The Most Ridiculous (& True) Theorem in Mathematics: The Banach-Tarski Paradox
Автор: Oscar Seurat
Загружено: 2025-06-27
Просмотров: 218
On the centenary of its discovery, I am presenting here an accessible description of a simple to state, yet mind boggling theorem called the Banach-Tarski Paradox. Since it is almost impossible to present a popularized account of this deep and counterintuitive result, I had to make a few shortcuts to make it fathomable (e.g., no Axiom of Choice, no countable unions). However, the explanation should give you a pretty good, 10,000-foot perspective on why such a result is possible.
Here are the links where you can verify that this incredible Paradox is a serious theorem and not a gimmick.
https://en.wikipedia.org/wiki/Banach%...
https://mathworld.wolfram.com/Banach-...
Chapters:
0:00 In Plain English
3:19 The Official Statement
4:36 "Refutation"
9:02 What is Volume? From Cubes to Measurable Sets
20:46 Cantor's Dust
24:56 Properties & Shortcomings of Any Self-Respecting Volume
32:13 The Answer!
34:07 About Banach & Tarski
More about the author of this post:
https://oscarseurat.com
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