# Amateur Mathematician Cracks A Longstanding Math Problem

For the first time in decades, there's been a breakthrough with the “Hadwiger-Nelson problem.” Aubrey de Grey/arXiv

After decades of stalemate, someone has made a breakthrough with the “Hadwiger-Nelson problem”, a fiendishly difficult mathematical problem that has remained unanswered since 1950. Most incredibly of all, the person who figured it out isn’t strictly even a mathematician, he’s a British computer scientist-turned-biologist who spends most of his energy trying to engineer a "cure" for aging.

Aubrey de Grey has recently helped to solve this decade-old dilemma in a paper called “The Chromatic Number of the Plane is at least 5”. The study has not yet been independently peer-reviewed, but you can find a preprint of the paper on arXiv.

The mathematical conundrum sounds relatively straightforward to the uninitiated but make no mistake, professional mathematicians have been unable to crack it for almost 70 years. Here’s how it goes: imagine a collection of points connected by lines of exactly the same length. If you were to color all the points, with no two connecting dots being the same color, how many different colors are required to color in an infinite plane?

Over the years, scientists have whittled down the estimation for the number of colors to somewhere between four and seven. Now, de Grey has shown that it is not possible to color all the points with just four different colors. Therefore, the minimum number of colors needed is at least five. Considering that researchers have been at a total standstill with this problem for decades, this is a pretty big breakthrough.

The discovery was made by playing around with a Moser spindle, a pattern that’s composed of seven dots and 11 edges. Using computer software, de Grey fused copies of the Moser spindle into a vast web of 20,425 connected points. He was then able to use this to show that at least five colors were needed to color in the dots using the “rules of the game”.

“I got extraordinarily lucky,” de Grey told Quanta Magazine. “It’s not every day that somebody comes up with the solution to a 60-year-old problem.”

When he isn’t busy cracking mind-melting math problems in his spare time, de Grey works on pioneering research geared towards extending the human lifespan. One of the 55-year-old scientist's biggest claims is that humans have the potential to live to the ripe old age of 1,000 years. It’s a bold claim, and his work isn’t without its critics, but de Grey continues to publish and promote some of the most pioneering regenerative medicine in the world.

[H/T: Quanta Magazine]