Jan 30, 2018 Aging is not a mystery, says famed researcher Dr. Aubrey de Grey, perhaps the world’s foremost advocate of the provocative view that medical technology will one day allow humans to control the aging process and live healthily into our hundreds—or even thousands.
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1 year agoApparently two days ago Aubrey de Grey published a paper on arXiv in which he presents the progress he made on the Hadwiger-Nelson problem, which standed unaltered in graph theory since 1950.
Paper: https://arxiv.org/pdf/1804.02385.pdf
Terence Tao - one of the most important mathematicians alive - talks about Aubrey's paper and his Polymath project to improve on the result: https://plus.google.com/+TerenceTao27/posts/QBxTFAsDeBp
Aubrey asked to verify his result on Twitter, and Landon Rabern verified: https://twitter.com/aubreydegrey
r/math thread: https://www.reddit.com/r/math/comments/8azc1a/arxiv_the_chromatic_number_of_the_plane_is_at/
Blog post with an additional verification of the result and relevant software download: https://dustingmixon.wordpress.com/2018/04/10/the-chromatic-number-of-the-plane-is-at-least-5/
Some people asked me if this is relevant for biology or at least bioinfomatics or AI. I think it's not, since it's quite theoretical, and the solutions for finite unit distance graphs (the ones that I expect could be relevant for applications in CS) should be much simpler to get.. although maybe if the graphs become big enough the complexity of the problem could be too high (I don't really know, just guessing). I may be wrong, since I'm a noob and it's the first time I encounter this problem. If someone knows more please comment.
From what I get Aubrey published it because he is an amateur mathematician (as confirmed by Terence Tao he participated in some other projects in the past). The problem, as stated, is quite simple if I understood it correctly: Take the infinite points in the euclidean plane and connect all the ones which have distance exactly one form each other. This is called a unit distance graph (but covering the entire plane). The problem is this: How many colours do you need to colour all the vertices so that no two connected vertices have the same colour? Till now (and since 1950) there were four possible answers: 4, 5, 6, 7. Aubrey restricted the possible answers to only 5, 6, 7.
I hope this doesn't contain mistakes.
21 comments
Posted by10% to lifespan.io, 5% SENS
1 year agoApparently two days ago Aubrey de Grey published a paper on arXiv in which he presents the progress he made on the Hadwiger-Nelson problem, which standed unaltered in graph theory since 1950.
Paper: https://arxiv.org/pdf/1804.02385.pdf
Terence Tao - one of the most important mathematicians alive - talks about Aubrey's paper and his Polymath project to improve on the result: https://plus.google.com/+TerenceTao27/posts/QBxTFAsDeBp
Aubrey asked to verify his result on Twitter, and Landon Rabern verified: https://twitter.com/aubreydegrey
r/math thread: https://www.reddit.com/r/math/comments/8azc1a/arxiv_the_chromatic_number_of_the_plane_is_at/
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Blog post with an additional verification of the result and relevant software download: https://dustingmixon.wordpress.com/2018/04/10/the-chromatic-number-of-the-plane-is-at-least-5/
Some people asked me if this is relevant for biology or at least bioinfomatics or AI. I think it's not, since it's quite theoretical, and the solutions for finite unit distance graphs (the ones that I expect could be relevant for applications in CS) should be much simpler to get.. although maybe if the graphs become big enough the complexity of the problem could be too high (I don't really know, just guessing). I may be wrong, since I'm a noob and it's the first time I encounter this problem. If someone knows more please comment.
From what I get Aubrey published it because he is an amateur mathematician (as confirmed by Terence Tao he participated in some other projects in the past). The problem, as stated, is quite simple if I understood it correctly: Take the infinite points in the euclidean plane and connect all the ones which have distance exactly one form each other. This is called a unit distance graph (but covering the entire plane). The problem is this: How many colours do you need to colour all the vertices so that no two connected vertices have the same colour? Till now (and since 1950) there were four possible answers: 4, 5, 6, 7. Aubrey restricted the possible answers to only 5, 6, 7.
I hope this doesn't contain mistakes.
21 comments