I don’t have much to say mathematically, or rather I do but now that there is a wiki associated with polymath1, that seems to be the obvious place to summarize the mathematical understanding that arises in the comments on the various blog posts here and over on Terence Tao’s blog (see blogroll). The reason I am writing a new post now is simply that the 500s thread is about to run out.
So let me quickly make a few comments on how things seem to be going. (At some point in the future I will do so at much greater length.) Not surprisingly, it seems that we have reached a stage that is noticeably different from how things were right at the beginning. Certain ideas that emerged then have become digested by all the participants and have turned into something like background knowledge. Meanwhile, the discussion itself has become somewhat fragmented, in the sense that various people, or smaller groups of people, are pursuing different approaches and commenting only briefly if at all on other people’s approaches. In other words, at the moment the advantage of collaboration is that it is allowing us to do things in parallel, and efficiently because people are likely to be better at thinking about the aspects of the problem that particularly appeal to them. (more…)