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Saturday, April 28, 2018

Amateur mathematician partially solves 60-year-old problem | Mathematics - 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" notes Bob Yirka, Phys.org

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 Grey has eliminated the possibility of four colors as the .

Read more at: https://phys.org/news/2018-04-amateur-mathematician-partially-year-old-problem.html#jCp
The 1581-vertex, non-4-colourable unit-distance graph G.
Photo: arXiv:1804.02385 [math.CO]
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 Grey has eliminated the possibility of four colors as the .

Interestingly, de Grey is well known for his work in his primary field, biology. More specifically, he has made public comments suggesting that some people alive today will live to be a thousand years old due incipient medical breakthroughs. He has established a foundation dedicated to reversing aging and continues working on the problem. His journey to math puzzle solver, he notes, has roots in his love of the game Othello. He used to be a competitive player, through which he befriended a group of mathematicians. They wound up teaching him some math theory, which he began to explore as a means of unwinding after a hard day at work. 
Read more... 

Additional resources 
The chromatic number of the plane is at least 5, arXiv:1804.02385 [math.CO] arxiv.org/abs/1804.02385

Journal reference  
arXiv

Source: Phys.Org


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