The ABC conjecture has still not been proved
Terry Tao&#x27;s comment in the comments section is particularly worth pointing out, I think:<p>&gt; I do not have the expertise to have an informed first-hand opinion on Mochizuki’s work, but on comparing this story with the work of Perelman and Yitang Zhang you mentioned that I am much more familiar with, one striking difference to me has been the presence of short “proof of concept” statements in the latter but not in the former, by which I mean ways in which the methods in the papers in question can be used relatively quickly to obtain new non-trivial results of interest (or even a new proof of an existing non-trivial result) in an existing field. In the case of Perelman’s work, already by the fifth page of the first paper Perelman had a novel interpretation of Ricci flow as a gradient flow which looked very promising, and by the seventh page he had used this interpretation to establish a “no breathers” theorem for the Ricci flow that, while being far short of what was needed to finish off the Poincare conjecture, was already a new and interesting result, and I think was one of the reasons why experts in the field were immediately convinced that there was lots of good stuff in these papers.   Yitang Zhang’s 54 page paper spends more time on material that is standard to the experts [...] but about six pages after all the lemmas are presented, Yitang has made a non-trivial observation, which is that bounded gaps between primes would follow if one could make any improvement to the Bombieri-Vinogradov theorem for smooth moduli. [...]<p>&gt; From what I have read and heard, I gather that currently, the shortest “proof of concept” of a non-trivial result in an existing (i.e. non-IUTT) field in Mochizuki’s work is the 300+ page argument needed to establish the abc conjecture. It seems to me that having a shorter proof of concept (e.g. &lt;100 pages) would help dispel scepticism about the argument. It seems bizarre to me that there would be an entire self-contained theory whose only external application is to prove the abc conjecture after 300+ pages of set up, with no smaller fragment of this setup having any non-trivial external consequence whatsoever.<p>(Comment link: <a href="https:&#x2F;&#x2F;galoisrepresentations.wordpress.com&#x2F;2017&#x2F;12&#x2F;17&#x2F;the-abc-conjecture-has-still-not-been-proved&#x2F;#comment-4563" rel="nofollow">https:&#x2F;&#x2F;galoisrepresentations.wordpress.com&#x2F;2017&#x2F;12&#x2F;17&#x2F;the-a...</a> )