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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?"
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?"
GIGO.
The quantity of GI does not effect the reality of GO.
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.
One very quickly learns the pointlessness of trying to explain to the Unskilled and Unaware of It that it would take about two years of education for them to even understand that they don't understand the issue.
And it only annoys the pig.
KFG
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
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 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.
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.
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
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.
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.