
The problem, now known as the Hadwiger-Nelson problem or the problem of finding the chromatic number of the plane, has piqued the interest of many mathematicians, including the famously prolific Paul Erdős. Researchers quickly narrowed the possibilities down, finding that the infinite graph can be colored by no fewer than four and no more than seven colors. Other researchers went on to prove a few partial results in the decades that followed, but no one was able to change these bounds.
Then last week, Aubrey de Grey, a biologist known for his claims that people alive today will live to the age of 1,000, posted a paper to the scientific preprint site arxiv.org with the title "The Chromatic Number of the Plane Is at Least 5." In it, he describes the construction of a unit-distance graph that can't be colored with only four colors. The finding represents the first major advance in solving the problem since shortly after it was introduced. "I got extraordinarily lucky," de Grey said. "It's not every day that somebody comes up with the solution to a 60-year-old problem."













Comment: See also: How smart phones make today's teens unhappy & cause dramatic shifts in behavior