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

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186 Questions Answered

TEDEd Animation

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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.

Bertrand Russell is credited for the famous quote, “The Axiom of Choice is necessary to select a set from an infinite number of socks, but not an infinite number of shoes.” Can you explain why this is true?

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About TED-Ed Animations

TED-Ed Animations feature the words and ideas of educators brought to life by professional animators. Are you an educator or animator interested in creating a TED-Ed Animation? Nominate yourself here »

Meet The Creators

  • Educator Jacqueline Doan, Alex Kazachek
  • Director Mads Lundgård, The Animation Workshop
  • Narrator Addison Anderson
  • Composer Salil Bhayani, cAMP Studio
  • Sound Designer Amanda P.H. Bennett, cAMP Studio
  • Director of Production Gerta Xhelo
  • Produced by Abdallah Ewis
  • Editorial Director Alex Rosenthal

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