While Polymath13 has (barring a mistake that we have not noticed) led to an interesting and clearly publishable result, there are some obvious follow-up questions that we would be wrong not to try to answer before finishing the project, especially as some of them seem to be either essentially solved or promisingly close to a […]| Gowers's Weblog
I have now completed a draft of a write-up of a proof of the following statement. Recall that a random -sided die (in the balanced-sequences model) is a sequence of length of integers between 1 and that add up to , chosen uniformly from all such sequences. A die beats a die if the number […]| Gowers's Weblog
It has become clear that what we need in order to finish off one of the problems about intransitive dice is a suitable version of the local central limit theorem. Roughly speaking, we need a version that is two-dimensional — that is, concerning a random walk on — and completely explicit — that is, giving […]| Gowers's Weblog
I hope, but am not yet sure, that this post is a counterexample to Betteridge’s law of headlines. To back up that hope, let me sketch an argument that has arisen from the discussion so far, which appears to get us close to showing that if and are three -sided dice chosen independently at random […]| Gowers's Weblog
I now feel more optimistic about the prospects for this project. I don’t know whether we’ll solve the problem, but I think there’s a chance. But it seems that there is after all enough appetite to make it an “official” Polymath project. Perhaps we could also have an understanding that the pace of the project […]| Gowers's Weblog
I’m not getting the feeling that this intransitive-dice problem is taking off as a Polymath project. However, I myself like the problem enough to want to think about it some more. So here’s a post with some observations and with a few suggested subproblems that shouldn’t be hard to solve and that should shed light […]| Gowers's Weblog