Rigorous academic arguments on whether AIs can replace all human workers?

I believe that it will one day be possible for AIs to do all work currently done by humans. Probably most people at LessWrong believe this too, and thanks to science fiction I wouldn’t be surprised if most people in the United States and Europe believed it too.

But it’s interesting to think about why we should believe this, and when I ask myself that question, I can come up with arguments, but I have a hard time thinking of examples of the arguments being made in a rigorous way in the academic literature. This is surprising because it’s a question with real practical import for humanity’s future.

The only prominent example I can think of is an argument against based on Godel’s theorem and similar math, what Turing called “The Mathematical Objection” and which has more recently been championed by Roger Penrose. But can anyone think of others?