Why you can't comb a hairy ball, and why we care

Unexpected applications and a beautiful proof. Looking for a new career? Check out https://3b1b.co/talent Supporters get early access to new videos: https://3b1b.co/support An equally valuable form of support is to simply share the videos. Home page: https://www.3blue1brown.com Credits: Senia Sheydvasser: Co-writing and sphere deformation animations, made in Blender Paul Dancstep: Those lovely fluffy sphere animations, made in Cinema4D Vince Rubinetti: Music Sphere Eversion clip by Carsten Steger https://commons.wikimedia.org/wiki/Fi... Timestamps: 0:00 - To comb a hairy ball 1:24 - Applications 8:46 - The puzzle of one null point 12:12 - The proof outline 16:41 - Defining orientation 21:44 - Why inside-out is impossible 25:59 - 3b1b Talent 27:44 - Final food for thought ------------------ These animations are largely made using a custom Python library, manim. See the FAQ comments here: https://3b1b.co/faq#manim Music by Vincent Rubinetti. https://vincerubinetti.bandcamp.com/a... https://open.spotify.com/album/1dVyjw... ------------------ 3blue1brown is a channel about animating math, in all senses of the word animate. If you're reading the bottom of a video description, I'm guessing you're more interested than the average viewer in lessons here. It would mean a lot to me if you chose to stay up to date on new ones, either by subscribing here on YouTube or otherwise following on whichever platform below you check most regularly. Mailing list: https://3blue1brown.substack.com Twitter:   / 3blue1brown   Bluesky: https://bsky.app/profile/3blue1brown.com Instagram:   / 3blue1brown   Reddit:   / 3blue1brown   Facebook:   / 3blue1brown   Patreon:   / 3blue1brown   Website: https://www.3blue1brown.com