In fact, I just heard that yesterday, without any details. Cool! The chromatic number of the unit-distance graph of R^n is a quantity that is both utterly natural and deeply inscrutable. (I bet it turns out to be 7 for R^2, and 15 for R^3.) —Dan Adam Goucher wrote: ------------------- Did you hear the exciting news that Aubrey de Grey has increased the lower bound on the chromatic number of the plane from 4 to 5? https://cp4space.wordpress.com/2018/04/15/assorted-news-3/ The best upper bound is 7 (from colouring the cells of a hexagonal lattice of appropriate size). The previous lower bound of 4 is from the Moser's spindle. ---------