Hallucinations are an intrinsic part of how LLMs work. OpenAI, literally the people with the most to lose if LLMs aren't useful, has admitted that hallucinations are a mathematical inevitability, not something that can be engineered around. On top of that, its been shown that for things like mathematical proof finding switching to more sophisticated models doesn't make them more accurate, it just makes their arguments more convincing.

Now, you might say "oh but you can have a human in the loop to check the AIs work", but for programming tasks its already been found that using LLMs makes programmers less productive. If a human needs to go over everything an AI generates, and reason about it anyway, that's not really saving time or effort. Now consider that as you make the LLM more complex, having it generate longer and more complicated blocks of text, its errors also become harder to detect. Is that not just shuffling around the necessary human brainpower for a task instead of reducing it?

So, in what field is this sort of thing useful? At one point I was hopeful that LLMs could be used in text summarization, but if I have to read the original text anyway to make sure that I haven't been fed some highly convincing falsehood then what is the point?

Currently I'm of the opinion that we might be able to use specialized LLMs as a heuristic to narrow the search tree for things like SAT solvers and answer set generators, but I don't have much optimism for other use cases.