Substrate

The Four Color Map Theorem (or colour!?) was a long-standing problem until it was cracked in 1976 using a "new" method... computers! A little bit of extra footage from this: https://youtu.be/laMkuPrad3s This video features Dr James Grime - http://jamesgrime.com More Grime videos: http://bit.ly/grimevideos This video supported by Squarespace: https://www.squarespace.com/numberphile 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. 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 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

A counterexample to Hedetniemi's conjecture - featuring Erica Klarreich. Get 3 months of Audible for just $6.95 a month. Visit https://www.audible.com/numberphile or text "numberphile" to 500 500 More links & stuff in full description below ↓↓↓ Read Erica Klarreich's Quanta article on this subject: https://www.quantamagazine.org/mathematician-disproves-hedetniemis-graph-theory-conjecture-20190617/ And visit her website: http://www.ericaklarreich.com/ Yaroslav Shitov's breakthrough paper: https://arxiv.org/abs/1905.02167 Thanks to Stephen Hedetniemi for providing us with photos and pages from his original dissertation. Some more graph theory on Numberphile... Four Color Maps: https://youtu.be/NgbK43jB4rQ An Unsolved Problem: https://youtu.be/niaeV_NHh-o Planar Graphs: https://youtu.be/xBkTIp6ajAg Perfect Graphs: https://youtu.be/C4Zr4cOVm9g Friends and Strangers: https://youtu.be/xdiL-ADRTxQ River Crossings: https://youtu.be/ZCVAGb1ee8A 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: https://teespring.com/stores/numberphile 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