Norman Wildberger: The Problem with Infinity in Math

LINKS MENTIONED:

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

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[njwildberger]

A big thanks to Curt for a fun interview, steering us toward lots of interesting and important topics. And thanks also to the audience members that contributed nice questions too.

[JustRonDon]

Curt, you are as earnest and sincere as it gets. How you remain so kind while still being fiercely passionate is very inspiring.

[wenzel]

This Professor seems like the nicest person and as a non-math-guy I found this conversation highly interesting.

[engimalover]

Professor Wilderberger's series of lectures on the history of mathematics is really great: check it out. I was delighted to see him being interviewed on this channel. Looking forward to the second interview.

[CandidDate]

I am infinitely grateful to all the knowledge I have gained in math by watching Norman's videos with his drumstick pointer and crisp and clean wall blackboards. He almost makes it too easy. I did buy his book as a means of supporting his efforts and I admire his cavalier attitude toward making only rational decisions in this one life we have.

[pauladamson]

Great interview. I've been a fan of Professor Wildberger for years now. You're both awesome.

[Penrose]

So happy to see you in the wild Norm, wishing you the best and want to say that I absolutely love your channel. I have learned so much from your teachings. Thank you Curt for inviting our guest today.

[OriginalApexTwin]

Always really interesting watching your videos Curt, but for some reason, this was very easy to follow and understand. Maybe it’s because you edited or possibly because you guys know how to communicate effectively. Either way, love you man!

[ryam]

Prof. Wildberger is a huge discovery for me. Thank you very much for this interview!

[DingDong-fqmo]

Thanks for this. Great questions. I look forward to part two.

[Burgher]

Just finished this episode on apple podcast. Was very interesting. Thanks curt!

[SpyWhoLovedHimself]

I have literally no idea what they're talking about, but I'm listening anyway.

[rezasahand]

Curt, man ! In 1:00:18 you asked the same question I was thinking about ! Is complex analysis affected by this? And honestly extracted the nugget of this podcast out, in a very humble and valuable way and thank you for that!

[lachenmann]

This was great! I've been a follower of Prof. Wildberger's channel for about 7 years, and I'm glad I got to know your project thanks to him. I would love to suggest mathematician Gregory Chaitin as a next guest. His work is amazing and too little known, and touches many of Wildberger's points and many others (including his work on Leibniz), critically Chaitin's Omega Number, or Chaitin's constant. Kudos Curt!

[Nonconceptuality]

Very much looking forward to this one.

[godynnel]

Great conversation!! I've often struggled with the concept of "infinity" and this was a great exploration of that topic 👏

[captainkosmo]

Curt you continue to be one of, if not THE, best casters on the net today, thanks for sticking with it! In Part 2 I'd love to hear the Professor's take on Eric Weinstein's statement that the hopf fibration is the most important construct in the universe. Secondly, that we can derive basically the entirety of physics from it and with changing only a few parameters can construct alternative physics (if I understand his contention correctly). As I'm sure you know, Eric mirrors the Professor's intuition that physicists can benefit from mathematicians understandings as they are fluent in the language that physicists use to express their domain.

[stephendevine]

I am in awe. I confess that this is the first time I have heard of Prof. Wildberger but was blown away by his clear ability to explain to a non mathemetician such as I.

I will be looking up his channel for sure. Prof. Wildberger showed such a deep appreciation for being included in the stellar 2022 Theories of Everything lineup.

Thank you Curt for giving me the opportunity to be exposed to such accomplished thinkers. This was a great episode, already watched it twice. 👍👍👍🏴󠁧󠁢󠁳󠁣󠁴󠁿

[deborahcoyle]

This was brilliant! Thank you to both of you.

[pmcate]

If not addressed in part one, I would like to hear what his thoughts are on finitary statements that require the notion of infinite sets to prove, such as the Paris-Harrington theorem.