[The puzzle](https://cornellmath.wordpress.com/2007/09/13/the-axiom-of-choice-is-wrong) that has prisoners wearing black and white hats having to guess their own hat color without communication seems to have such a crazy result that it should indicate the axiom of choice to be false?
So why is the axiom of choice an axiom if it’s so controversial and leads to paradoxical?
In: Mathematics
An axiom doesn’t have to be universally accepted to be an axiom. An axiom is just a statement that is assumed to be true in order to make further arguments. You can reject an axiom, but that also means rejecting all the proofs that rely on it and you may have to come up with new proofs or systems.
That said, the consensus view among mathematicians is definitely that the axiom of choice is true, and a lot of other math relies on it.
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