To generalize two results*, Zhang has a nice approach to hard problems: he's looking at relaxed versions of them. If his approach to this problem is sound, we

To generalize two results*, Zhang has a nice approach to hard problems: he's looking at relaxed versions of them. If his approach to this problem is sound, we can expect Gowers et al to follow it up with tighter bounds. I wouldn't expect this to solve RH, but it's a major step in that direction where we have seen no movement for a very long time. * one verified, one in review