Norman Wildberger: Why Infinity Is a Mathematical Mistake

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Previously titled “Norman Wildberger on the Problem with Infinity, The Foundations of Mathematics, Finitism, and the Real Numbers” — renamed by the publisher on Aug 3, 2026

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Recorded09 Feb 2022

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Professor of mathematics Norman Wildberger expounds on the nature of the infinite and the real numbers. YouTube link: https://youtu.be/l7LvgvunVCM Sponsors: https://brilliant.org/TOE for 20% off. For Algo's podcast https://www.youtube.com/channel/UC9IfRw1QaTglRoX0sN11AQQ and website https://www.algo.com/. Patreon: https://patreon.com/curtjaimungal Crypto: https://tinyurl.com/cryptoTOE PayPal: https://tinyurl.com/paypalTOE Twitter: https://twitter.com/TOEwithCurt Discord Invite: https://discord.com/invite/kBcnfNVwqs iTunes: https://podcasts.apple.com/ca/podcast/better-left-unsaid-with-curt-jaimungal/id1521758802 Pandora: https://pdora.co/33b9lfP Spotify: https://open.spotify.com/show/4gL14b92xAErofYQA7bU4e Subreddit r/TheoriesOfEverything: https://reddit.com/r/theoriesofeverything Merch: https://tinyurl.com/TOEmerch LINKS MENTIONED: -Prof. Norman Wildberger's YouTube channel: https://www.youtube.com/njwildberger -Rational Trigonometry (YouTube series): https://www.youtube.com/playlist?list=PL3C58498718451C47 -Rational Trigonometry (book): https://amzn.to/3rEygVW TIMESTAMPS: 00:00:00 Introduction 00:03:29 Behind the scenes banter 00:08:08 Overview of Norman's philosophy of mathematics 00:09:35 The problem with the concept of "infinity" in mathematics 00:14:46 Algorithmic reality and Wolfram's model 00:16:03 Physics and infinity (Riemann sphere and Spinors) 00:19:14 Infinity cannot be "done" 00:42:26 Physics doesn't actually use infinities 00:45:03 What about the wave function of half spin up / spin down? 00:47:25 Learning Tip for Math / Physics: Constantly ask "what is REALLY going on here?" 00:48:32 What is Rational Trigonometry and what led to it? 00:53:23 What compels Norman to rethink the foundations? 01:01:49 Is beauty (like in complex analysis) removed or added in the construcitivist approach 01:04:52 The simplicity of Norman's courses (links in the description) 01:08:31 On non-standard analysis 01:10:42 Why set theory has problems (even without the Axiom of Choice) 01:13:57 Roger Penrose's and Ed Witten's view on real numbers 01:16:09 Pure mathematicians vs physicists 01:17:17 [062985593] How would Wildberger rephrase the intermediate value theorem? 01:19:31 If math is currently vitally flawed, then why no inconsistencies 01:21:21 How do constructionists base their foundations in physics, when physics is couched in mathematics? 01:27:21 [Sam Thompson] Do you see problems with having infinite index sets? 01:32:13 [DivergentCauchy] Cranks and Platonism 01:34:30 Dealing with calumny as a creator 01:36:33 Norman is extremely interested in UFOs as well * * * Just wrapped (April 2021) a documentary called Better Left Unsaid http://betterleftunsaidfilm.com on the topic of "when does the left go too far?" Visit that site if you'd like to watch it. Learn more about your ad choices. Visit megaphone.fm/adchoices

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