I just presume that a biological brain is a network of neurons with connections between them, including feedback connections, at least this is what we see under the microscope. In terms of math, this structure corresponds to a cyclic directed computational graph - this only fact makes it Turing-complete.
Currently it is just a highly plausible conjecture, not a formal proof. However, I think I can prove it. But should I?
We don't know how the brain works. Neuron activity is one aspect, and clearly an important one, but it's not everything.
And even if the connectome can be modeled as a graph, the dynamics on the graph could be totally alien to us. It might be computable by a Turing machine. But it also might involve some not computable process we can't imagine. Perhaps it involves fundamentally unknown physics. (I consider the last option to be quite likely. I think rather few actually entertain the idea that physics as we understand it today could give rise to consciousness. But here we are.)
Currently it is just a highly plausible conjecture, not a formal proof. However, I think I can prove it. But should I?