There will be a documentary broadcast tomorrow in Japan on Mochizuki’s claimed proof of the abc conjecture. I was interviewed for this by the filmmakers last year, but don’t know anything about whether and how that footage will be used. I’d be curious to hear reports from any Japanese-speaking readers who see the documentary tomorrow.
Over the years there has been a detailed coverage of this story here on the blog. To make it more accessible, I’ve added an abc conjecture category. In case the documentary doesn’t make this clear, the current consensus of experts in the field is that there is no proof. Peter Scholze and Jacob Stix identified a problem with Mochizuki’s proof in 2018 (discussed in detail by Scholze and others here), and Mochizuki has not provided a convincing answer to their objections. No one else (including the journal editors who published the proof in PRIMS) has been able to provide a clear explanation of the problematic part of the proof.
Taylor Dupuy is still making implausible claims that Scholze’s criticism of the proof is invalid. To judge for yourself, see here a long detailed discussion of the issue between them involving several other experts.
Reports I’m seeing from those who have watched the program say that it does correctly explain that the proof is not accepted by many experts.