This is more of a comment and philosophical opinion, but I don’t believe that there are any problems an AI couldn’t solve, that a human can. Being new to this forum, I cannot make it a comment on the question (and it would probably be too long) — I preemptively ask for your forgiveness.
AI Eventually Will Mimic Humans (and surpass them)
Humans by nature are logical. Logic is learned or hardwired, and influenced by observation and chemical impulses.
As long as an AI can be trained to act like a human, it will be able to act like one. Currently, those behaviors are limited to technology (space, connections, etc), which the human brain has been optimized to rule out or disregard certain “fluff” automatically enabling it certain super capabilities. For instance, not everything seen is registered through the brain; often, the brain performs differential comparisons and updates for changes to reduce processing time and energy. It will only be a matter of time before AI can also be programmed to behave this way, or technological advancements will allow it to not need some of this function, which will allow it to leapfrog humans.
In the current state, we recognize humans are sometimes irrational or inconsistent. In those cases, AI could mimic human limitations with configured randomization patterns, but again, there really won’t be a need since it can be programmed and learn those patterns automatically (if necessary).
It all comes down to consumption of data, retention of information, and learned corrections. So, there is no problem that a human can perform (to my knowledge) that AI couldn’t theoretically ever perform. Even in the case of chemistry. As we are manufacturing foods and organs, an AI could also, theoretically, one day reproduce and survive via biological functions.
Instead of the question being binary about human capability vs that of artificial intelligence, I’d be more interested to see what people think are the more challenging things humans can do, which will take AI time to accomplish.