* Super-powered thesaurus
A traditional thesaurus can only take a word and provide alternative words; with an LLM, you can take a whole phrase or sentence and say: "give me more ways to express the same idea".
I have done this occasionally when writing, and the results were great. No, I do not blindly cut-and-paste LLM output, and would never do so. But when I am struggling to phrase something just right, often the LLM will come up with a sentence which is close, and which I can tweak to get it exactly the way I want.
* Explaining a step in a mathematical proof.
When reading mathematical research papers or textbooks, I often find myself stuck at some point in a proof, not able to see how one step follows from the previous ones. Asking an LLM to explain can be a great way to get unstuck.
When doing so, you absolutely cannot take whatever the LLM says as 'gospel'. They can and will get confused and say illogical things. But if you call the LLM out on its nonsense, it can often correct itself and come up with a better explanation. Even if it doesn't get all the way to the right answer, as long as it gets close enough to give me the flash of inspiration I needed, that's enough for me.
* Super-powered programming language reference manual
I have written computer software in more than 20 programming languages, and can't remember all the standard library functions in each language, what the order of parameters are, and so on.
There are definitely times when going to a manpage or reference manual is better. But there are also times when asking an LLM is better.