> then you must accept that the question is settled in favor of Penrose. That's obviously beyond the realm of mathematics.

Not necessarily. You are assuming (AFAICT) that we 1. have perfect knowledge of physics and 2. have perfect knowledge of how humans map to physics. I don't believe either of those is true though. Particularly 1 appears to be very obviously false, otherwise what are all those theoretical physicists even doing?

I think what the paper is showing is better characterized as a mathematical proof about a particular algorithm (or perhaps class of algorithms). It's similar to proving that the halting problem is unsolvable under some (at least seemingly) reasonable set of assumptions but then you turn around and someone has a heuristic that works quite well most of the time.