Why is AC so controversial? it's intuitively obvious that

The real bad thing about the AC is that it leads to non-constructive proofs.

>>9116810
But there are nonconstructive proofs that don't rely on AC. And what's wrong with nonconstructive proofs in first place?

The Axiom of Choice is obviously true, the well-ordering principle obviously false, and who can tell about Zorn's lemma?
—Jerry Bona

because it doesnt have a clear physical analogue

it's like saying "im magical aware of every single atom in the observable universe and im going to pick one in the middle of a star a couple galaxies away and then just hold it in my hand, nevermind how i get it back from there or find it or how i knew it existed"

>>9116851
wildberger pls go

>>9116836
Why do brainlets say that the well-ordering principle is not intuitive?

>>9116824
>But there are nonconstructive proofs that don't rely on AC.
True, and complaining about the AC for something other than it is stupid.

>And what's wrong with nonconstructive proofs in first place?
They're useless in practice because you can't use them to explicitly build what you claim exists (except in some particular cases where you know a lot about your objects). I don't mind theorems that don't have any constructive proof, but like any sane individual, I'd rather trust a constructive proof than a non-constructive one for non-trivial shit.