As part of my ongoing research to explore models for online collaboration I have recently been reviewing the Polymath project1 which exploits collaborative principals in resolving mathematical problems. The Polymath project created by the British …

]]>Upper and lower bounds for .

Trying to find different proofs of Sperner’s theorem with better chances of generalizing to density Hales-Jewett.

Obstructions to uniformity and density arguments.

Is there a new regularity lemma that would work inside the is-disjoint-from graph?

General discussion of strategies for proving the theorem.

Using Szemerédi’s original proof as a model.

Some of the above are connected, and some of them (such as e.g. the Sperner thread) could be split into further subthreads (e.g. pair removal, pushing slices around, etc.).

So two questions here. First, what should the threads be if we split into threads? Secondly, who’s prepared to write summaries? (I’m happy to do some of them — it’s probably fairly obvious which ones I feel most involved with.)

]]>I’ll be watching here, but if anyone has ideas about what’s missing from the simple blog format that would be useful in this sort of collaborative effort, or information about current forums/blogs/wikis/other tools that might be suited to the task, your input would be most welcome.

]]>A number of interesting mathematical questions have been thrown up as a result of the discussion. With some of these there might be a case for a new post that briefly explains the question and why it came up, with the expectation that comments about that question would then go with that post. The advantage of that is that it would bring related comments closer together. A potential disadvantage of doing it in general is that the subconversations would become more isolated from each other and it would be harder to discuss connections between them. At this stage it’s not clear to me which of these considerations outweighs the other. (And of course they may not be the only considerations.)

]]>The problem of the CV line remains both important and unsolved.

]]>*Aliens invade the earth and threaten to obliterate it in a year’s time unless human beings can find the Ramsey number for red five and blue five. We could marshal the world’s best minds and fastest computers, and within a year we could probably calculate the value. If the aliens demanded the Ramsey number for red six and blue six, however, we would have no choice but to launch a preemptive attack. *

This is indeed a promising start. It feels like the dynamic I have experienced with multi-author collaborations in the same room, but also resembles collaborations I have had with authors in different time zones (as one gets the uncanny feeling that progress is being made on the problem while one sleeps).

I think we are beginning to bump up against the limits of the wordpress environment though. For instance, the only way to migrate comments from one thread to another is by hand, which is quite tedious. I would be hesitant to “fix” what isn’t “broken” yet, and so would leave the single massive thread as it is, at least until there is a clear divergence into two largely non-interacting subthreads, with one of them ripe for a recap post.

One of the beauties of a digital medium such as this, though, is that any cleaning up of the organisational structure can always be done *ex post facto*; the important thing, at this stage, is just to get the thoughts and ideas entered into the system somewhere, and it can be sorted out later.

If things carry on as they are, then at some point I think I’ll write a post in which I make various suggestions about how to organize further comments (such as starting dedicated threads devoted to subproblems) and invite comments on those suggestions.

And now I’ve got to go and type in yet another thought provoked by one of the existing comments.

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