> Assuming the Church-Turing thesis is true, the existence of any brain now or in the past capable of proving it is proof that such a program may exist.
Doesn't that assume that the brain is a Turing machine or equivalent to one? My understanding is that the exact nature of the brain and how it relates to the mind is still an open question.
That is exactly the point.
If the Church-Turing thesis is true, then the brain is a Turing machine / Turing equivalent.
And so, assuming Church-Turing is true, then the existence of the brain is proof of the possibility of AGI, because any Turing machine can simulate any other Turing machine (possibly too slowly to be practical, but it denies its impossibility).
And so, any proof that AGI is "mathematically impossible" as the title claims, is inherently going to contain within it a proof that the Church-Turing thesis is false.
In which case there should be at least one example of a function a human brain can compute that a Turing machine can't.