The 1581-vertex, non-4-colourable unit-distance graph G. Credit: arXiv:1804.02385 [math.CO]
April 24, 2018 (Phys.org) -- Professional biologist and amateur mathematician Aubrey de Grey has partially solved the Hadwiger-Nelson problem, which has vexed mathematicians since 1950.
He has published a paper describing the solution on the arXiv preprint server.
The Hadwiger-Nelson problem came about when Edward Nelson and Hugo Hadwiger wondered about the smallest number of colors necessary to color all of the points on a graph, with no two connected points using the same color.
Over the years, mathematicians have attacked the problem, and have narrowed the possibilities down to four, five, six or seven.
Now, de Gay has eliminated the possibility of four colors as the solution.