I certainly can't claim to understand the nature of the problems that are posed and discussed, but I'll be watching closely how this experiment evolves.
He calls his experiment the Polymath project, and Polymath 1 is here and here. He has also given a fair bit of attention to the rules and procedures, which have been made better and sharper with community feedback.
For quite sometime, folks in humanities and (to a lesser extent) social science have felt comfortable talking about some of their preliminary research ideas on their blogs. Some of them even state explicitly that they want to use the ensuing discussions to sharpen their ideas, explore related questions, etc.
In the sciences, however, I have not seen much of this sort of stuff. While many science bloggers do a great job of explaining 'existing science', there is very little in their blogs devoted to some thinking aloud on research problems that they are working on. [Maybe I'm hanging around the wrong blogs, but I think what I'm saying here is generally correct.]
In fact, someone said (I think it's P.Z. Myers, but I'm not able to locate the post/comment) he's against this sort of stuff because of the danger of being scooped; as I recall, he said he was a victim of one such incident: he posed an idea on his blog, and someone else ran with it and published it first. Academic credit (or, 'Idea ownership', or 'who got there first') appears to be important to scientists (much more than it is for humanities folks).
Therefore, I'll be watching Gowers' experiment on how it handles this tricky issue when Polymath 1 nears completion.
To be fair, Gowers has thought about the 'credit sharing' problem as well as the 'getting scooped' problem. He seems to think that community norms may change to take care of them. Here he is on the first:
Why would anyone agree to share their ideas? Surely we work on problems in order to be able to publish solutions and get credit for them. And what if the big collaboration resulted in a very good idea? Isn’t there a danger that somebody would manage to use the idea to solve the problem and rush to (individual) publication?
Here is where the beauty of blogs, wikis, forums etc. comes in: they are completely public, as is their entire history. To see what effect this might have, imagine that a problem was being solved via comments on a blog post. Suppose that the blog was pretty active and that the post was getting several interesting comments. And suppose that you had an idea that you thought might be a good one. Instead of the usual reaction of being afraid to share it in case someone else beat you to the solution, you would be afraid not to share it in case someone beat you to that particular idea. And if the problem eventually got solved, and published under some pseudonym like Polymath, say, with a footnote linking to the blog and explaining how the problem had been solved, then anybody could go to the blog and look at all the comments. And there they would find your idea and would know precisely what you had contributed. There might be arguments about which ideas had proved to be most important to the solution, but at least all the evidence would be there for everybody to look at.
True, it might be quite hard to say on your CV, “I had an idea that proved essential to Polymath’s solution of the *** problem,” but if you made significant contributions to several collaborative projects of this kind, then you might well start to earn a reputation amongst people who read mathematical blogs, and that is likely to count for something. (Even if it doesn’t count for all that much now, it is likely to become increasingly important.) And it might not be as hard as all that to put it on your CV: you could think of yourself as a joint author, with the added advantage that people could find out exactly what you had contributed.
And here he is, on the 'getting scooped' problem:
And what about the person who tries to cut and run when the project is 85% finished? Well, it might happen, but everyone would know that they had done it. The referee of the paper would, one hopes, say, “Erm, should you not credit Polymath for your crucial Lemma 13?” And that would be rather an embarrassing thing to have to do.
I haven't thought much about the use of blogs for collaborative problem solving, so what I have now are just a bunch of (not particularly well posed) questions. Let me get them out:
Assuming that Gowers' experiment succeeds, how can it be extended to experimentally oriented fields? For example, can it be transplanted to pose and solve a research problem at the cutting edge of a biomedical field?
I can think of two other settings where collaborative problem solving is quite common: industrial R&D and open source software development. How does credit-sharing work in these other settings? Is it all just peer recognition?
Also, in industrial R&D and OSS development, what kinds of collaboration tools do they use? Would Gowers' experiment benefit -- which is based largely on the discussion threads in his blog, right now -- from some of those tools?
As I said, all I have are questions. In the meantime, Gowers has already started his experiment. Let me wish him all the best!