Any mindblowing math theorem to suggest?

I am a math-fag, I admit it.
I love to find these relatively small paradoxal theorems that are so obvious, but at the same time so hard to believe in.
Think for instance (in theory of computation) at the Göedel incompleteness theorems that from the assumption that Peano's Arithmetic (PA) is consistent prove that PA's consistance is not provable in itself and that there are Natural numbers properties that are basically not provable due to the limits of our logic systems (and our minds).
Or better the Banach-Tarski theorem that states that given a sphere splitting it in 5 parts and applying rototranslation to them you can get two identical spheres with the only assumption that Zermelo's axiom of choice is true (and I believe that's true, but I do not want to start a debate about this).
Or the Tarski incompleteness theorem itself.

Things like these.


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  • umm there are better forums for math geeks than GaG. lol

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