The Puzzling Fourth Dimension (and exotic shapes) - Numberphile

Featuring Ciprian Manolescu from Stanford University. More links & stuff in full description below ↓↓↓ Ciprian Manolescu: https://web.stanford.edu/~cm5/ Sphere art at the end of the video by https://www.adistu.ro/ Perfect Shapes in Higher Dimensions: https://youtu.be/2s4TqVAbfz4 Numberphile is supported by the Simons Laufer Mathematical Sciences Institute (formerly 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 The Akamai Foundation - dedicated to encouraging the next generation of technology innovators and equitable access to STEM education - https://www.akamai.com/company/corporate-responsibility/akamai-foundation 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 Animation by Pete McPartlan Patreon: http://www.patreon.com/numberphile Numberphile T-Shirts and Merch: 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 Special thanks to: Ben Delo Juan Benet Jeff Straathof Ken Baron Andy B Michael Dunworth James Bissonette Jubal John Jeremy Buchanan Steve Crutchfield Adam Savage Ben White Andrei M Burke RAD Donato Matthew Schuster Nat Tyce Ron Hochsprung Ubiquity Ventures John Zelinka Gnare Kannan Stanz OnlineBookClub.org Matt Tiblow Heather Liu Jordan W Oja Tracy Parry Ian George Walker Arnas Bernd Sing Valentin Alfred Wallace Alex Khein Mirik Gogri Doug Hoffman Xavier F. G. John Loach