[horseAMcharlie]

I'm not really familiar with math beyond linear algebra and googling was not very helpful; could you please give an example of an obviously incorrect result enabled by the axiom of choice? No need for detail, just the name of an example is good enough for me.

[bawolff]

As far as axiom of choice goes, they were probably referring to https://en.wikipedia.org/wiki/Banach%E2%80%93Tarski_paradox

Whether or not it is "wrong" is in the eye of the beholder. Why should infinite things be intuitive? After all even "real" things in the universe are highly unintuitive - e.g. quantum mechanics sounds obviously "wrong" at first glance.