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The following is a quote from Surely you're joking, Mr. Feynman . The question is: are there any interesting theorems that you think would be a good example to tell Richard Feynman, as an answer to his challenge? Theorems should be totally counter-intuitive, and be easily translatable to everyday language. (Apparently Banach-Tarski paradox was not a good example.)

Then I got an idea. I challenged them: "I bet there isn't a single theorem that you can tell me - what the assumptions are and what the theorem is in terms I can understand - where I can't tell you right away whether it's true or false."

It often went like this: They would explain to me, "You've got an orange, OK? Now you cut the orange into a finite number of pieces, put it back together, and it's as big as the sun. True or false?"

"No holes."

"Impossible!

"Ha! Everybody gather around! It's So-and-so's theorem of immeasurable measure!"

Just when they think they've got me, I remind them, "But you said an orange! You can't cut the orange peel any thinner than the atoms."

"But we have the condition of continuity: We can keep on cutting!"

"No, you said an orange, so I assumed that you meant a real orange."

So I always won. If I guessed it right, great. If I guessed it wrong, there was always something I could find in their simplification that they left out.

  • 7
    Your example is more about real-world limitations (physics) than "everyday language".2010-11-09
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    Based on what's been offered 'till now I think I'll start calling this "Feynman's conjecture".2013-12-18
  • 0
    Odd spheres differ from even spheres.2015-03-31
  • 0
    The Tychonoff Theorem :Is a product of compact spaces compact? The H-W-P theorem: If $X_r$ is a separable space for each $r\in R$, is $\prod_{r\in R}X_r$ separable? If ZFC is consistent then neither CH nor its negation is a theorem of ZFC.The sum of the reciprocals of the primes is finite.(This is false,If Feynman didn't know it,would he have guessed correctly?) $\sum_{n=1}^{\infty}1/n^2=\pi e/5$ (Another ringer.It's actually $\pi^2/6.$)2015-10-24
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    If 30 people are randomly chosen,the probability that at least 2 of them have the same birthday is more than 1/2.2015-10-24

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