How An Infinite Hotel Ran Out Of Room @veritasium

Uploaded May 2026 | Updated September 2026, 2 weeks ago

If there's a hotel with infinite rooms, could it ever be completely full?

Could you run out of space to put everyone?

The surprising answer is yes -- this is important to know if you're the manager of the Hilbert Hotel.

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$The Closest We’ve Come to a Theory of Everything The single principle that underpins all of physics. Head to https://brilliant.org/veritasium to start your free 30-day trial and get 20% off an annual premium subscription. A massive thank you to Prof. Steven Strogatz for his expertise and enthusiasm. As an exclusive bonus for our Patreon members, weve posted a longer interview with Prof. Strogatz over there: https://www.patreon.com/posts/principle-of-116042877 A huge thank you to Prof. Haithem Taha, Prof. Anthony Bloch, Dr. Carl-Fredrik Nyberg Brodda, Dr. Sarah Millholland, and Dr. Andrew Mitchell for all their help with finding the story and getting it right. A special thanks to Dr. Aurèle Adam, Ron Haaksman, Marc Serra Peralta, and everyone at the Delft Makerspace for their help with preparing and performing experiments. 00:00 One rule that replaces all of physics 00:51 The problem of fastest descent 05:09 Fermats principle 07:17 Bernoullis solution 10:38 Maupertuis principle 12:28 Maupertuis attacked and ridiculed 14:01 Euler & Lagrange to the rescue 17:22 The general approach to solving these problems 19:32 Writing the principle into its modern form 23:17 Why the principle works 27:08 Another way to do mechanics 30:19 A “spooky” breakthrough ▀▀▀ Join us on Patreon for early access videos and exclusive bonus content https://ve42.co/PatreonDE Patrons: Adam Foreman, Anton Ragin, Balkrishna Heroor, Bertrand Serlet, Bill Linder, Blake Byers, Burt Humburg, Chris Harper, Dave Kircher, David Johnston, Evgeny Skvortsov, Garrett Mueller, Gnare, gpoly, I. H., John H. Austin, Jr., john kiehl, Josh Hibschman, Juan Benet, KeyWestr, Kyi, Lee Redden, Marinus Kuivenhoven, Martin, Matthias Wrobel, Max Paladino, Meekay, meg noah, Michael Krugman, Orlando Bassotto, Paul Peijzel, Richard Sundvall, Sam Lutfi, Stephen Wilcox, Tj Steyn, Toni , TTST, Ubiquity Ventures, wolfee If you’re looking for a molecular modeling kit, try Snatoms, a kit I invented where the atoms snap together magnetically - https://ve42.co/SnatomsV ▀▀▀ Key references: A fantastic book on the history of the Principle of Least Action: Rojo, A. and Bloch, A. The Principle of Least Action: History and Physics. - https://ve42.co/Bloch2018 Coopersmith, J. (2017). The lazy universe: an introduction to the principle of least action. Oxford University Press. - https://ve42.co/LazyU 3Blue1Brown. The Brachistochrone, with Steven Strogatz via Youtube - https://ve42.co/Brach3B1B Vsauce. The Brachistochrone via Youtube - https://ve42.co/BrachV PBS Space Time. Is ACTION The Most Fundamental Property in Physics? via Youtube - https://ve42.co/PBSAction Full list of references: https://ve42.co/LeastActionRefs Images & Video: Voltaire. (1753). Diatribe du Docteur Akakia. - https://ve42.co/DiatribeAkakia Philosophical Transactions cover. via Wikimedia Commons - https://ve42.co/PhilTransImage Kids Fun Science. (Jun 28, 2017). Refraction of Light with a arrow experiment via Youtube - https://ve42.co/RefractionFunSci Physics with Simon Poliakoff. Refraction demonstration with water and laser via Youtube - https://ve42.co/SimonPoliakoff Mercury Transit Across Sun. via Nasa.gov - https://ve42.co/MercTransit ▀▀▀ Directed by Casper Mebius Written by Casper Mebius and Derek Muller Edited by Trenton Oliver Animated by Fabio Albertelli, Ivy Tello, Mike Radjabov, Gregor Čavlović, Emma Wright, James Finnemore and David Szakaly Illustrated by Jakub Misiek, Emma Wright, and Maria Gusakovich Filmed by Derek Muller and Casper Mebius Additional research by Gabe Strong, Gregor Čavlović, and Geeta Thakur Produced by Casper Mebius, Derek Muller, Rob Beasley Spence, Gabe Strong, Gregor Čavlović, and Tori Brittain Thumbnail contributions by Jakub Misiek, Ren Hurley and Peter Sheppard Additional video/photos supplied by Getty Images, Storyblocks, and NASA SVS Music from Epidemic Sound$

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