To add nuance to this picture, while you’re right that the broader community has neither accepted nor refuted his proof of the abc conjecture, I just learned from James Boyd’s writeup that there’s been growing interest in his broader work outside of RIMS:
Before explaining the details, I want to make a sudden turn and, setting the fate of abc aside, share a somewhat optimistic point on a different matter. So, I agree that Scholze-Stix are able to make their argument without the algorithms. One might ask if anyone has looked at the math beyond the basics critiqued by Scholze-Stix. The fascinating wrinkle in the story – to talk inside baseball – is that this mathematics is of interest to some mathematicians, and they are engaging with IUT; they mostly come from anabelian geometry and related fields, and – importantly – generally have no interest in abc. It’s sometimes supposed that these mathematicians must just be cajoled students or abc “true believers”, but, in fact, much of the interaction is happening in collaboration with CNRS, the largest science funder in Europe.
What happened is twofold. On the one hand, the abc proof strategy provoked a global controversy. On the other hand, looking at some of the math in the IUT papers and setting aside abc, a relationship between aspects of IUT, anabelian geometry, and related topics such as étale homotopy and Grothendieck-Teichmüller theory did prove attractive to some mathematicians in those areas. …
(there’s a section further down expanding on this)
To add nuance to this picture, while you’re right that the broader community has neither accepted nor refuted his proof of the abc conjecture, I just learned from James Boyd’s writeup that there’s been growing interest in his broader work outside of RIMS:
(there’s a section further down expanding on this)