The Chromatic Number of the Plane is at Least 5 - Aubrey de Grey

by Scott Garrabrant 1y11th Apr 20185 comments

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This is a long standing open problem in math. Many people learn about it as early as high school as an example of an open problem, because it is so easy to state:

How many colors does it take to color every point in the plane so that ever pair of points of distance exactly 1 from each other have different colors?

There are simple proofs that anyone here can understand that this number is between 4 and 7, and those were the only bounds we knew for a long time.

The lower bound was improved to 5 recently by Aubrey de Grey! The same Aubrey de Grey that you probably think of as the face of solving aging! He points at a concrete subset of 1567 points in the plane that cannot be colored with four colors.

This is super exciting. I think this is basically the main example of a simple open problem in math that we (used to) have no progress on.

I hope Aubrey de Grey negotiated the moral trade with the mathematicians successfully, and now that he solved one of their most beloved problems, they will start working on solving aging.