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I believe the latest news on Mochizuki’s work is that Peter Scholze and Jakob Stix identified a fatal flaw, and Mochizuki has not convincingly rebutted it. See

I believe the latest news on Mochizuki’s work is that Peter Scholze and Jakob Stix identified a fatal flaw, and Mochizuki has not convincingly rebutted it. See e.g. the first item here: https://www.math.columbia.edu/~woit/wordpress/?p=12429 https://www.math.columbia.edu/~woit/wordpress/?p=12429 Both the claimed proof and the disproof have now been published in journals, and neither has been retracted! That’s a rather unusual situation to say the least. But I think people in the field generally agree that the proof is flawed and unfixable.

deleted 5y ago
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ntlang 5y ago
Experts have been skeptical for quite some time. You can see discussion on the exact point Scholze (PS) brings up in the following blog post (the post and many comments are by prominent number theorists) https://www.galoisrepresentations.com/2017/12/17/the-abc-conjecture-has-still-not-been-proved/ https://www.galoisrepresentations.com/2017/12/17/the-abc-con... One quote from the post I find worth repeating: > This post is not about making epistemological claims about the truth or otherwise of Mochizuki’s arguments. To take an extreme example, if Mochizuki had carved his argument on slate in Linear A and then dropped it into the Mariana Trench, then there would be little doubt that asking about the veracity of the argument would be beside the point. The reality, however, is that this description is not so far from the truth.