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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?"
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.''
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.
I'd be surprised if anything really unique or surprising came out of the project.
I'd agree, with two caveats: this project might attract some math prodigy that isn't working on these problems (Ramanujan, anyone?). Also, this project will help a lot of people learn how to think about the most abstract parts of mathematics.
The possibility of either result would justify this project in my eyes.
Einstein was a patent clerk.
You're making a critical assumption that they let anyone post or edit. Just because Mediawiki allows anonymous users to edit sections does not mean that the QEDen website will. They could make the wiki read only for anyone who doesn't sign in. They may allow anyone to sign in, but cut them off if they start adding a lot of garbage instead of contributing things of value. If they wanted to allow anonymous contribution (in case there is a Ramanujan in the mix that is hesitant about logging in as you occassionaly find in Slashdot Anonymous Cowards or in case they want to have a place where young potential math specialists can have a place), they could section off a place for it, but separate it from the "legitimate discussions" so that anyone no interested in looking for hidden pearls doesn't have to deal with it.
In short, no-one needs to be annoyed if it's done right.
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.
It's true that being educated does not necessarily make one a good researcher, nor does being uneducated mean one can't have good ideas. I'm not someone who would say that the current system is perfect or that the right people always get opportunities - it's not and they don't. I think the wiki is a great idea and I wish it luck, but I worry that in practice it will get bogged down and neglected. Ramanujan was a genius who did not have the opportunity for an advanced education. There may be people like that, but it's not so clear that they will (1) work on math problems (most people don't have the time to devote to such things) or (2) have extensive access to the internet and the wiki. I expect that this wiki will be mostly filled with postings from people who have both time and a good internet connection: people in the industrialized nations, not Ramanujans. My feeling is that the vast bulk of the postings by amateurs will be honest attempts to get up to speed or crackpot theories. Experts will attempt to describe things to the newbies and respond to the crackpots, but they'll eventually get tired. Crackpots have astonishing amounts of time to promote their views and an incredible resistance to seeing their errors. The site is unlikely to be able to discover the next Ramanujan because (as other posters have pointed out) the signal-to-noise in the entries is likely to be low enough that experts will stop reading it in detail. It may, however, turn out to be a great resource for understandable descriptions of current research on these problems.
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. ...
That's an excellent idea, and I can see how that this could be an incredible tool for researchers. Ideally, whenever someone has a paper published, they would put a statement of the results into such a wiki. (Ideally the proof would also be included, but copyrights might cause some problems there.) Each lemma or theorem would then have its own database item, with a field telling the publication that contains the result.
A tool like this could serve much the same purpose as MathSciNet, but I think it would be more useful since the database items would be individual lemmas and theorems, which would make it easier to find an intermediate result that didn't make it into a paper's abstract. It would probably make sense for there to be separate wikis for different subdisciplines.