I thought it might be good to have a post where I tried to take stock and assess the chances that Polymath5 will actually result in a solution to the Erdős discrepancy problem. But before I talk about that, I want to make the point, which I have made before, that solving the problem one sets out to solve is not a necessary condition for the attempt to count as worthwhile. There is easily enough material on the blog now for it to be possible to base a publishable paper on it, even if quite a lot of that paper ends up being a combination of a survey about the problem and a report on the interesting phenomena that have become apparent as a result of computations, some of which we understand reasonably well and some of which are still rather mysterious.

I am not saying this in order to hint that I think that it might be time to give up. At the moment it feels to me as though we still have momentum, so my enthusiasm is not flagging. What is mathematical momentum? I might define it as follows: an assault on an open problem has momentum if one’s understanding of the problem is continuing to develop. Right now I feel as though with each passing day I understand things about EDP that I did not understand before — and I presume that applies to everyone else too. And for as long as that is the case, one can never quite be sure that the problem won’t suddenly yield. (more…)