The other end of the Church-Turing intuition is that if we couldn't possibly do it then the machines can't do it either. What they're doing is the same, it's not only not magically less powerful it's also not not magically more powerful.
You seem to be imagining that Gödel is just a small problem you can carve off and ignore, but it applies for everything powerful enough to do arithmetic.
Of course we can have the AI muddle along with intuition, but that's not actually an improvement, our mathematicians can already use intuition and they've got a lot more experience.
You seem to be imagining that Gödel is just a small problem you can carve off and ignore, but it applies for everything powerful enough to do arithmetic.
Of course we can have the AI muddle along with intuition, but that's not actually an improvement, our mathematicians can already use intuition and they've got a lot more experience.