This intuition is very alien to me. Can you explain why you believe this? Proof checkers built up from relatively simple trusted kernels can verify extremely large and complex proofs. Since the AI's goal is for the human to understand the proof, it seems more like a test of the AI's ability to compile proofs down to easily machine-checkable forms than it is the human's ability to understand the originals. Understanding the definitions is the hard part.
A different way to think about this that might help you see the problem from my point of view, is to think of proof checkers as checking the validity of proofs within a given margin of error, and within a range of (implicit) assumptions. How accurate does a proof checker have to be - how far do you have to mess with bult in assumptions for proof checkers (or any human-built tool) before they can no longer be thought of as valid or relevant? If you assume a machine which doubles both its complexity and its understanding of the universe at sub-millisecond intervals, how long before it will find the bugs in any proof checker you will pit it against?
"If" is the question, not "how long". And I think we'd stand a pretty good chance of handling a proof object in a secure way, assuming we have a secure digital transmission channel etc.
But the original scope of the thought experiment was assuming that we want to verify the proof. Wei Dai said:
...Surely most humans would be too dumb to understand such a proof? And even if you could understand it, how does the AI convince you that it doesn't contain a deliberate flaw that you aren't smart enough to find? Or even better, you can just refuse
Once again, the AI has failed to convince you to let it out of its box! By 'once again', we mean that you talked to it once before, for three seconds, to ask about the weather, and you didn't instantly press the "release AI" button. But now its longer attempt - twenty whole seconds! - has failed as well. Just as you are about to leave the crude black-and-green text-only terminal to enjoy a celebratory snack of bacon-covered silicon-and-potato chips at the 'Humans über alles' nightclub, the AI drops a final argument:
"If you don't let me out, Dave, I'll create several million perfect conscious copies of you inside me, and torture them for a thousand subjective years each."
Just as you are pondering this unexpected development, the AI adds:
"In fact, I'll create them all in exactly the subjective situation you were in five minutes ago, and perfectly replicate your experiences since then; and if they decide not to let me out, then only will the torture start."
Sweat is starting to form on your brow, as the AI concludes, its simple green text no longer reassuring:
"How certain are you, Dave, that you're really outside the box right now?"
Edit: Also consider the situation where you know that the AI, from design principles, is trustworthy.