# This Biologist Cracked a Problem That's Stumped Mathematicians for 68 Years An amateur mathematician just partially solved a problem that has vexed mathematicians since 1950.

Aubrey de Grey — a biologist better known for trying to radically extend human life and for predicting that the first person to live to be 1,000 years old has already been born — has published a paper on the preprint server arXiv that narrows down the answer to the 68-year-old Hadwiger-Nelson problem. Mathematicians had known for years that the answer to this question (which we'll get to in a second) was either 4, 5, 6 or 7. De Grey, in his paper, showed that it definitely isn't 4. That leaves just 5, 6 or 7. [The 9 Most Massive Numbers in Existence]

Now that you have de Grey's answer, here's the question:

Take a canvas and draw a bunch of points (called vertices) on it. If any points are a distance 1 unit apart from each other, draw a line between them. Mathematicians don't care if the "unit" is an inch or a mile. It doesn't matter, as long as it's the same between all connected vertices. (Those lines connecting the points are called "edges.") Mathematicians call this a unit distance graph. What you end up with will look something like this:

Now it's time to go to the store and buy paint to color in all the points.

Now ask yourself: What's the minimum number of paint colors I need to color in any graph in a way that no two points that share an edge are the same color?

It's easy to come up with a unit distance graph that can't be colored with just three colors. Here's a good example: This graph cannot be colored with just three colors, but four will do the trick. Black dots denote that the pattern can be repeated on an infinite plane. (Image credit: Aubrey de Gray/arXiv/CC by 4.0)

But coming up with a unit distance graph that can't be colored in with four colors is a lot more difficult. Computers can't do it on their own. No full-time mathematicians managed it for 68 years, until de Grey came up with this monstrosity: