As a follow-up to a previous post, let’s mention that a few days ago Mochizuki has put online a report concerning activities devoted to the verification of his Inter-universal Teichmuller Theory (IUTeich).
A fascinating read, I can’t remember anything of the sort from a serious mathematician in the past two decades (correct me if I’m wrong).
A few selected sentences (but you’d better read it entirely) :
page 2: Yamashita has been writing a survey since 2013 concerning IUTeich […] It appears that the survey will come to a total of roughly 200 ∼ 300 pages in length (i.e., roughly a tenth of the size, in terms of the number of pages, of the original papers — a quite staggering compression ratio!).
page 2: Yamashita warned that if you attempt to study IUTeich by skimming corners and “occasionally nibbling” on various portions of the theory, then you will not be able to understand the theory even in 10 years; on the other hand, if you study the theory systematically from the beginning, then you should be able to
understand it in roughly half a year.
page 7: I have been participating for over 20 years now, as author, referee, editor, and editor-in-chief, in the refereeing of countless papers for mathematical journals, and, as far as I can see, the verification activities on the part of the three researchers discussed above already exceed, by a quite substantial margin
— i.e., in their content, thoroughness, and meticulousness — the usual level of refereeing for a mathematical journal.
page 7: I have yet to hear of even a single problem that relates to the essentialthrust or validity of the theory
page 8: My understanding, at present, concerning the verification
of IUTeich is that at least with regard to the substantive mathematical aspects of such a verification, the verification of IUTeich is, for all practical purposes, complete; nevertheless, as a precautionary measure, in light of the importance of the theory and the novelty of the techniques that underlie the theory, it seems appropriate that a bit more time be allowed to elapse before a final official declaration of the completion of the verification of IUTeich is made.
page 8: my current sense is that some date during the latter half of the 2010’s would be an appropriate time for the termination of such precautionary measures.
He then goes on to discuss what the “next step” should be and says :
page 9: in light of the present state of affairs, the only reasonable course of action lies in taking a long-term appproach to promoting the dissemination of IUTeich by cultivating a collection of researchers, one by one (and perhaps over many years of time), who gradually attain a deep understanding of IUTeich by studying the theory carefully and systematically from the beginning, i.e., in the style of Yamashita.
Unfortunately, however, there appear to exist, especially among researchers outside Japan, quite strongly negative opinions and antagonistic reactions to the idea of “studying the theory carefully and systematically from the beginning”.
He then presents five mathematico-sociological hypotheses that may explain that, and adresses each one.
I’m curious to see if that report will initiate some changes in attitude towards his work, or any fruitful dialog. It does read as a completely sane and serious text.