Polymath 9 has answered one of the questions it asked apparently. The idea that was being tried didn’t work there was a counterexample. It could possibly continue if the method could be modified to avoid the counterexample which is here. Meanwhile Polymath 8 has spawned a new project Polymath 8b. this is the latest post of this project.
Polymath 8 is working towards publication and it looks like Polymath 9 might be starting up. See this post.
There is a new Polymath project proposal. It is about bounded gaps between primes. The proposal is here.
There has been some progress in the polymath 7 project. See the new thread here.
A paper related to a polymath project has been published. “A new proof of the density Hales-Jewett theorem” will appear in May in Annals of Mathematics.