Tim Gowers has published a new proof of Roth’s theorem (link to Polymath5) as part of the project. He extends previous polymath work of Kevin Obryant (and himself) to reach Roth’s exact bounds. All this in a very elegant and accessible way. The draft is a really good start to join the project and watch or contribute to a trend-setting and outstanding form of mathematics in the net.
Polymath5 – Roth’s theorem (again)