Slashdot Mirror
Wiki to Help Solve Millennium Problems?
MattWhitworth writes "A new wiki has been set up over at QEDen to try to gather a community to solve the Millennium Problems. The problems are seven as yet unsolved mathematical problems that continue to vex researchers today. What do you think of this effort? Will gathering a community of people help solve problems such as P=NP, or do you think it requires a lot more than a semi-qualified community to approach the problem?"
The requested URL (science/06/04/15/158257.shtml) was not found.
If you feel like it, mail the url, and where ya came from to pater@slashdot.org.
Why does Slashdot have so much difficulty linking from the front page to its own postings?
3/4 of the people will argue about their misunderstanding of the problems involved, the other won't even know what the problems are but think they do. The very few people who actually do understand the problems and the underlying issues will eventually stop trying to explain what the real issue is.
How about spelling Millennium right in the headline? The article itself managed it.
"Will gathering a community of people help solve problems such as P=NP, or do you think it requires a lot more than a semi-qualified community to approach the problem?"
Just look at how slashdot has helped solve global hunger, or set corrupt governments straight.
Kofi Annan and Jeffrey Sachs set up a wiki to solve the Millennium Development Goals which mind-bogglingly manages to be even less successful.
English is easier said than done.
or do you think it requires a lot more than a semi-qualified community to approach the problem?
(sorry about the bad spelling)
well I'm completely unqualified in every sense for these things, but being a political scientist I should be able to have a stab at the last question... Concordat's jury theorum suggests that with more people your chance of getting a right answer increases, say if everyone has about 60% chance of getting it right for example then with a few hundered people that chance should have increased to over 80%... which would lead me to believe yes it will work, still, i tend to think that the more people you have the less productive you are capable of being as people will disagree, and if the two most experienced people disagree then it could polarise the views of the less experienced people and split the project... so basically, it could go either way...
*''I can't believe it's not a hyperlink.''
People will graffiti the page with things like P=My Pee Pee.
Wiki to be created to solve Grand Unified Theory of Everything, this will take over because physicists, chemists, mathematicians have failed to do it, so the idea is to lob it out there. First step will be to resolve the problems between gravity and quantum mechanics.
Lets put it this way, if there was a Wiki on solving complex DNA evolution problems, 50%+ of the posts would be from wackos talking about ID and Creationism.
I hate to break it to people, but Maths and Physics make computing look like a liberal arts degree.
An Eye for an Eye will make the whole world blind - Gandhi
That's a simple one. The missing mass is vaporware from all the features that Microsoft was promising for Windows Vista and all the promises the Duke Nukem Forever will be released. Once Windows Vista is fully featured and Duke Nukem Forever is released, the equations should work correctly. The odds of that happening is... like a spaceship being swallowed by a large dog in space. :)
If you put a million monkeys banging on a million type writers you will eventually end up with the works of Shakespeare. If you put a million intelligent people trying to solve unsolved math problems they will have a solution if one exists. ...eventually
"He hoped and prayed that there wasn't an afterlife. Then he realized there was a contradiction here and merely hoped.
If you have something significant towards a proof of the Riemann Hypothesis, surely you're going to publish that in a peer-reviewed journal, not throw it online in a wiki. I'm not sure what the incentive is for mathematicians to use this.
I think ideas like this should definitely be encouraged. Personally, I don't think a band of semi-qualified people will be able to accomplish much. These problems require a very deep knowledge of mathematics to understand and appreciate them, let alone solve them.
However by involving everyone, including the layman in these fascinating problems will help increase appreciation for the beauty of mathematics amongst the general public and that to me is equal in worth to actually solving these problems.
Keep in mind that there already is a kind of wiki-like "collaboration" within the academic circles. The only difference being that the circle is relatively small compared to a "wiki".
But then, more people working on it doesn't necessarily improve things. For one, you will expect a very bad noise to signal ratio, where there would be a bunch of smart ass ideas that have already been disproved decades ago, or ideas which are so obviously wrong that no academic would even think of writing a paper for.
Basically the whole thing is based on the assumption that "monkeys banging on typewriters will eventually produce all the works of shakespear". It works in theory, but remember that it takes either an infinite number of monkeys, or infinite time -- whereas you could find a group of talented people to do the same job more effectively.
Expect a dozen claims of "TSP solved in P time!" from this site within a month, and nothing more afterwards.
Don't quote me on this.
Will gathering a community of people help solve problems such as P=NP, or do you think it requires a lot more than a semi-qualified community to approach the problem?
Proofs are not really found by committee. This Wiki might be a good way to share research and in that sense it may aid the effort but above and beyond that it's not going to contribute much.
It will take a unique insight and a particularly sharp mind to get to the bottom of these problems.
Simon
I think this is a great approach. Its effectiveness is questionable, but that is the story with everything else. Seems as though it should at least help shed some light on different approaches to some of the problems and maybe help those that are truly the 'professionals' that have been cranking on these problems to see some insight and fresh ideas. Kinda just rolls with the oss philosophy of having as many eyes and brains as possible looking at code to find the bugs and to provide creativity...so why not math. Maybe this will also open up more opportunity for those with gifts in programming to find methods to help design new methods for computational approaches to these problems. Will it cure cancer, stop hunger, prevent aids/hiv...no. But basic research is basic research, so why not.
my site of misleading and incorrect information!
The people that work in these areas usually write scientific papers on a fairly regular basis, they might even read some as well. The understanding and science is therefore usually quite open. Now, a wiki might make 'communication' faster, and more available to the general public, but it will hardly speed up the solution finding.
For the perfect anti-Unix, write an OS that thinks it knows what you're doing better than you do and let it be wrong.
10,000 monkeys with 10,000 typewriters...
If a group of people had a higher collective intelligence than any one individual, this might be the case. Unfortunately, IQ is not cumulative.
GJC
Gregory Casamento
## Chief Maintainer for GNUstep
Ahhh the smell of a fresh wiki and all the goatse-flood opportunities to come....
The important difference there was that this project was only open to those actually actively involved in working on this problem. A public wiki will likely be bogged down by people who don't truly understand the problem or the approaches used to solve them - instead of everyone being able to contribute a little (as is possible in Wikipedia, which effectively just requires a transcription of information) the vast majority of people won't have anything to offer at all. And of course, those that are actively involved in working on these projects and want to share their work are in all likihood already doing so - with other people in the same field.
This project will likely attract those who do not have the particlar interest, time or background to work in a focused fashion on the problem, and consequently I'd be surprised if anything really unique or surprising came out of the project.
Oh nos! The calendar lied - the Y2K = 2012, the end of the earth! I need to go buy gallons of water, a generator, canned food and some fresh soil to bury my head in!!
The only helpful thing this will do is allow the people who need to be working on to access the currently existing literature on the subject. But it probably won't be that great a benefit - most grad students (and bright undergrads) these days will have a professor latch onto them and be able to point them in the right direction.
;)
The other way this website will be useful will be to let everyone see the latest developments in the field. Solving any of the Millenium Problems generally requires getting very very deep into certain fields of mathematics.
This web page could be quite instructional. But that thermometer is going to stay at zero. At least if someone affiliated with that web page does solve one, they would've done it by themselves anyway.
This site could be a great way to teach beginning/amateur computer scientists why they are wrong
"Here's a question. How do we define the power of a computer. Because computing power tends to double every year. Even if this is true, how much does productivity with it change (measured in terms of the entropy of their processing)? If it increases roughly exponentially, then it's possible that P=NP, via observation."
They should really set up a website dedicated to solving how not to get Slashdotted.
Did you ever notice that *nix doesn't even cover Linux?
I'm a professional mathematician and I find the idea interesting.
Real researchers are familiar with cranks on newsgroups (James S Harris on sci.math for example) who year in year out claim to have proved this or that famous conjecture. Or, these people send proofs to real researchers, expecting attention when page one of their "proof" contains an error. So my hopes are not high that a community of semi-qualified people could solve the problems, but....
Suppose that this community set about collating and putting in context all of the material related to those problems that exists in the **research level** literature and **expounding** it in an extremely clear way. And suppose that real researchers were interested and joined the effort. This resource could be a HUGE contribution to the effort.
Unfortunately, the only joint efforts in mathematics on the web so far, do not deal seriously with the literature, but approach mathematics at a level of understanding of a first year graduate student. Problems that are well understood by the most brilliant minds on the planet are not going to be solved by people with an understanding as limited as that. It isn't as though some tough problems haven't been solved with elementary methods (the Kayal-Agrawal-Saxena result being a case in point), nor is it true that cranks do not occasionally come up with the goods (de Branges proof of the Bieberbach conjecture being a case in point), but the fact is, these are exceptions to the rule and the vast majority of difficult problems had immensely difficult solutions which took new developments in mathematics over periods of many years before they could be solved. Will a community of non-researchers make developments in modern mathematics? Personally I doubt it.
But, this is a new idea, hasn't been tried, so who knows where it will lead. As a research mathematician, the idea intrests me, and I would be involved if it headed in the right direction and didn't become a place for cranks to meet and fiddle with polynomials over an unspecified ring.
"The very few people who actually do understand the problems and the underlying issues will eventually stop trying to explain what the real issue is."
And then proceed to move to another forum like Kiroshin.
Of course in a Wiki, that's going to be the "P=np" article.
"The title of this article is incorrect..."
-merv.
Wasn't all the monkeys hired to produce system code instead?
or do you think it requires a lot more than a semi-qualified community to approach the problem?
Gee, that's not a loaded question, eh?
Good News! I've just solved P=NP. It's true if N = 1, and trivially true if P=0. Please donate my $1 million dollars to KDE and tell them to fix the PDF rendering. Maybe my computer science breakthrough will help?
Personally, I don't think the wiki will do any good. Good collaboration requires face-to-face contact. Anything else is really equivalent to the modern email/conference/preprint system in math. After all, who wants to share their million-dollar insight on a wiki only to get scooped? Double-plus-ungood: how do you decide which researcher did the critical part of the problem? It's tough to say now (and mostly irrelevant, but intellectual pissing matches have been with math since at leave Liebnitz vs. Newton), and it would be harder to decide in the mixed-up collaborative world of the wiki.
Use the Firehose to mod down Second Life stories!
While there are critics, 'wiki style' collaboration is a good thing. It often takes seeing a problem from different perspectives to understand the real nature of the problem. Sure, there will be idiots trying to help out or make their mark on the wiki, but the concept of shared thinking is more powerful than anyone knows. The promise that was HTML added to many people thinking of how to understand something is incredibly faster than the process that eventually created the atomic bomb.
So, jokes and criticism aside, the OST (open source thinking) is a good plan. Execution may have some drawbacks, but it has goodness in it.
Support NYCountryLawyer RIAA vs People
The real>/i> question is, will this Wiki be able to reach its solutions in non-Polynomial time?
Let's combine the wiki with an infinite number of typing monkeys. Eventually one of them will type up a LaTeX file that the STOC or FOCS conference reviewers would accept as a solution finally disproving P=?NP.
It's one of those things quantum computers are good at.
/and the n-body problem, you're next.
Now all we need is another Newton to discover the necessary quantum mathematics to describe it.
A lot of people on Slashdot are degree-obsessed; at an early age they have bought into the idea that everybody who does not have a formal academic education to at least PhD level is necessarily unable to contribute anything to research. (This is not just the chip on my shoulder talking, but as someone with a degree from Fen Poly who has recruited a fair number of graduates over the years, I know it takes far more than a degree or two to make a scientist, mathematician or even a developer. Curiosity, persistence, the ability to see connections are all important.) Although this Wiki may well fail, it might just bring to light a few more Ramanujans. The world does not consist solely of North Americans, and there are doubtless plenty of educated people in other cultures who do not have access to the networks that bring some people to the fore while others, equally well endowed, may never get an opportunity.
Pining for the fjords
Until I read the entry on the P vs NP problem, I thought I understood what the problem was. Now, I'm not so sure. What confuses me (from the article) is this: The article mentions that you must pare down the number of students receiving dorm rooms from 400 to 100 and that no pair can be composed of two students with incompatibilities. At first glance, I'm not sure HOW this is an "unsolvable" problem. Would I not just select and group 100 students at random then rearrange the pairs as I found incompatibilities? Can someone clue me in to what I'm missing here?
Anthony Papillion
Advanced Data Concepts, Inc.
"Quality Custom Software and IT Services"
This will only attract cranks and pretentious people. This will spew out garbage - results will be stated without formal proof etc etc, the community will fold and collapse quickly. I'll give them a month.
These problems are hard, this is why they are unsolved, and to make any progress requires hugely talented people working solidly on the problem. These people are already involved in research. I do not believe that mathematics lends itself well to a wiki format - its going to end up fragmented and without direction. You need direction in a proof, a proof is made up of many stages, but it also needs a general direction and insight. This will not work. Important results are published in journals - not by a community of amateurs.
The only good that this will have, is in raising awareness of the problems and of mathematics in general - a commendable effort, but not one that will create important new results.
Nothing sucks like a Vax, nothing blows like a PowerMac G4
In a sense, the Online Encyclopedia of Integer Sequences, hosted by AT&T Research, does this job already.
With over 100,000 web pages, searchable, with posters' email addresses given, and both internal and external hotlinks and citations to hardcopy literature, this has been the leading collaborationware in Mathematics. The Online Encyclopedia of Integer Sequences (or OEIS) recently faced a problem with increasing numbers of clueless postings.
The distinguished panel of editors, under Dr. Neil J. A. Sloane, first added a keyword of "probation." Submissions so tagged, unless okayed by an editor, are deleted after a reasonable time. At my urging, citing the history of Slashdot, they even more recently adopted the keyword "less" -- meaning less than interesting, but better than probation. "Less" sequences stay in the database, but are given minimum priority in searches.
Similarly, MathWorld is a form of collaborationware or pseudowiki. Although edited by Dr. Eric W. Weisstein and his staff, it encourages submission by form from anyone, and posts attribution to such submissions, and lists of contributors.
I contend that web-based systems have substantially affected the practice of Mathematics. Social mechanisms such as pioneered by Slashdot contribute to weeding out useless from interesting contributions. As with Wikipedia, one's academic credentials mean nothing here. What matters is the quality of one's submissions, as evaluated by one's online peers.
There also many fine Math blogs, but that's another topic.
-- Jonathan Vos Post
Speaking as someone with a Ph.D. in mathematics ...
...
These problems are all incredibly difficult. A lot of very good mathematicians have thought about them, in some cases for over a hundred years. In some cases, even understanding the problem requires an advanced mathematical education. If there was anything approaching an easy solution, it would have been found already. That said
Problems like these always require some insight. Typically, either a way to relate the problem to some other unexpected area, or some new kind of machinery that creates a leverage against the problem.
Personally, I wouldn't expect that from such an effort.
The logical outcome of people using the new wiki.
This experiment has already been performed, although on a much smaller scale. In the experiment, the monkeys resorted to flinging feces at the machine. If you extrapolate their performance, that's a lot of feces.
10,000 monkeys with 10,000 typewriters...
The problem with your analogy is that's a situation in which eventually one copy will be made among the many, many other copies. In a wiki, you need 10,000 monkeys with 10,000 keyboards to write Shakespeare on the same piece of paper.
Einstein was a patent clerk.
However this is a very specialized topic where even people who think they know something don't know anything. I've been witness to even small-scale wikis become completely useless because of either misguided "knowledgeable" people or in fighting.
Even if something useful is contributed, how is someone going to be able to separate the signal from the noise? Peer reviewed publications have some kind of bar to keep from having to look at every crackpot idea. Wiki's have... what?
However it will give a little more coverage to the problems, so in general it's good PR. But the wiki thing... ugh.
Disclaimer: They've been /.'d so I can't see what they've done.
... that Einstein had advanced training in physics. He was working as a patent clerk because professorships were hard to come by.
I often wonder if the "Einstein was a patent clerk who had difficulty with math" mythos has empowered far too many crackpots who don't understand the problems they write about.
That simply does not work. If you have a million monkeys, on a million typewriters, you'll end up with millions and millions of pages of garbage, with maybe a correct solution in there somewhere. That's not even the problem we're trying to solve. The real problem is finding a million qualified people to screen the random text the monkeys are producing, and find a solution. And if you were to somehow manage to do so, that would be a million less qualified people actually working on a solution. So in the end, after all this effort getting the monkeys and the typewriters, you've actually done more harm than good.
And the l33t shall inherit the 34r7h.
Well, no problems will be solved because the wiki is down. :D
I remember when I was in high school and someone first explained the P=NP problem to me. This was certainly someone who was very smart. I remember he had made big bucks at Microsoft doing some sort of software work. He told me he was reading a book about the problem (I'm not sure which one, there are many), and was going to "work on it". He told me about the millenium prize competition. But he said something else that really underlined for me the disconnect between Academia and the business world:
He told me that if he he solved the problem by showing P=NP (instead of P!=NP, which "most mathematicians believe"), he wouldn't publish his proof. Instead, he would setup a website that would take credit card payments to solve problems quickly (for example, packing boxes into the back of a UPS truck, or various traveling salesman problems). At the time, I though this was a little antisocial, but not much more.
Later, when I had more mathematical training, I looked back on this and realized how revealing this attitude was: of course, if someone proves P=NP, the proof will almost certainly not be accompanied by practical algorithms which are significantly better than those used already for problems on most scales. Of course, the idea that he was going to solve this problem without any collaboration or formal education in logic or complexity theory demonstrated the arrogance typical of many super-successful business-people. I can't help but remark that for all the stupid patents on software "ideas" and sometimes algorithms, we're lucky that, most of the time, theoretical advances are made not by people like this... and and so people publish their results, and are rewarded with respect rather than dollars.
Imagine the state of our theoretical knowledge in mathematics and computer science if, even in Academia, every discovery of a new algorithm or idea resulted in a patent application, and was jealously guarded as a secret which could produce profit. Unfortunately, this is already largely the state of things in the wet sciences (unnecessarily so, I would argue, and point to mathematics as my evidence).
As for the wiki thing: I don't think most ordinary people are like this guy, so hey, good for the wiki. (I think this attitude is taught by the business world, and not somehow the other way around). Unfortunately, I fear that the millenium problems are deep enough that amateurs will have trouble making a big impact. There are a few amateur contributions to mathematics occasionally, but there hasn't been a significant one in a long time. (The last was arguably by Marjorie Rice, a housewife who essentially resolved the question of the number of different ways to tile the plane with convex pentagons). Astronomy is probably the last big field where amateurs play a really significant role.
How would he vouch for the security of the CC payments?
think about it, you could take the http://en.wikipedia.org/wiki/Riemann_hypothesis? and create a boinc client to test the theory with different #'s.
find an example that fails, and split the million with the client that proved/disproved the result.
every day http://en.wikipedia.org/wiki/Special:Random
http://www.bearnol.pwp.blueyonder.co.uk/Math/riema nn.htm
..if they just dropped the math. Right? Isn't that what people said when "Brief History of Time" came out. I'd try to prove that you have to agree with me, but I lack the logical calculus to communicate my idea. So I'll just tell you how dumb everyone else is. (Hopefully Gene Ray doesn't have a process patent on that.)
We just have to test the IQ of everyone on the planet. Once we have the one with the higher IQ we can ask him every question we have and ... voila, we will get all the answers at once.
I think people need an informal definition of NP. Here it goes: A decision problem is a yes/no question. A decision problem is in P if we can solve it in polynomial time. Example: is n divisble by 3? The length of the input to the algorithm is log n (the number of binary digits in n). We can divide a number by 3 in quadratic time in the length of the input. So we can certainly decide in essentially (log n)^2 steps if n is divisible by 3. (log n)^2 is a polynomial (of degree 2) in the length of the input to the algorithm (log n). So this decision problem in in P. Consider another decision problem: is n composite? It's not obvious how to quickly determine if a large number is composite, short of trying all possible divisors up to the square root of n. The square root of n is exponential in the length of the input (log n) so this does not give a polynomial time algorithm. On the other hand, if someones else knows the factorization of n, they can tell you the factorization, and you can quickly use it to check that n is composite (by multiplying the factors together). THIS means that this decision problem is NP: if the answer is yes, there is a (short) "witness" that, if someone tells you the witness, lets you check in polynomial time that the answer is yes. It turns out that this second problem is actually in P as well--that is, you can solve this problem without the witness. This was proved in 2002, and is not simple at all. If P=NP, then this would always be true: anything you can solve quickly with the right witness can be solved without the witness. Proving P!=NP amounts to proving that there is some problem in NP which cannot be solved in polynomial time. There are many problems in NP known to be at least as hard as all the rest (called NP-complete), so if P!=NP, these can't be solved in polynomial time. Now, you just need to prove this...
""Any scientist who cannot explain to an eight-year-old what he is doing is a charlatan" --Kurt Vonnegut in Cat's Cradle
I agree!
"What can I tell you about baking a cake if you have never heard of flour, butter or milk?". -- Eienstien (paraphrase).
I agree! -- with both quotes?
The wiki could be cream or crap, it all depends on how it is set up, how moderators are selected and who can post (requires email, sign in, ect). The whole idea of a wiki is that it automatically points to other parts of the wiki for definitions of "flour", "NP" or whatever.
In otherwords a wiki has the potential to serve as "the explaination" for the hoards of casual participants. OTOH: It has the potential to become a steaming pile of crap.
And did you exchange a walk on part in the war for a lead role in a cage? - Pink Floyd.
Their progress thermometer runs from 0 to 7... but it's missing a tick; the tick labelled 7 should actually be 6.
...someone who is coming into the field with a clean slate. It's because of the current ways of dealing with numbers, equations, and topography that these problems appear to be unsolvable. I'm all for the wiki and people education themselves about the problems (reading and thinking about them reinvigorated -my- interest in mathematics) but I don't think that a session of collaborative "group think" will help solve these problems. The answers will almost surely come as a "divine spark" of genius to someone who's approaching the problems in a new light.
In fact, it's widely thought (by the creators of the Millenium Problems no less)that the P=NP problem will be solved by someone with virtually no experience in the problem at all.
I think the Wiki is a good idea to inform new people (with potentially new ideas) of the problems, but I don't gathering a bunch of likeminds to solve them will yield many results.
It's Not Like Random People Could generate something as complicated as, say, LINUX and actually have it stable and secure, right?
Never underestimate the value of adding a couple of newbies into the stew with people who can filter out the wheat from the chaff.
A quick story:
Back in the 70's the the standard example for teaching first-time programmers while loops was generally binary search algorithm... However, for kids doing pretty much their first program, this turned out to be a bit on the difficult side, and not quite trivial to wrap their brains around.
(remember: late '70s. kids hadn't grown up with computers as anything other than huge machines with spinning tapes in the movies.)
Lots of students would write the program as told, and just walk away scratching their heads.A little while later, we'd get around to doing recursion, and they'd use the simplest example that you can find for recursion -- the factorial:
It's pretty simple, but when taught in a classroom setting, about 20-30% of students would get it confused with for loops.
I knew that these examples were bad, but I couldn't really pinpoint precisely what the problem (read: solution) was.Well, one day in the lab, when we'd just gotten to while loops (and binary search), this kid walks up to me and sheepishly asks if what he has is even legal, because it's really different than what the professor described, but it just makes sense to him (they hadn't talked about recursion yet). He'd defined binary search recursively, and it made perfect sense! I almost kissed him.
What he had taught me was that we had it backwards... Factorial is too simple for recursion.. It's to obvious to use a loop (and a good example for that). A binary search, on the other hand, is about the simplest example which shows off how recursion can simplify the understanding of a problem.
I took the example to my prof, and it changed the way that loops and recursion have been taught at the University of Alberta (if not worldwide).
My point here is: It took a stupid question from a first year student to solve a problem that had been around for at least a decade, if not longer.
(oh: and his answer was also wrong since he was supposed to be implementing loops, not recursion!)
Free Software: Like love, it grows best when given away.
I thought one of them had been solved?0 7/0019257
http://science.slashdot.org/article.pl?sid=04/09/
What happened to this proof?
Now I've looked at the site more thoroughly, and I don't believe it anymore.
Context: I'm a graduate student in Theoretical Computer Science, so I do know something about P vs. NP and the current obstacles to solving it.
The first information (beyond the basic definitions) that anyone should know if they hope to approach the P vs. NP question is 1. The Baker-Gill-Solovay result that P vs. NP does not relativize and 2. The Razborov-Rudich result that "natural proofs" can't show P != NP. Both of these are fairly technical results, but still explainable to a relatively broad audience. Between the two of them, they rule out every currently known lower bound proof technique as a method of proving P != NP, which means that if we hope to prove P != NP we need some radically new ideas. If someone claims to have a viable approach to proving P != NP, the first (well, maybe second or third) thing any trained theoretician will ask is how the approach works around these two papers, particularly the second. (I went to a talk at Harvard by someone presenting a new approach, and that was in fact one of the major questions he was asked.)
These two results are summed up as two bullet points on the wiki.
Now, on the other side of things, more focused on cranks who give bogus proofs of P vs. NP one way or the other -- the wiki has links to dozens of them, and discussion pages about several of them. One page says, regarding a particular "proof" that P = NP, that it "seems like a very reasonable approach that will require a high level of scrutiny." Here's a hint: No it won't. Studying these claims is a waste of time. I looked at the pdf of the paper in question, and there are about a dozen warning flags that the author is a crank (in addition to the major one that the author publicly claims to have resolved P vs. NP but hasn't gotten any major computer scientists to believe him). These people are a terrible source of "ideas" for resolving P vs. NP, especially when I can't even find links on the wiki to some of the possibly legitimate, peer-reviewed approaches for resolving the question (e.g. the Mulmuley-Sohoni approach via algebraic geometry, or Joel Friedman's ideas about cohomology and topos theory).
Please don't respond saying "Well it's a wiki, you should add that information yourself!" I'll look more at the site and might add some things, but my point is that the site's community as a whole is devoting a lot of time and effort to dead-ends, and none to actual published academic papers. My fixing a few pages or adding information about one or two things is not going to change the direction of the entire site...
I am the man with no sig!
For a Wiki which already exists which archives existing knowledge on computational complexity in great detail, particularly the P=NP question, see The Complexity Zoo.
:)
The website isn't exactly lightning-fast, so I'm sure they'll thank me for the link...
Proof: Wiki users will not contribute to the millennium problem
Counter Example
Suppose: Problem will be solved
Suppose: Wiki users > 0
Suppose: All educated members of the community do not work on the wiki
Thus: EU educated users
: WU wiki users
: MP is problem with MP being millennium problem
Since we know that P will be solved, we know that EU likelyhood of solving problem + ~EU likelyhood of solving problem are == 1
Thus, by examining the chances of EU we will know what the likelyhood of someone else solving the problem.
The number of EU members is fixed, because only members of EU are able to solve the problem and no one is born having the skills to be a member of EU.
The number of ~EU is infinite being that there is no known event that will destroy the human race.
so EU/~EU is infinitely small and therefore the chance of someone in group EU solving the problem is also infinately small because the maximum possibility of EU solving the problem is 1 and 1/infinity is pretty damn small, but not 0
However, now the likelyhood of ~EU solving the problem is approximately 1.
And since we know that no members of eu are members of the wiki and we know that the number of members of the wiki are greater than 1. This means that the there is a possibility of that the person who solves the problem to be a member of the wiki.
It seems pretty simple to me, but maybe I am wrong... Wait a sec, I came up with the question therefore I am an expert and since no one else is an expert I must be correct because only experts can solve problems.
Seems like an odd stance for most of Slashdot to take, but I guess I'm too old. Since I am just now starting college after only 24 years of professional computer experience what right do I have to find any flaws with my instructors. After all some of them have had 4 years of academic computer experience.
Also, if we are to believe that a wiki member has no chance to solve the problem... Then we must assume that there is no reason for anyone to seek an education, because they are noting going to be able to learn anything that is not known. I guess it's time to stop investigating anythin if you are not an expert.
Shrug,
/* TODO: Spawn child process, interest child in technology, have child write a new sig */
let all who want to participate do so
and have the professionals moderate and approve
back in the day we didnt have no old school
If someone proves that P != NP, it won't affect most of the world. There would not be much use for such a proof.
A proof that P == NP would change the computing world forever.
My bet's on P != NP, but I also believe that public-key cryptography is impossible (IE, that RSA and such will eventually be broken).
Melissa
"Screw Sun, cross-platform will never work. Let's move on and steal the Java language." - Visual J++ Product Manager
But maybe that's useful... perhaps I should try editing some of the mathematics articles at Wikipedia.
Danny.
I have written over 900 book reviews
At the end of the page, I found the following quote:
"I never let my schooling get in the way of my education." -- Mark Twain
Slashdot must have a great oracle hidden somewhere. If only they published it, at least the P=NP problem would be solved.
I have an MSc in Quantum Field Theory and am working on a degree in computational neuroscience. Five years of world class education in theoretical physics. But my friend, the pure mathematician, needn't even try to explain me what he is working on -- I literally wouldn't understand a single word.
Rest assured, the people who are capable of solving any of these "Millenium Problems" are already working together. They don't need a wiki. Wikis are good for problems that need a lot of different views on one subject. They are useless for questions that take years of daily full time mental effort just to be understood, let alone solved.
Question is, does this apply to wikis, blogs and (perish the thought) /. as well?
./ poster (or a monkey) comes up with it.
As you say, with the works of Shakespeare the evaluation process could be automated, since the "correct" answer is known. But with vexing unsolved problems in math and physics, the solution is NOT known in advance. It's not clear if anyone will recognize the correct solution once a
Just think, THIS VERY MESSAGE COULD BE THE SOLUTION TO ONE (OR MORE) OF THE PROBLEMS!
I hope I'm not going to lose sleep over this.
Om
It appears obvious that throwing a pile of laymen at these problems will only injure the 3 or 4 people with a chance to solve the problems. Still, I find it interesting to imagine the 11 year old closet math geek who becomes enamored of the problems on the Wiki and solves them all in a day or so (and tosses the math community into several years of utter turmoil.
As I was totally ignorant to what the "Millenium Problems" actually are, thinking this post was going to be about creating a Wiki where the global citizenry could collectively work to solve our world's problems of hunger, war and lack of a universal code of human rights. My bad.
Absolute Michigan
Hmm. P=NP N=1 Solved. May I have a cookie?
It all boils down to whether you think an infinite number of monkeys (monkeys being non-experts in this case) can produce the works of Shakespeare. Even if they do, they propably wouldn't know the difference because they lack the meta-cognitive abilities to differentiate crap from genious. Furthermore, specialization works up to a certain point for this kind of mega-problems. You can write something interesting in Wikipedia with respect to, say, Chinese steam engines of 1960 without having an engineering PhD, but you can't add anything to the solution of these problems without having at least graduate mathematics training.
I suppose the only value in this "experiment" is to bring together the 0.001% of the people around the world that know what they are talking about and to give them the possibility to collaborate (if they already don't...) and some visibility (funding, fame, wild hot naked girls etc). I fully support this effort in that sense but I don't expect this "wiki" thing to be of real use for non-experts.
P.
P.S. Try reading the official description for the Hodge conjecture...
That depends. Conceivably, a non-constructive proof for P=NP could be delivered. That would put us in the perverse situation that in that case we would know that polynomial-time (or space, if you will) solutions exist for NP-complete problems, without actually having any of the actual solutions delivered to us.
If someone claims to have a solution to ALL 7 problems - Drink!
If someone claims that P vs NP is an Algebra problem or tries to factor P out of NP - Drink!
If someone claims that they need notarized assurances that the Clay Institute is prestigious enough for THEIR solution - Drink!
If someone claims that they need time on the Institute Supercomputer because solving one of the Millennium Problems is part of their Mission, A Mission From God - CHUG!
If you are at all serious about your solution to these problems, you will pursue them in a better manner then trying to find back channel entry into academia. You can start by actually getting a degree in Mathematics and learning that the Maths community already has ways and means to consider and judge any solution you think you have. Trust me on this one, I've seen the underside to their tables.
Unruhe
What do you have to loose? This people so or so would have spend time on their own on the problem.
This project is great.
think about it:
If it fails, then it fails. Ok, what is the matter? We know then, that community does not help really.
If it not fails, then GREAT! Go on building communties solving difficult problems!
But why not to try it from beginning? There is not much to loose than some useless invested time.
See it as an adventure. Not as a question of life and death.
Just my two cents.
Today's quote-of-the-day is:
"Success covers a multitude of blunders." -- George Bernard Shaw
Do you know how much a patent clerk makes?
My apologies. I am not an employee of the Clay Institute, or associated with it. I have never been to their offices or any site they maintain. This posting was not based on policy of the Clay Institute or any activities that have occured there, but was the result of a conversation with annother person, also not associated with Clay Institute, after hearing how many calls they receive from people claiming to have solutions to these problems, but do not.
In short, I am retracting my comments about the Clay Institute.
My apologies. I am not an employee of the Clay Institute, or associated with it. I have never been to their offices or any site they maintain. This posting was not based on policy of the Clay Institute or any activities that have occured there, but was the result of a conversation with annother person, also not associated with Clay Institute, after hearing how many calls they receive from people claiming to have solutions to these problems, but do not.
In short, I am retracting my comments about the Clay Institute.