s*****V
发帖数: 21731 | 1 Scholze:Thanks for the wonderful post! I agree with everything that was said
.One small thing I would like to add is that most accounts indicate that no
experts have been able to point to a place where the proof would fail. This
is in fact not the case; since shortly after the papers were out I am
pointing out that I am entirely unable to follow the logic after Figure 3.8
in the proof of Corollary 3.12 of Inter-universal Teichmüller theory part
III: “If one interprets the above discussion in terms of the notation
introduced in the statement of Corollary 3.12, one concludes [the main
inequality].” Note that this proof is in fact the *only* proof in parts II
and III that is longer than a few lines which essentially say “This follows
from the definitions”. Those proofs, by the way, are completely sound,
very little seems to happen in those two papers (to me). Since then, I have
kept asking other experts about this step, and so far did not get any
helpful explanation. In fact, over the years more people came to the same
conclusion; from everybody outside the immediate vicinity of Mochizuki, I
heard that they did not understand that step either. The ones who do claim
to understand the proof are unwilling to acknowledge that more must be said
there; in particular, no more details are given in any survey, including
Yamashita’s, or any lectures given on the subject (as far as they are
publicly documented). [I did hear that in fact all of parts II and III
should be regarded as an explanation of this step, and so if I am unable to
follow it, I should read this more carefully… For this reason I did wait
for several years for someone to give a better (or any) explanation before
speaking out publicly.]One final point: I get very annoyed by all references
to computer-verification (that came up not on this blog, but elsewhere on
the internet in discussions of Mochizuki’s work). The computer will not be
able to make sense of this step either. The comparison to the Kepler
conjecture, say, is entirely misguided: In that case, the general strategy
was clear, but it was unclear whether every single case had been taken care
of. Here, there is no case at all, just the claim “And now the result
follows”. |
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