The Man Who Almost Broke Math (And Himself...)
How do you make infinite choices? 👉 To try everything Brilliant has to offer for free for a full 30 days, visit http://brilliant.org/veritasium. You’ll also get 20% off an annual premium subscription.Try Snatoms! A molecular modelling kit I invented where the atoms snap together.
https://ve42.co/SnatomsV
▀▀▀
A huge thank you to Dr Asaf Karagila, Prof. Alex Kontorovich, Prof. Joel David Hamkins, Prof. Andrew Marks, Prof. Gabriel Goldberg and Prof. Elliot Glazer for their invaluable expertise and contributions to this video.
▀▀▀
0:00 What comes after one?
2:42 Some infinities are bigger than others
6:17 The Well Ordering Principle
10:32 Zermelo And The Axiom Of Choice
17:22 Why is the axiom of choice controversial?
23:16 The Banach–Tarski Paradox
27:53 Obviously True, Obviously False
29:58 Your Proof Your Choice
▀▀▀
References:
Up and Atom - https://www.youtube.com/watch?v=X56zst79Xjg
Minutephysics - https://www.youtube.com/watch?v=A-QoutHCu4o
PBS Infinite Series - https://www.youtube.com/watch?v=hcRZadc5KpI&t=125s
Vsauce - https://www.youtube.com/watch?v=s86-Z-CbaHA&t=474s
Ernst Zermelo via Wikipedia - https://ve42.co/zermeloBio
Axiom of choice via Wikipedia - https://ve42.co/choiceAxiom
Georg Cantor via Wikipedia - https://ve42.co/cantorMath
Gregory H. Moore (2013). Consequences of the Axiom of Choice. Dover Publications - https://ve42.co/choiceBook
Georg Cantor (1874). On a property of the class of all real algebraic numbers. Journal für die Reine und Angewandte Mathematik - https://ve42.co/MeyerCantor1874
Heinz-Dieter Ebbinghaus (Dec 2012). Zermelo and the Heidelberg Congress 1904. Historia Mathematica - https://ve42.co/SciDirect1904
Herbert B. Enderton (1977). Elements of Set Theory. - https://ve42.co/SciDirectGCH
Additional References - https://ve42.co/AoCAdRefs
Images & Video:
Foundations of a general theory of sets by Georg Cantor via ViaLibri - https://ve42.co/grundlagen
Alfred Tarski by George Bergman via Wikimedia Commons - https://ve42.co/tarski
Alfred Tarski Offprint Group by Alfred Tarski via Bonhams - https://ve42.co/tarskipaper
La mission strasbourgeoise de Maurice Fréchet by Laurent Mazliak via Images des mathematiques - https://ve42.co/frechet
Kurt Gödel by Alfred Eisenstaedt via New Yorker - https://ve42.co/godel
Leopold Kronecker by Granger via Fine Art America - https://ve42.co/kronecker
Lashi Bandara (2006). Zermelo-Frankel Set Theory and Well Orderings. ResearchGate - https://ve42.co/zermelofrankel
Heidelberg, Germany 1936 by Wagner & Debes via Ward Maps - https://ve42.co/heidelberg
Pythagoras by J. Augustus Knapp via the marginalian - https://ve42.co/pythag
Paul Cohen by C. J. Mozzochi via C. J. Mozzochi - https://ve42.co/paulcohen
Instituto de Matemática Pura e Aplicada. Lecture 01: Introduction: a non-measurable set via Youtube - https://www.youtube.com/watch?v=llnNaRzuvd4&t=834s
Simons Foundation. Fields Medal: James Maynard. Youtube https://www.youtube.com/watch?v=un-z8kgOrV0&t=8s
▀▀▀
Special thanks to our Patreon supporters:
Adam Foreman, Albert Wenger, Alex Porter, Alexander Tamas, Anton Ragin, Autodidactic Studios, Balkrishna Heroor, Bertrand Serlet, Blake Byers, Bruce, Dave Kircher, David Johnston, David Tseng, Evgeny Skvortsov, Garrett Mueller, Gnare, gpoly, Greg Scopel, HydrochloRick, Jon Jamison, Juan Benet, Keith England, KeyWestr, Kyi, Lee Redden, Marinus Kuivenhoven, Matthias Wrobel, Meekay, meg noah, Michael Krugman, Orlando Bassotto, Paul Peijzel, Richard Sundvall, Sam Lutfi, Tj Steyn, TTST, Ubiquity Ventures, wolfee
▀▀▀
Directed by Kaela Albert
Written by Kaela Albert and Emily Zhang
Edited by Jack Saxon and Luke Molloy
Assistant Edited by James Stuart
Animated by Fabio Albertelli, Andrew Neet, Alex Zepharin, Mike Radjabov, Emma Wright and Ivy Tello
Illustrations by Jakub Misiek, Maria Gusakovich, Cainejan Esperanza, Tommy A. Steven and Emma Wright
Additional research by Emilia Gyles, Gabe Bean, Geeta Thakur and Vincent Cheng
Produced by Kaela Albert, Casper Mebius, Derek Muller, Emily Zhang, Zoe Heron, Rob Beasley Spence, and Tori Brittain
Additional Editing by Luke Molloy and James Stuart
Thumbnail contributions by Ben Powell, Peter Sheppard and Ren Hurley
Additional video/photos supplied by Getty Images and Storyblocks
Music from Epidemic Sound Receive SMS online on sms24.me
TubeReader video aggregator is a website that collects and organizes online videos from the YouTube source. Video aggregation is done for different purposes, and TubeReader take different approaches to achieve their purpose.
Our try to collect videos of high quality or interest for visitors to view; the collection may be made by editors or may be based on community votes.
Another method is to base the collection on those videos most viewed, either at the aggregator site or at various popular video hosting sites.
TubeReader site exists to allow users to collect their own sets of videos, for personal use as well as for browsing and viewing by others; TubeReader can develop online communities around video sharing.
Our site allow users to create a personalized video playlist, for personal use as well as for browsing and viewing by others.
@YouTubeReaderBot allows you to subscribe to Youtube channels.
By using @YouTubeReaderBot Bot you agree with YouTube Terms of Service.
Use the @YouTubeReaderBot telegram bot to be the first to be notified when new videos are released on your favorite channels.
Look for new videos or channels and share them with your friends.
You can start using our bot from this video, subscribe now to The Man Who Almost Broke Math (And Himself...)
What is YouTube?
YouTube is a free video sharing website that makes it easy to watch online videos. You can even create and upload your own videos to share with others. Originally created in 2005, YouTube is now one of the most popular sites on the Web, with visitors watching around 6 billion hours of video every month.
