An important question is therefore whether Mochizuki himself will at some point no longer endorse his proof in the form that it was published in RIMS. I think the likelihood of this is rather low but find it hard to go below 10%.
Would “the proof as written contains errors but is basically correct; here’s how to fix them” count? These errors might include typos but also things like “the proof of lemma 3.2 relied on theorem 2.9, but the preconditions of that theorem weren’t satisfied. But here’s another way to prove a weaker version of the lemma, which is sufficient for our purposes”.
(IIRC Wiles’ proof of Fermat’s Last Theorem had a significant error corrected only shortly before he revealed it publicly.)
Would “the proof as written contains errors but is basically correct; here’s how to fix them” count? These errors might include typos but also things like “the proof of lemma 3.2 relied on theorem 2.9, but the preconditions of that theorem weren’t satisfied. But here’s another way to prove a weaker version of the lemma, which is sufficient for our purposes”.
I think this depends on how big the error is. No mathematical proof written in natural language is fully explicit, so there’s always room for deductions which aren’t fully justified, details which are not fully elaborated, etc.
If the error is big enough that it breaks the whole argument and a major new idea is needed to salvage the proof, then I would count that as Mochizuki no longer endorsing the proof in the form it appeared in RIMS. This was actually true for the error in Wiles’ proof of FLT; he needed a whole new idea to save his proof. His original idea didn’t work in some case and he had to realize that he had in the past tried something else which failed in general but was suited for handling this specific case.
If Wiles had published his proof in its original form (before he noticed the error) and then publicly stated that this proof had an error in it, I think the question should resolve positively. If it’s just a typo or some computational mistake which doesn’t affect the rest of the proof, however, then it shouldn’t resolve on that basis alone.
Would “the proof as written contains errors but is basically correct; here’s how to fix them” count? These errors might include typos but also things like “the proof of lemma 3.2 relied on theorem 2.9, but the preconditions of that theorem weren’t satisfied. But here’s another way to prove a weaker version of the lemma, which is sufficient for our purposes”.
(IIRC Wiles’ proof of Fermat’s Last Theorem had a significant error corrected only shortly before he revealed it publicly.)
I think this depends on how big the error is. No mathematical proof written in natural language is fully explicit, so there’s always room for deductions which aren’t fully justified, details which are not fully elaborated, etc.
If the error is big enough that it breaks the whole argument and a major new idea is needed to salvage the proof, then I would count that as Mochizuki no longer endorsing the proof in the form it appeared in RIMS. This was actually true for the error in Wiles’ proof of FLT; he needed a whole new idea to save his proof. His original idea didn’t work in some case and he had to realize that he had in the past tried something else which failed in general but was suited for handling this specific case.
If Wiles had published his proof in its original form (before he noticed the error) and then publicly stated that this proof had an error in it, I think the question should resolve positively. If it’s just a typo or some computational mistake which doesn’t affect the rest of the proof, however, then it shouldn’t resolve on that basis alone.