I tried to search for surveys of mathematicians on the axiom of choice, but couldn’t find any. I did find one survey of philosophers, but that’s a very different population, asked whether they believed AC/The Continuum Hypothesis has an answer rather than what the answer is: https://thephilosophyforum.com/discussion/13670/the-2020-philpapers-survey
My subjective impression is that my Mathematician friends would mostly say that asking whether AC is true or not is not really an interesting question, while asking what statements depend on it is.
I tried to search for surveys of mathematicians on the axiom of choice, but couldn’t find any. I did find one survey of philosophers, but that’s a very different population, asked whether they believed AC/The Continuum Hypothesis has an answer rather than what the answer is: https://thephilosophyforum.com/discussion/13670/the-2020-philpapers-survey
My subjective impression is that my Mathematician friends would mostly say that asking whether AC is true or not is not really an interesting question, while asking what statements depend on it is.
Yes sorry to be clear I’m not talking about whether it is true, I am talking about whether they would use it or not in proving ‘standard’ results.