> any kind of theorem or idea communicated to another mathematician needs to be serialized into language which would make it computable.

This is a fallacy. Just because you need to serialize a concept to communicate it doesnt mean the concept itself is computable. This is established and well proven:

https://en.wikipedia.org/wiki/List_of_undecidable_problems

The fact that we can come up with this kind of uncumputable problems is a big plus in supprt of Penrose's Idea that consciousnes is not computable and goes way beyond compatability.