Amateurs Just Solved a 30-Year-Old Math Problem

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Get Nebula using my link for 40% off an annual subscription: https://go.nebula.tv/upandatom Watch Becoming Human: https://nebula.tv/becominghuman Videos mentioned: Turing Machines https://youtu.be/PLVCscCY4xI The Halting Problem https://youtu.be/sG0obNcgNJM Quanta Article: https://www.quantamagazine.org/amateur-mathematicians-find-fifth-busy-beaver-turing-machine-20240702/ Hi! I'm Jade. If you'd like to consider supporting Up and Atom, head over to my Patreon page :) https://www.patreon.com/upandatom Visit the Up and Atom store https://store.nebula.app/collections/up-and-atom Subscribe to Up and Atom for physics, math and computer science videos https://www.youtube.com/c/upandatom For a one time donation, head over to my PayPal :) https://www.paypal.me/upandatomshows *A big thank you to my AMAZING PATRONS!* Raz Tirosh, Michael Seydel, Brian Wilkins, Thorsten Auth, Chris Flynn, Izzy Ca, Tate Lyles, Richard O McEwen Jr, Fabio Manzini, Scott Ready, John H. Austin, Jr., David Johnston, Thomas Krause, Ave Eva Thornton, Andrew Pann, Anne Tan, Robert Walker, John Doe, Dirk Wouters, Stoney Bair, Jeffrey Dutt, Joseph Lamoree, Francisco, Marc-Antoine, Thomas Urech, chuck zegar, David Tuman, Ben Mitchell, Tyler Simms, James Mahoney, Jim Felich, Jeremy, Robin High, KiYun Roe, Ron Hochsprung, Andi B, James Matheson, Kevin Anderson, Alexander230, Tim Ludwig, Justin Smith, Mark Littlehale, Tony T Flores, Dagmawi Elehu, Jeffrey Smith, Alex Hackman, Blue Cardinal, bpatb, Joel Becane, Cy 'kkm' K'Nelson, eris esoteric, Paul Barclay, 12tone, John Lakeman, Jana Christine Saout, Jeff Schwarz, Yana Chernobilsky, Louis Mashado, Michael Dean, Chris Amaris, Matt G, Dag-Erling Smørgrav, John Shioli, Susan Jones, AudioFreak, Lauren Fish, Boris Lets Kuslitskiy, Keith, Steve Platt, Matthew Lewis, y.k., B Henke, Bryan Hughes, Trance Maharaj, Matt, Jonathan Rayback, geek1027, Smarter Every Day, Miles Freeman, Bunny Lushington, Jake!, Motty Porat, Yaw Mintah, Carlos Escolar, Anthony Docimo, robert lalonde, Cassandra Durnord, Paul Bunbury, Richard Rensman, David Shlapak, Kent Arimura, Phillip Rhodes, Michael Nugent, Roland Gibson, Piotr Klos, Joe McTee, Oleg Dats, Simon J. Dodd, Tang Chun, Michelle, William Toffey, James Horsley, omg.science, Cameron Tacklind, Lance Ahmu, Steve Watson, Potch, Thomas P Taft, Indrajeet Sagar, Pablo de Caffe, Taylor Hornby, Colin Byrne, Nick H, Jesper de Jong, Sofia Fredriksson, Spuddy, Sascha Bohemia, Stephen Britt, KG, Hansjuerg Widmer, John Sigwald, O C, Carlos Gonzalez, James Palermo, Marc Catapano, Chris Teubert, Fran, Wolfgang Ripken, Jeremy Bowkett, Vincent Karpinski, Nicolas Frias, Louis M, ROBERT C PAYNE, Moose Thompson, Rick DeWitt, S, Garrett Chomka, Gene Levitsky, Pat Gunn, George Fletcher, RobF, Vincent Seguin, Michael Brunolli, Shawn, Jesse Clark, Steven Wheeler, Lynn Shackelford, Philip Freeman, Armin Quast, Jareth Arnold, Simon Barker, and Simon Dargaville. Creator - Jade Tan-Holmes Script - Daniel Inafuku Animations - Alexia Barakou Music - epidemicsound.com Sources and further reading https://discuss.bbchallenge.org/ https://www.scottaaronson.com/papers/bb.pdf Chapters 0:00-1:21 Intro 1:21-5:41 The busy beaver game 5:41-7:57 The Goldbach Conjecture 7:57-9:25 Why finding busy beavers is hard 9:25-10:50 BB(3) 10:50-11:44 BB(4) 11:44-17:02 BB(5) 17:02 ...BB(6)?