T-Mobile 5G Home Internet. https://T-Mobile.com/HomeInternet Do we need new math to explain dark matter? Neil deGrasse Tyson and comedian Paul Mecurio explore unsolved problems in math, simulation theory, base systems and more with mathematician Terence Tao. We take a look at the boundary between pure and applied mathematics. You’ll learn intentional simplifications of a messy world that allow researchers to isolate complex truths. Terence explains how curiosity-driven research into patterns often leads to accidental breakthroughs, such as how abstract group theory eventually paved the way for faster, more efficient MRI scans. We then tackle some famous unsolved problems in the field, including the Collatz Conjecture (the "hailstone sequence"). What does it mean to prove something in math? We explore chaos, where iterating simple operations creates vast complexity. We work though fan-submitted Cosmic Queries talking about the history of base systems from Babylonian base-60 to computer binary. We discuss the emotional hurdles of math education. Do we need a new math to explain dark matter and dark energy? Finally, we look at the Simulation Theory through the lens of Bayesian probabilities. Could a cutoff in the cosmic microwave background be the glitch in the matrix that proves we’re living in a program? From the idiosyncratic life of Paul Erdős to the "malice" of an unsolved proof, we’re revisiting the universe of math. Thanks to our Patrons Drake Mccammon, Lourosa Thomas, Christopher, WireRider, Kevin Walter, Erik Majsai, Zoe Briskey, Roger W. Cavallo Jr., Tibi Chiorean, Maggie, Guy Cummins, Sean E, Sebastian, Ty Powell, Iceo Bergins, Anissa Aponte, Keith Autry, Guy_%, Kyle Kern, Scott Morris, Francisco Cueto, Psychoquark, Joe Rivera, Chris Coyle, Brian White, Michael Boring, Adrian Mihai, Rowdy Payton, Ben Huang, Jerred Cook, KennyS, Gonzalo Oria, Herb Tobias, Kevin Revels, Sean Taylor, AndersonRobotics, Faruk Arslan, Antonio Alcala, Rudolfo Munguia, Tim Winter, B Boyette, Pilar Rodriguez, Justin Brackenbury, Kosta Papageorgiou, Mickey Mouse, Charles Garcia, Sultan Bin Zaal, Brian Rall, Mike, Dave, Rodolphe Phelouzat, Joshua Fisher, Xan Kriegor, Michael L. Price, Wendy Welch, RichInDC, Justin Lebron, Brad Cook, Auralen Isara Maelis, Obi Wan Kenobi, Avinav Abraham, Stanko, Colton Murphy, Patrick Quinn, Haze, John Stamm, Roberto Delgado, Hans Gab, Richard Nolan, Tony R, Trisha Hadden, Stephen Flenley, Robby Vasquez, Abraham, Dr. Bebop, Damon, Richard Thompson, Prince N., David Rivanis, Daniel Slack, Guy Bergeson, Shawna Couplin, MrFish, Lisette Ramos-Voigt, Scott Mccoy, Steffen Thomas, Cassio Magellan Campos, Rodger Reinhardt, Michael Becker, Billie Lyons-Super, Todd Chambers, Mo Elzeinab, Talal, Joseph Glynn, John Hermanns, TheNaden, Mark Parker, Seth Davison, Anon328648926, and David Bentley for supporting us this week. Timestamps: 00:00 - Introduction: Terence Tao 7:38 - Pure vs. Applied Math 10:58 - Toy Models & Intentional Simplified Reality 14:13 - Unsolved Problems in Math 18:26 - Collatz Conjecture & Hailstones 23:57 - Are We Getting Closer to Solving Unsolved Problems? 26:29 - Erdos problem 1026 32:36 - Useful Pure Math Discoveries 37:11 - If We Didn’t Use Base Ten 40:13 - How Would You Change Teaching Math? 40:37 - How to Work on a Proof 46:18 - Will We Need New Math to Explore Space? 49:30 - Can Math Prove We Are Not in a Simulation? Check out our second channel, @StarTalkPlus Get the NEW StarTalk book, 'To Infinity and Beyond: A Journey of Cosmic Discovery' on Amazon: https://amzn.to/3PL0NFn Support us on Patreon: https://www.patreon.com/startalkradio FOLLOW or SUBSCRIBE to StarTalk: Twitter: http://twitter.com/startalkradio Facebook: https://www.facebook.com/StarTalk Instagram: https://www.instagram.com/startalk About StarTalk: Science meets pop culture on StarTalk! Astrophysicist & Hayden Planetarium director Neil deGrasse Tyson, his comic co-hosts, guest celebrities & scientists discuss astronomy, physics, and everything else about life in the universe. Keep Looking Up! #StarTalk #NeildeGrasseTyson