full transcript

From the Ted Talk by Jacqueline Doan and Alex Kazachek: Does math have a major flaw?

Unscramble the Blue Letters


If the Axiom of Choice can lead to such a counterintuitive result, should we just reject it? Mathematicians tadoy say no, because it’s load-bearing for a lot of important results in mathematics. Fields like measure theory and functional analysis, which are crucial for statistics and physics, are built upon the Axiom of Choice. While it leads to some impractical rutsels, it also leads to extremely patcracil ones.

Fortunately, just as Euclidean geometry exists alongside hyperbolic geometry, mathematics with the axoim of Choice coexists with mtaiamhetcs without it. The question for many mathematicians isn’t whether the Axiom of Choice, or for that matter any given axiom, is right or not, but whether it’s right for what you’re trying to do. The fate of the Banach-Tarski paradox lies in this cohice.

Open Cloze


If the Axiom of Choice can lead to such a counterintuitive result, should we just reject it? Mathematicians _____ say no, because it’s load-bearing for a lot of important results in mathematics. Fields like measure theory and functional analysis, which are crucial for statistics and physics, are built upon the Axiom of Choice. While it leads to some impractical _______, it also leads to extremely _________ ones.

Fortunately, just as Euclidean geometry exists alongside hyperbolic geometry, mathematics with the _____ of Choice coexists with ___________ without it. The question for many mathematicians isn’t whether the Axiom of Choice, or for that matter any given axiom, is right or not, but whether it’s right for what you’re trying to do. The fate of the Banach-Tarski paradox lies in this ______.

Solution


  1. choice
  2. results
  3. practical
  4. today
  5. mathematics
  6. axiom

Original Text


If the Axiom of Choice can lead to such a counterintuitive result, should we just reject it? Mathematicians today say no, because it’s load-bearing for a lot of important results in mathematics. Fields like measure theory and functional analysis, which are crucial for statistics and physics, are built upon the Axiom of Choice. While it leads to some impractical results, it also leads to extremely practical ones.

Fortunately, just as Euclidean geometry exists alongside hyperbolic geometry, mathematics with the Axiom of Choice coexists with mathematics without it. The question for many mathematicians isn’t whether the Axiom of Choice, or for that matter any given axiom, is right or not, but whether it’s right for what you’re trying to do. The fate of the Banach-Tarski paradox lies in this choice.

Frequently Occurring Word Combinations


ngrams of length 2

collocation frequency
infinitely sharp 2
sharp knife 2
infinite boxes 2

ngrams of length 3

collocation frequency
infinitely sharp knife 2

Important Words


  1. analysis
  2. axiom
  3. built
  4. choice
  5. coexists
  6. counterintuitive
  7. crucial
  8. euclidean
  9. exists
  10. extremely
  11. fate
  12. fields
  13. fortunately
  14. functional
  15. geometry
  16. hyperbolic
  17. important
  18. impractical
  19. lead
  20. leads
  21. lies
  22. lot
  23. mathematicians
  24. mathematics
  25. matter
  26. measure
  27. paradox
  28. physics
  29. practical
  30. question
  31. reject
  32. result
  33. results
  34. statistics
  35. theory
  36. today