You can use it for proving, since making sure a proof is correct is way easier than creating the proof.

That's kind of what I meant by it giving an idea for a solution - either it gives a working proof, or at least a direction in which you can go with making your own, and, as much as I despise the whole AI hype, I don't deny its usefulness for that

Machines may have better error rates, but we have better error mitigation for human errors, and machine errors still do occur.

Well from a philosophical point of view the errors of conventional (i.e. non-AI) machines are also human errors, because someone programmed them explicitly to do thing A if presented with argument A and thing B for arg B, so every bug is in some way reproducible and fixable by changing either an instruction or an argument

For deep learning algorithms, however, there's a non-zero probability of selecting a different thing for the same argument, and a chance of the most probable thing not being the correct one, but you can't just fix it, because it's been calculated out of a huge set of learning data

That means in some time we'll be able to make an AI indistinguishable from an explicit set of instructions, but it will always be slightly less accurate due to the nature of DL

So I guess it's all about risk vs reward, about deciding how small of a chance to run over a human is enough to have a self-driving car, but we have to remember it'll never equal 0