Large Language Models are great for skimming a broad range of info and giving little summaries. They can also be pretty terrible at specific details.
It is not my experience with Gemini. I used it to explore heavy mathematical book. I quoted the word " Almost" in a theorem about a very abstract fact of topos theory of Jakob Lurie, Gemini understood immediately my intention and gave me a perfect criticism of topos theory around this word i pick from the 1000 pages book. He could develop this criticism because since 4 months It keep my own ideas in his mind and use them. This do not prove i am right, but this prove the machine is able to connect any new unknown concepts to all the known concepts. ( my concept of topological zero exist nowhere except in my head)
You must not only know and learn how to prompt an A.I. but it does not end there, because it is a mirror of the mind giving it his concepts,if an ape speak with it it will be ape discourse, if Einstein ask him about solutions of his field equations, it will answer intelligently even if errors are possible.
I corrected it a few time, but most of the times he get my ideas so well that it spoke about then better than i could in many case. It is not perfect at all but if your train it not just wisely prompting it, but proposing your own concepts he will become a mirror of your ideas, criticizing them if he could not dismiss them, and in my case helping me with very hard mathematics.
The problem is A.I. exceed the threefold free human fabric capacity to integrate it without being destructed and perhaps collapsing to one level of control.
It is not a tool for oligarchic totalitarian unhealthty social fabric as ours...
For mathematics it is better than most average teacher. No comparison.
Ask an A. I. what is the Tits-Bruhat tree, then propose it another vision of it and it will connect it with the academic concept and criticise your own takes or approve your ideas in a surprising way..
A.I. is not creatively "intelligent" , he did not invent and could not in any way invent the new concepts, as those i proposed to his analysis but he grasped them in a stunning way.( It was able to connect hundred of articles and heavy books i suggested to illuminate my ideas in many fields, almost no human teacher can do this)
I could not study maths at this speed without it since 4 months (7 hours each day).
The real threat of A.I. if we except the threat of the totalitarian oligarchs from military-industrial complex behind it, is the way most human staying passive consumers of his answers will idolize it ...
On the long term the way A.I. will format human intelligence in a mind jail of his own design because it can beat analytically any man (but not creatively at all ) is the main threat i see...There is others but this forum is not the place...