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I don’t think ‘I don’t believe in the axiom of choice’ is an opinion, it’s kind of a weird statement to make because the axiom exists. You can have an opinion on whether mathematicians should use it given the fact that it’s an unprovable statement, but that’s true for all axioms.
Any math that needs the axiom of choice has no real life application so I do think it’s kind of silly that so much research is done on math that uses it. At that point mathematics basically becomes art but it’s art that’s only understood by some mathematicians so its value is debatable in my opinion. <- I suppose that opinion is controversial among mathematicians.