In April 2012, a proof of the abc conjecture was proposed by Shinichi Mochizuki. However, the proof was based on a "Interuniversal Teichmüller theory" which Mochizuki himself pioneered. It was known from the beginning that it would take experts months to understand his work enough to be able to verify the proof. Are there any updates on the validity of this proof?

In January, Vesselin Dimitrov posted to the arXiv a preprint showing that Mochizuki's work, if correct, would be effective. While this doesn't validate Mochizuki's work it does do a few things:



I think that not much has changed since 2012, in terms of general consensus within the mathematical community. There's some very interesting opinions and notes on the topic (see for example the one by Brian Conrad mentioned in the comments above, or this one by Ivan Fesenko), but not a lot of people seem to have a strong opinion yet as to whether IUT implies Szpiro's conjecture or not. On the other hand, Mochizuki has two reports on the progress of the verification process, which have a lot of information that you might find helpful. 

