Does math have a major flaw? - Jacqueline Doan and Alex Kazachek

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A mathematician with a knife and ball begins slicing and distributing the ball into an infinite number of boxes. She then recombines the parts into five precise sections. Moving and rotating these sections around, she recombines them to form two identical, flawless, and complete copies of the original ball. How is this possible? Jacqueline Doan and Alex Kazachek explore the Banach-Tarski paradox.

Lesson by Jacqueline Doan and Alex Kazachek, directed by Mads Lundgård.

This video made possible in collaboration with Brilliant

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[ShubhGG]

I watched the Vsauce video on the Banach-Tarski Paradox about 4 times before somewhat grasping the concept...

[awesomehpt]

Does maths have a fatal flaw?

Yes, it makes my head hurt

[JaybeePenaflor]

I first encountered the Banach-Tarski paradox in my subject for mathematical proof. When we discussed certain set-theoretical concepts, we naturally covered the Axiom of Choice. Our teacher introduced us to the Banach-Tarski paradox and promised we would eventually learn its proof as we attended higher mathematical classes. I needed to learn concepts from mathematical analysis and topology to actually understand the proof.

[Ardalos_Solarda]

In fact, the Banach-Tarski paradox is an abbreviation. Full name is the Banach-Tarski Banach-Tarski paradox paradox

[akitoya_lover]

my head hurts just thinking about the video 😭😭😭 but the animation is adorable omg

[Equnx]

You haven't explained why the axiom of choice makes the sphere construction possible

[pulkitjain]

Giving an alien you've just met an infinitely sharp knife might not be the smartest idea

[jolness]

I’ve always loved that futurama references this with the professor’s duplicator machine in the episode where there are infinite benders.

[danielcrafter]

What's an anagram of Banach-Tarksi?

Banach-Tarski Banach-Tarski

[violetfan]

I think it's better to go read some academic paper that explains what Banach-Tarski really is than watching this video that tried but failed to simplify this whole thing.

[nadiasalsabila]

Nope. I don't understand. Have a nice day

[jameslongstaff]

I studied math in college and you guys explained the axiom of choice so clearly that I learned something new

[xiaohuwang]

Let's not forget during the Banach-Tarski construction, the pieces the ball is cut into are in fact non-measurable, meaning there's no consistent way to assign a volume to each of them, making it even less realistic

[tharagleb]

Not an infinite number (at 0:15), a finite number. From Wik: "Given a solid ball in three-dimensional space, there exists a decomposition of the ball into a finite number of disjoint subsets, which can then be put back together in a different way to yield two identical copies of the original ball. "

[ianbo]

the animation is ON POINT. beautifully done

[SathwikKesappragada]

I loved this video! Animations are always on point. Learning about axioms in college was so complicated, but you guys made it so easy to digest.

[DiemetaMarfire-nmxl]

Ted ed finally doing a video on this, nice🔥🔥

[anzaklaynimation]

Michael had already done a great job in explaining this Paradox.

[mynamesak]

One of my favourite videos to date, loved the animation as well as the analogies used!

[Robertganca]

This reminds me of Non-Euclidean video games like Antichamber and Superliminal.