This is the eighth “research” thread of the Polymath16 project to make progress on the Hadwiger–Nelson problem, continuing this post. This project is a follow-up to Aubrey de Grey’s breakthrough result that the chromatic number of the plane is at least 5. Discussion of the project of a non-research nature should continue in the Polymath proposal page. We will summarize progress on the Polymath wiki page.
Here’s a brief summary of the progress made in the previous thread:
– We now have a human proof that for .
There is ongoing work to improve Thomassen’s result so that the tiles need not be strictly smaller than 1 nor have distance strictly larger than 1. This would produce new obstructions to 6-coloring the plane.