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This 826-vertex graph requires at least five colors to ensure that no two connected vertices are the same shade.
In 1950 Edward Nelson, then a student at the University of Chicago, asked the kind of deceptively simple question that can give mathematicians fits for decades. Imagine, he said, a graph - a collection of points connected by lines. Ensure that all of the lines are exactly the same length, and that everything lies on the plane. Now
color all the points, ensuring that no two connected points have the same color. Nelson asked: What is the smallest number of colors that you'd need to color any such graph, even one formed by linking an infinite number of vertices?
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: Not only is the story fake and being used to push an agenda, but considering recent discoveries, it's clear that our knowledge of the natural world is a work in progress; sometimes twisted by bias and other times just because we've yet to make the discovery, see: Super-colony of 1.5 Million Adélie penguins discovered on Danger islands, Antarctica
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