So far that was a hot summer. With all written and oral exams finished and with bearable temperatures returning I plan to spend some free time to think about the Erdös Discrepancy Conjecture. Is it wise to post this plan? I think so. It puts some pressure on me and this is good.
The idea is that we have probably not made maximal use of Tim Gowers’s proof of Roth’s theorem. Behind all the numbers and estimates there could be some abstract/infinitary content. If this is the case, then it might be easier to generalize or at least to spot the limits of the method.
Intuition or wishful thinking? Maybe the later, but I want to know for sure.