Qiaochu_Yuan comments on AI box: AI has one shot at avoiding destruction - what might it say? - Less Wrong Discussion
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Presumably the reason we created the AI in the first place is so it could solve problems for us, so someone needs to ask it questions. It might be safe-ish to restrict it to answering yes or no to purely mathematical questions.
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.