6

In Global character of ABC/Szpiro inequalities, Peter Scholze says that he thinks Joshi's proof of the abc conjecture in his paper has a mistake in Proposition 6.10.7. However, for the proof of Proposition 6.10.7, Kirti Joshi merely says that

Proof. This is the last equation on [Mochizuki, 2021d, Step (v) on Page 658, Proof of Theorem 1.10] and its proof is all of step (v).

Does the mistake in Proposition 6.10.7 also invalidate Mochizuki's original proof of Theorem 1.10 in IUTT IV, thus invalidating Mochizuki's original proof of the abc conjecture?

Madeleine Birchfield
  • 2,454
  • 15
    I don't think MathOverflow is the best venue for hashing these things out. – Sam Hopkins Mar 31 '24 at 12:07
  • 13
    @SamHopkins The precedent is that this is a perfect use for MathOverlow, assuming (a) users are interested in engaging with the mathematics and (b) the discussion is about specific mathematics and not general editorial comments. Indeed, I see that you gave a very nice and precise criterion for when correctness-of-the-published-literature questions are appropriate. Maybe you can suggest to OP how they can improve their question to meet your criterion? – Theo Johnson-Freyd Mar 31 '24 at 12:14
  • 16
    @TheoJohnson-Freyd fair enough and I do stand by my defense of "is this paper correct" being sometimes an acceptable MO question - for instance, if a graduate student is struggling to understand the literature related to their thesis question. But all of this Mochizuki stuff is just hype & drama, I'm afraid. – Sam Hopkins Mar 31 '24 at 12:18
  • 3
    @TheoJohnson-Freyd I concur with Sam Hopkins. Mochizuki is a special case. Regardless of where the mathematical truth lies, Mochizuki has repeatedly and publicly demonstrated that he responds very poorly to any perceived criticism of his work. I cannot see much good coming of publicly questioning the correctness of Mochizuki's proof on MO. To be clear, this is not the OP's fault, but Mochizuki's; nevertheless, I'm voting to close this question. – Timothy Chow Mar 31 '24 at 18:01
  • 5
    It's already Monday here in NZ and there is an obvious April's Fools joke to be made but I will leave the details to the reader. – Felipe Voloch Mar 31 '24 at 18:48
  • 15
    I'm more afraid that this is an instance where the cited reference does not match the statement that is claimed. The critical difference between Joshi and Mochizuki is that "Joshi's version of Mochizuki's Corollary 3.12" (=Joshi's Theorem 9.11.1) has a purely local proof and hence cannot have the same content as Mochizuki's Corollary 3.12. However, it may be correct on its own; then the mistake is a mismatch between what Joshi has to compute in Proposition 6.10.7, and what Mochizuki actually computed in IUT IV. But I agree with Sam Hopkins that this discussion is not fruitful. – Peter Scholze Mar 31 '24 at 20:11
  • 16
    To summarize: There is a clear problem with Joshi's proof, as there is a contradiction between Proposition 6.10.7 and the local inequality proved in the proof of Theorem 9.11.1. The mistake could be in Proposition 6.10.7 (and, given that the proof isn't written down, is the first suspicious place) but it might as well be a mistake in the proof of Theorem 9.11.1. In any case, this whole discussion is only about Joshi's proof, not Mochizuki's; I do not think that there is a real error internally in IUT IV. – Peter Scholze Mar 31 '24 at 20:23

0 Answers0