I was given to understand that his work was more like Grothendieck's, where he's developing this entirely new, super general system. But you can imagine if Grothendieck for example had done all of his work for years and years in isolation and then presented Schemes, Topoi, and Motives to everyone all at once, using them in combination to prove something familiar, and expecting other mathematicians to just learn and understand them all in order to verify a single proof.
I think in that case, folks would not have been immediately so interested in the new constructions Grothendieck had come up, viewing it initially as mountains of unnecessarily alien concepts built up just to give other mathematicians a hard time ;)
(Not to identify the two mathematicians overly—I'm not sure how appropriate that really is—but I remember that being my impression when first digging into Mochizuki's work, and I haven't seen it mentioned here yet.)
It's not sufficient to have a great idea, or even to be right about it. You have to be able to explain it thoroughly enough that other qualified peers can understand your logic enough to weigh in on it. That seems not to have happened yet hear.
This sounds like a variant of the Turing test.
Mochizuki and your pet dog both claim to have proven the ABC conjecture. The ABC conjecture has been proven when you can understand one proof but not the other.
Mochizuki and your pet dog both claim to have proven the ABC conjecture. The ABC conjecture has been proven when you can tell the difference between the two proofs.
At this point, it seems clear that we do not have a proof of the ABC conjecture. Perhaps someone will be able to improve this to make a real proof - after all, there were some errors in the first Wiles proof of Fermat's Last Theorem, but they ended up being minor errors that were fixed up once they were found. But what we have is not a proof.