James Grime on the Hadwiger–Nelson problem. Check out Brilliant (get 20% off their premium service): https://brilliant.org/numberphile (sponsor) Extra footage from this interview: https://www.youtube.com/watch?v=7nBtRKvUox4 The Four Color Map Theorem: https://www.youtube.com/watch?v=NgbK43jB4rQ More on James Grime (you can book him for talks): http://singingbanana.com/ More James Grime videos: http://bit.ly/grimevideos The de Grey paper: https://arxiv.org/abs/1804.02385 A good write up on this topic via Quanta Magazine: https://www.quantamagazine.org/decades-old-graph-problem-yields-to-amateur-mathematician-20180417/ The Marijn Heule counterexample: http://www.cs.utexas.edu/users/marijn/CNP/553.png More links & stuff in full description below ↓↓↓ Numberphile is supported by the Mathematical Sciences Research Institute (MSRI): http://bit.ly/MSRINumberphile We are also supported by Science Sandbox, a Simons Foundation initiative dedicated to engaging everyone with the process of science. https://www.simonsfoundation.org/outreach/science-sandbox/ And support from Math For America - https://www.mathforamerica.org/ NUMBERPHILE Website: http://www.numberphile.com/ Numberphile on Facebook: http://www.facebook.com/numberphile Numberphile tweets: https://twitter.com/numberphile Subscribe: http://bit.ly/Numberphile_Sub Videos by Brady Haran Patreon: http://www.patreon.com/numberphile Numberphile T-Shirts: null Brady's videos subreddit: http://www.reddit.com/r/BradyHaran/ Brady's latest videos across all channels: http://www.bradyharanblog.com/ Sign up for (occasional) emails: http://eepurl.com/YdjL9