We can record a lot of parrot speech and train LLMs against it and eventually build a translator.

They are making good progress on similar research programmes for many cetaceans.

In the case of our stochastic parrots it's even easier, since they already speak something like human language. And for the math proofs it's even easier, because once they are formalised into something like Lean the humans only need to understand the statement of the theorem, and a mechanical computer program can check the proof.