The Most Controversial Idea In Math

From the creator

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 Sign up to the Veritasium newsletter for weekly science updates - https://ve42.co/Newsletter ▀▀▀ 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. Head over and sign up to our Patreon for some exclusive behind the scenes footage, showing how the animations and illustrations for this video were made - https://www.patreon.com/posts/patreon-behind-126443880?utm_medium=clipboard_copy&utm_source=copyLink&utm_campaign=postshare_creator&utm_content=join_link ▀▀▀ 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

Published 2025-04-02 · Watch on YouTube ↗
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