> If the Church-Turing thesis is true, then the brain is a Turing machine / Turing equivalent
This is simply technically not true. You can look up the https://en.wikipedia.org/wiki/Church%E2%80%93Turing_thesis and it does not talk about brains, or intelligence.
There's some generalised versions of the thesis that do.
See https://en.wikipedia.org/wiki/Church%E2%80%93Turing_thesis#V... and https://en.wikipedia.org/wiki/Church%E2%80%93Turing_thesis#P...
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.