Computers do not do mathematics. Rather, they compute a set of rules we give them, which may or may not be consistent. It is up to the programmer to give them rules that are consistent and correspond to some abstract mathematical concept. However, the computational rules themselves are not mathematics.
I am not sure what does the thinking, but whatever it is, it cannot be the brain if thinking consists of uncomputable and non physical faculties.
That's a rather strange and nebulous "definition" of mathematics, and quite contrary to how it actually works; the rules define the abstract concepts that build mathematics, and the rules are followed by people too whenever they do maths, because they are the maths. For example, "numbers" are an abstract mathematical concept, totally unphysical, defined purely by rules, and used by people and computers. Actual mathematics can certainly be done with computers, and is, every day, by mathematicians (among others).
There's nothing demonstrably uncomputable or unphysical about thinking. On the contrary, the brain is an enormously complex network of neurons and synapses, clearly intricate enough to physically perform all known mind functions, and all in principle simulatable on a powerful enough computer system. Your magical antenna idea has no basis in reality, it is massively outweighed by real-world evidence, and you have failed to present any actual evidence to support it.
I cited a number of first hand pieces of evidence that are more directly evident to everyone than the speculation you provide, and you accuse me of not providing any evidence. I guess there is nothing further to be said.
I am not sure what does the thinking, but whatever it is, it cannot be the brain if thinking consists of uncomputable and non physical faculties.