I think yes/no to mathematical questions wouldn’t be safer than yes/no to other questions: you still have a real-world reason for asking them, and the AI can lie about as well as it can on any yes/no question.
Asking for formalized proofs might be more promising, if you are able to produce a proof-checker that you have high confidence can’t be hacked (this seems difficult but possible; proof checkers can be very simple programs but you need to guard both against ordinary attacks against the entire stack you’re running on and against creative attacks like waiting for a cosmic ray making a transistor malfunction). You’d also want to not have a human look at the proof, of course, since that would give the AI a much broader communication channel.
I think yes/no to mathematical questions wouldn’t be safer than yes/no to other questions: you still have a real-world reason for asking them, and the AI can lie about as well as it can on any yes/no question.
Asking for formalized proofs might be more promising, if you are able to produce a proof-checker that you have high confidence can’t be hacked (this seems difficult but possible; proof checkers can be very simple programs but you need to guard both against ordinary attacks against the entire stack you’re running on and against creative attacks like waiting for a cosmic ray making a transistor malfunction). You’d also want to not have a human look at the proof, of course, since that would give the AI a much broader communication channel.