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.

Well. That's really, really, really crazy.

Also, from Noam Elkies on Math Overflow:

If the 1567 figure is wrong, Aubrey de Grey needs to amend that arXiV paper... Also I wouldn't put too much trust in a result that was reached "by a SAT solver" either, unless either the SAT results came with a proof certificate that can be fed to a

formally correctchecker, or (in the UNSAT case) the solveritselfwas formally verified to provide correct and complete results.From Scott Aaronson today:

And de Grey commented:

Haha, this would be wonderful. Let's get Terence Tao on the aging problem!

Terence Tao even talked about this in his Google+ profile.