Here is an example of a task that I do not believe this generation of LLMs can ever do but that is possible for a human: design a Turing complete programming language that is both human and machine readable and implement a self hosted compiler in this language that self compiles on existing hardware faster than any known language implementation that also self compiles. Additionally, for any syntactically or semantically invalid program, the compiler must provide an error message that points exactly to the source location of the first error that occurs in the program.
I will get excited for/scared of LLMs when they can tackle this kind of problem. But I don't believe they can because of the fundamental nature of their design, which is both backward looking (thus not better than the human state of the art) and lacks human intuition and self awareness. Or perhaps rather I believe that the prompt that would be required to get an LLM to produce such a program is a problem of at least equivalent complexity to implementing the program without an LLM.