Yeah, I've heard about this "notorious difficulty" in verifying proof checkers before, and I don't understand what it could mean. Humans are way more unverifiable.
I bet the real purpose of qea is that it allowed its author to avoid learning to use something else. But I find it interesting that he recognizes the importance of computer verification for something like this, and maybe it indicates that this has been in the works for a while. It doesn't have to be half-baked to be wrong, though.
Yeah, I've heard about this "notorious difficulty" in verifying proof checkers before, and I don't understand what it could mean. Humans are way more unverifiable.
I think the idea is that for a point this controversial he is well aware that mathematicians may actually object to his trustworthiness (they've objected to less questionable things in the past), and want to verify the proof for themselves. I think he may well be right in this. However, I don't see why he can't give a full explanation (his current paper isn't) for humans as well, since this would probably be finished sooner and would probably save a lot of his own time if there is a mistake.
We've discussed Edward Nelson's beliefs and work before. Now, he claims to have a proof of a contradiction in Peano Arithmetic; which if correct is not that specific to PA but imports itself into much weaker systems. I'm skeptical of the proof but haven't had the time to look at it in detail. There seem to be two possible weakpoints in his approach. His approach is to construct a system Q_0^* which looks almost but not quite a fragment of PA and then show that PA both proves this system's consistency and proves its inconsistency.
First, he may be mis-applying the Hilbert-Ackermann theorem-when it applies is highly technical and can be subtle. I don't know enough to comment on that in detail. The second issue is that in trying to show that he can use finitary methods to show there's a contradiction in Q_0^* he may have proven something closer to Q_0^* being omega-inconsistent. Right now, I'm extremely skeptical of this result.
If anyone is going to find an actual contradiction in PA or ZFC it would probably be Nelson. There some clearly interesting material here such as using a formalization of the surprise examiation/unexpected hanging to get a new proof of of Godel's Second Incompleteness Theorem. The exact conditions which this version of Godel's theorem applies may be different from the conditions under which the standard theorem can be proven.