | (#33183754)

At a 100 pages its going to be a while before I can say I have RTFA, but I'll get back with any relevance in a few days after I have digested it. I suggest any post claiming other wise are a bit hasty.

## Not Only Time But Several Disciplines (4, Interesting)

## eldavojohn (898314) | about 4 years ago | (#33183838)

At a 100 pages its going to be a while before I can say I have RTFA, but I'll get back with any relevance in a few days after I have digested it. I suggest any post claiming other wise are a bit hasty.

You can read section one (the introduction) and get a high level walk through of what he's doing. Just be prepared to have a requisite in the following to make it through that:

In order to apply this analysis to the space of solutions of random constraint satisfaction problems, we utilize and expand upon ideas from several fields spanning logic, statistics, graphical models, random ensembles, and statistical physics.

My computer science, math and statistics are still fairly sharp but the physics and graph theory are a bit much. Indeed this will take a while to digest. If he hasn't made a mistake in something like bridging together least fixed point logic and functions [wikipedia.org] with Markov-Gibbs properties (correspondence and equivalence) [ia.ac.cn] .

On the one hand it seems this will take a general expert in the math related sciences to verify but on the other you would think that -- like with the E8 and Lie groups -- this sort of proof would require a rather large unified theory to be able to reduce the N=NP? problem down to a provable situation. I'm no expert and it's been three or four years since I've even been in academia but even the subsections of this paper are noteworthy if they are true. It could be we're looking at something that jumps so far ahead like the famous papers of Turing and Shannon.

## Re:I think this is going to take a while. (2, Funny)

## Niobe (941496) | about 4 years ago | (#33184016)

At a 100 pages its going to be a while before I can say I have RTFA, but I'll get back with any relevance in a few days after I have digested it. I suggest any post claiming other wise are a bit hasty.

Aren't the best theories supposed to be elegantly simple? This looks a mess.

Wait.. that's just how my head feels after reading the abstract.

## Re:I think this is going to take a while. (0)

## Anonymous Coward | about 4 years ago | (#33184204)

Depends, the 4-color Theorem still requires computer aided proof.

## Well, shoulders of giants and all (1, Insightful)

## Anonymous Coward | about 4 years ago | (#33183762)

As far as I know, this is the first very public proof attempt- its likely it will have flaws, but it may pave the way for someone else or further attempts from the same source even if flaws are found.

## Let me be the first to say (1)

## Zaphod The 42nd (1205578) | about 4 years ago | (#33183764)

## How dare you say "OH YEAH!!!!!" (3, Funny)

## Anonymous Coward | about 4 years ago | (#33183844)

## Re:How dare you say "OH YEAH!!!!!" (1)

## EmagGeek (574360) | about 4 years ago | (#33184106)

Whatchoo talkin' about, AC????

## What would the impacts of this be for cryptography (3, Interesting)

## HungryHobo (1314109) | about 4 years ago | (#33183770)

What would the impacts of this be for cryptography?

from a theoretical point of view at least?

I was under the impression that a lot of cryptography was based upon the hope that P!=NP and while in practice this wouldn't change much about anyone acts it might have an impact on how people think about the old cryptology vs cryptanalysis race.

## Re:What would the impacts of this be for cryptogra (4, Informative)

## jjohnson (62583) | about 4 years ago | (#33183796)

Off the top of my head, if P = NP, then a lot of cryptography like RSA and elliptic curve cryptography become, in principle, mathematically solvable. Much of their security is premised on the idea that their equations are prohibitively difficult to brute force because they're NP.

If this proof holds up, then RSA and ECC become provably secure in a way they weren't before.

## Re:What would the impacts of this be for cryptogra (1, Informative)

## Anonymous Coward | about 4 years ago | (#33183928)

My analysis said DH would hold even if P=NP.

I had a lower bound on the order of the polynomial for breaking DH and it was something like 256. There's really not much practical difference between n256n for n = 4096. Both are practically intractable.

## Re:What would the impacts of this be for cryptogra (1)

## Peach Rings (1782482) | about 4 years ago | (#33183940)

No. Even if there are found to be integer factorization algorithms theoretically in P, there's still no practical way to crack it. This is all asymptotic complexity (what happens as your key size goes to infinity), which might be important when we start using tebibit symmetric keys, but in the real world the constant coefficients (which are thrown away in asymptotic analysis) would be really high.

Elliptic curve crypto is different though, I think.

## Re:What would the impacts of this be for cryptogra (2, Informative)

## Peach Rings (1782482) | about 4 years ago | (#33183962)

I meant asymmetric, which is what RSA is. Symmetric keys are usually exchanged relying on the discrete logarithm problem (RSA problem [wikimedia.org] ), not the integer factorization problem.

## Re:What would the impacts of this be for cryptogra (0)

## Anonymous Coward | about 4 years ago | (#33183984)

Well, just because something is in "P" doesn't mean it's trivial. For instance, if you discovered a prime number factorization algorithm that was O(b^100) it would not be useful for an RSA attack.

Also, it's not even known that factoring primes is NP-complete, co-NP, or even P. It's known to be P in a quantum computer (O(b^3), to be precise) and *suspected* to be not P in a Turing machine, but I don't think anyone has proven that.

Now I know you said "in principle, mathematically solvable".. but by that standard RSA is already solvable. It just isn't known to be solvable quickly. P=NP would not change that.

But all of this is moot since the alleged proof is that P!=NP which is what almost everybody assumed already. So the practical impact of this proof would be minimal, but it still would be a milestone in mathematics. At this stage I'd recommend caution though, there have been many "proofs" for P=NP and P!=NP over the years. This one has a pretty decent pedigree, but it's still very early in the review process. It's very possible that a subtle flaw will be found.

## Re:What would the impacts of this be for cryptogra (2, Informative)

## kenryd (1727522) | about 4 years ago | (#33184094)

Off the top of my head, if P = NP, then a lot of cryptography like RSA and elliptic curve cryptography become, in principle, mathematically solvable. Much of their security is premised on the idea that their equations are prohibitively difficult to brute force because they're NP.

If this proof holds up, then RSA and ECC become provably secure in a way they weren't before.

The security of RSA is based on the idea that it is very difficult to factor large integers. However, this has not been shown to be an NP-hard problem and so really doesn't have anything to do with this.

## Re:What would the impacts of this be for cryptogra (1)

## mdmkolbe (944892) | about 4 years ago | (#33184144)

I thought RSA might still be P even if P!=NP because we don't know if integer factorization is NP complete.

## Re:What would the impacts of this be for cryptogra (1, Insightful)

## Anonymous Coward | about 4 years ago | (#33184224)

It's not. Although it might be NP-hard.

## Re:What would the impacts of this be for cryptogra (0)

## Anonymous Coward | about 4 years ago | (#33184160)

No, that's wrong.

P, NP and NP-hardness are properties of *classes* of problems, and they say something on how fast (or slowly) the problems in the class get harder as size of the problem increases.

If a class is NP-hard and NP != P then this class is not P, yes. But it may still be easy for any instance under a billion bits, which would make it easy for practical purposes.

So even if ECC is NP-complete (NP and NP-hard, and I'm really not sure if we know that this is the case), and even if TFA is Tantalizingly Fucking Accurate, this alone doesn't prove the security of any specific system. Although, in practice, in the case of ECC, I'm sure you can count on it.

As for RSA, it's not known to be NP-hard, but again this doesn't rule it out as practically a very secure system.

## Re:What would the impacts of this be for cryptogra (4, Interesting)

## Zaphod The 42nd (1205578) | about 4 years ago | (#33183820)

## Re:What would the impacts of this be for cryptogra (1, Interesting)

## Anonymous Coward | about 4 years ago | (#33183960)

Really, P = NP would have far reaching implications to security, essentially proving that method of security will never be secure.

Wrong.

1. Polynomials can sill be really big. n^100000000 is in P, but an O(n^100000000) algorithm would not be practical.

2. There are complexity classes above NP which are provably not equivalent to P.

## Re:What would the impacts of this be for cryptogra (1)

## maraist (68387) | about 4 years ago | (#33184218)

And I'm not sure what you're saying with n^1E8 . Consider what it would mean to have such a coefficient. 100 million nested loops?? Where practically speaking are you going to have that kind of coefficient in a polynomial algorithm? (I only bring it up because you mentioned practical).

The practical problem class is factorial or exponential n ^ x, which occur in combinatorial problem sets (meaning with every new element, you have to consider every existing element's permutations or combinations). Most interesting problems live here.

That being said, I've never formally studied P/NP, and personally find it a boring subject (especially given how much face time the subject gets)

## Re:I guess its good for cryptography. (1)

## snikulin (889460) | about 4 years ago | (#33184052)

And it's bad for the rest of us the mere mortals who is sweating optimizing some mundane algorithms to allow them run on slow but power-efficient ARMs of today.

## Re:I guess its good for cryptography. (1)

## Zaphod The 42nd (1205578) | about 4 years ago | (#33184142)

## Re:I guess its good for cryptography. (1)

## maraist (68387) | about 4 years ago | (#33184238)

## Re:What would the impacts of this be for cryptogra (5, Insightful)

## Kjella (173770) | about 4 years ago | (#33184168)

Really, P = NP would have far reaching implications to security, essentially proving that method of security will never be secure. If it is P != NP, then that means that you can have problems which take longer than polynomial time to calculate but only polynomial time to verify.

I think it's important to realize that even if they are "unresolved problems" of mathematics, it's not like both answers are equally likely like the flip of a coin. For example the Riemann hypothesis states that all non-trivial zeros of the Riemann zeta function have real part 1/2. It's true for every non-trivial zero we've ever found, but it's not

proventrue for all the infinitely many zeros. However, outside of mathematics a proof it's true will be met with "yeah, that's what we thought" and a proof it's false with "OMG what's going on here?". Another example is the prime twin conjecture, are there inifinte pairs like (3,5) (5,7) (11,13) (17,19) and so on. There's very good reason to believe it's true but nobody has able to formally prove it. There's a lot of problems today that appear to support the idea that P != NP, and that's what most people believe the answer is. However, stringing together formal proof that it's so is much harder. If this paper turns out to be true, surely it's a great leap for mathematics but it's the answer that doesn't change the world.## Re:What would the impacts of this be for cryptogra (3, Interesting)

## maraist (68387) | about 4 years ago | (#33184176)

## Re:What would the impacts of this be for cryptogra (0)

## mikeee (137160) | about 4 years ago | (#33183874)

Short form:if P=NP, crypto is something of a futile effort - that implies that there's a non-brute-force crack to

every possibleprivate-key algorythm. I suppose it might still be slow enough for the crypto to be useful, but I woudl expect you would end up needing gigantic keys.Most everybody assumed that P!=NP, but nobody has been able to prove it.

## Re:What would the impacts of this be for cryptogra (3, Interesting)

## hardburn (141468) | about 4 years ago | (#33183876)

Practically, not much. It means we can breathe easy that a lot of crypto out there is now provably secure. It's been long considered likely that P != NP, because a lot of NP-complete problems are very old and nobody has gotten very far in solving them, and the extra focus in the last 40 years in breaking public key crypto hasn't produced much more progress on the problem. It was just the nagging issue of nailing down a proof.

A proof that P = NP would have resulted in a lot of cryptographers committing Seppuku. The contrary proof doesn't have many huge implications, though.

## Re:What would the impacts of this be for cryptogra (2, Insightful)

## z-j-y (1056250) | about 4 years ago | (#33183916)

It means we can breathe easy that a lot of crypto out there is now provably secure.

Wrong. It doesn't prove that there is no faster factoring algorithm.

## Re:What would the impacts of this be for cryptogra (1)

## noidentity (188756) | about 4 years ago | (#33183968)

## Re:What would the impacts of this be for cryptogra (2, Interesting)

## Peach Rings (1782482) | about 4 years ago | (#33184002)

If I were a cryptographer, I'd be positively :)

itchingfor someone to break RSA. A 30 year old univerally-used secure cryptosystem means no job.In a world where no crypto is really secure, everyone hires their own cryptographer to build a custom cryptosystem. Let's see Bletchley Park mathematicians try to cleverly crack gigabytes of junk encrypted data when the keys wouldn't fit in all the notebooks required to fill their entire building floor to ceiling.

## Re:What would the impacts of this be for cryptogra (1, Insightful)

## Anonymous Coward | about 4 years ago | (#33183902)

## Re:What would the impacts of this be for cryptogra (2, Informative)

## Anonymous Coward | about 4 years ago | (#33184132)

Large integer factorization has not been shown to exist in NP-Complete (it is doubtful it does), it is know to exist in both NP and co-NP, it could exist in P (but it is doubtful) we just don't know. RSA public key crypto depends on the difficulty of factoring very large numbers. Currently there is no known efficient mechanism for determining the factors of a very large number. If P != NP we don't get a whole lot more than we have at the moment because we don't know exactly what complexity class integer factorization lives in. If P == NP then we have a serious problem because that requires there to be an efficient integer factorization algorithm. It is interesting that if P != NP we could very well end up in a situation where there are problems that have no efficient solution (not in P) but are not in the class NP-Complete (the "hardest" of the problems in NP). Integer factorization could very likely fall within this area.

## Re:What would the impacts of this be for cryptogra (0)

## Anonymous Coward | about 4 years ago | (#33184236)

Luckily, my cryptographic scheme based on large Busy Beaver numbers remains theoretically sound.

## Well that was an overly complex solution (0)

## Anonymous Coward | about 4 years ago | (#33183774)

P != NP because it has an N there.

Well, wait, N could be 0 and P could still be zero, so in essence i made nothing from something.

Be right back, building a blackhole machine

## They took our jobs! (-1, Offtopic)

## Anonymous Coward | about 4 years ago | (#33183778)

P.S. On an H1-B here myself; pissed off at all the hatred.

## Re:They took our jobs! (0, Offtopic)

## gd2shoe (747932) | about 4 years ago | (#33184182)

Misplaced hatred. (yes, this is off topic)

H1-B is a good thing for the US, but is sometimes abused by firms who wish to pay very low salaries with no benefits (sometimes practically holding the employee hostage). This behavior is bad for both the visa holder, and for the job market as a whole (supply and demand get skewed).

I apologize for those who cannot follow simple logic. (We'll just need to keep working on them.) The Xenophobes can apologize for themselves.

## Re:They took our jobs! (0)

## Anonymous Coward | about 4 years ago | (#33184210)

Don't you have hedges to trim? We don't do siesta" here in America you lazy sod. Now get back to work before I deport your ass.

## Wait and see (0)

## Anonymous Coward | about 4 years ago | (#33183782)

It will be awhile before his proof is confirmed but I was hoping that P=NP

## From the wikipedia discussion page (1)

## Spyware23 (1260322) | about 4 years ago | (#33183822)

"Deolalikar's result is that "P (does not equal) NP (intersect) co-NP for Infinite Time Turing Machines". This is a special context - infinite time Turing machines are not the same thing as standard Turing machines, but are a kind of hypercomputer. Dcoetzee 09:07, 8 August 2010 (UTC)"

From http://en.wikipedia.org/wiki/Talk:P_versus_NP_problem#Potential_Solution [wikipedia.org]

## Re:From the wikipedia discussion page (1)

## Zaphod The 42nd (1205578) | about 4 years ago | (#33183880)

Or am I way off?

## Re:From the wikipedia discussion page (4, Informative)

## 1729 (581437) | about 4 years ago | (#33183894)

"Deolalikar's result is that "P (does not equal) NP (intersect) co-NP for Infinite Time Turing Machines". This is a special context - infinite time Turing machines are not the same thing as standard Turing machines, but are a kind of hypercomputer. Dcoetzee 09:07, 8 August 2010 (UTC)"

From http://en.wikipedia.org/wiki/Talk:P_versus_NP_problem#Potential_Solution [wikipedia.org]

That was a different paper, published in 2005:

http://portal.acm.org/citation.cfm?id=1185240 [acm.org]

## oh dear (1)

## pdbaby (609052) | about 4 years ago | (#33183832)

## View from the future (4, Informative)

## Citizen of Earth (569446) | about 4 years ago | (#33183840)

## Makes my job easier... (1)

## offrdbandit (1331649) | about 4 years ago | (#33183848)

## Re:Makes my job easier... (4, Informative)

## Zaphod The 42nd (1205578) | about 4 years ago | (#33183862)

## Re:Makes my job easier... (4, Informative)

## loufoque (1400831) | about 4 years ago | (#33183980)

There are fast solutions to the TSP, they're just not fast in pathological cases.

## Re:Makes my job easier... (0)

## Anonymous Coward | about 4 years ago | (#33184066)

There's a difference between a solution and an approximation.

There are no fast solutions to the TSP, if there were, then P would be = NP.

## Re:Makes my job easier... (2, Funny)

## Surt (22457) | about 4 years ago | (#33184258)

You forgot 'and I'm lazy'. Because NP is just hard, not impossible.

## P != NP ? (0)

## Anonymous Coward | about 4 years ago | (#33183890)

But I thought that was how transistors work!

Is my computer now broken because of this guy?

## Drat. (1)

## kylemonger (686302) | about 4 years ago | (#33183922)

## XKCD was right (5, Funny)

## wdsci (1204512) | about 4 years ago | (#33183950)

## Re:XKCD was right (1)

## John Hasler (414242) | about 4 years ago | (#33184062)

Of ocurse he left out the part where it is the department head's name that goes on all those papers while the student is informed that this is not suitable material for his thesis...

## Is there a link to the actual preprint / paper? (0)

## Anonymous Coward | about 4 years ago | (#33183996)

I don't know what kind of system scribd is trying to be, but it doesn't work with my browser, and I suspect it isn't the original / most direct link to the paper's preprint / public form. Isn't there just a simple direct PS / PDF / DVI / whatever link so one doesn't have to deal with scribd's brokenness (for me anyway)?

## it's a constructive proof!!! (2, Funny)

## PJ6 (1151747) | about 4 years ago | (#33184024)

## formal proof please (-1, Flamebait)

## StripedCow (776465) | about 4 years ago | (#33184038)

Can we please have a formal proof. A proof written in natural language and with a length of a hundred pages almost certainly contains some flaw. Just like a program of more than a few thousand lines of code is certain to contain at least one bug.

## Re:formal proof please (0)

## Anonymous Coward | about 4 years ago | (#33184212)

Can we please have a formal proof. A proof written in natural language and with a length of a hundred pages almost certainly contains some flaw. Just like a program of more than a few thousand lines of code is certain to contain at least one bug.

But, extending that analogy, there's some problems you can't solve without a few thousand lines of code.

## Re:formal proof please (4, Insightful)

## iris-n (1276146) | about 4 years ago | (#33184240)

Are you raving mad?

Of course there will be an error with this proof. Many errors, actually. Most of them irrelevant.

Maybe one of them is not. You know what? It will be caught in peer-review, exactly as it's been happening in the last centuries.

There's a reason noone uses formal proofs in mathematics. They're dull. They're slow. And we trust peer-review (for correctness, anyway).

What would be the use of a proof that no human can understand?

## The new new HP way (0)

## Anonymous Coward | about 4 years ago | (#33184044)

So on about the same day CEO Mark Hurd collected a $53 million severance package from HP's board for either sexually harassing a contractor, or keeping said contractor as a mistress on an HP expense account, HP researcher Deolalikar submitted a paper which

mightearn him $1 million for proving one of the seven biggest unsolved problems in all of mathematics?## Pictures .... or it didn't happen (2, Interesting)

## davidwr (791652) | about 4 years ago | (#33184054)

Pictures, er, I mean, peer review, or it didn't happen.

## Two questions (1)

## slasho81 (455509) | about 4 years ago | (#33184070)

## Re:Two questions (1)

## blitzkrieg3 (995849) | about 4 years ago | (#33184172)

You could try your hand at the other unsolved Millenium Prize Problems [wikipedia.org] .

## Re:Two questions (1)

## slasho81 (455509) | about 4 years ago | (#33184184)

## There is a God! (1)

## Sinan H (1548991) | about 4 years ago | (#33184086)

## Re:There is a God! (1)

## siride (974284) | about 4 years ago | (#33184178)

## paper is close but wrong (0)

## Anonymous Coward | about 4 years ago | (#33184090)

random k-SAT ensembles chosen have a flaw related to k,a factor graph ensemble. the paper is based on a statistical physics model which may also have probs but im unfamiliar with stat phy theory. -37028

## Pulls up chair (1)

## Schnoogs (1087081) | about 4 years ago | (#33184110)

## Re:Pulls up chair (0)

## Anonymous Coward | about 4 years ago | (#33184242)

## Isn't it... (0)

## Anonymous Coward | about 4 years ago | (#33184116)

I thought it was:

P / [ N^(-x) * N^(x)] = P

Tim R.

## Not in arXiv? (5, Interesting)

## iris-n (1276146) | about 4 years ago | (#33184154)

I think this is the first time a serious researcher publishes a paper through email. Makes me wonder if he is actually publishing it or just asking for peer-review from his colleagues.

Or maybe he is trying to best Perelman in insanity. After all, even Perelman put the paper in arXiv.

Anyway, about the paper itself; I am a physicist, and he does say correct things about the Ising model and phase transitions. Unfortunately, it is only a small part of his proof that I can grasp. So I think he is dead serious.

Also, nice typography.

## P= NP (1)

## Surt (22457) | about 4 years ago | (#33184180)

The 'proof' says so right on page 1.

## Proof by example? (2, Interesting)

## Anonymous Coward | about 4 years ago | (#33184188)

I recall reading that Minesweeper was an NP complete, or at least NP Hard problem. Doesn't P mean that a solution is computable is a reasonable time? If that's the case, then P!=NP by minesweeper.

Imagine you're almost done with a game of Minesweeper. 5 mines left. Your grid looks like this:

+----

| * * 2

| * * 3

| * * 2

| 2 2 1

Now, obviously each of the blocks on the outside, four of them, are mines. Which leaves two that you have no information about and can't _GET_ any information about. Which of the remaining two blocks is a mine?...

Would this be an example of P != NP, assuming Minesweeper is NP?

## A real achievement... (4, Funny)

## adamofgreyskull (640712) | about 4 years ago | (#33184206)