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John_Baez comments on The Least Convenient Possible World - Less Wrong
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Assuming the entity in question is cooperative, try this:
Ask it if P=NP is true, and for a proof for its answer to that in a form that you can easily understand. There's three possible outcomes:
If you get something that appears like an elegant proof, memorize it and recheck it every now and then. If your mind is sufficiently malfunctioning that it can't distinguish an elegant proof for P=NP from something that isn't, you may not be able to notice that from inside. There's still a chance whatever is afflicting you will get better over time; hence, do periodic rechecks, and pay particular attention to any nagging doubts about the proof you get while performing those.
In the meantime, interpret the fact that you've gotten an apparent proof as significant evidence for the entity in question being real and very powerful.
Or: it says "This is undecidable in Zermelo-Fraenkel set theory plus the axiom of choice". In the case of P=NP, I might believe it
I would not believe a purported god if it said all 9 remaining Clay math prize problems are undecidable.
If it really is undecidable, God must be able to prove that.
However, I think an easier way to establish whether something is just your hallucination or a real (divine) being is asking them about something you couldn't possibly know about and then check if it's true.