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I don’t really have time to write seriously about this, and there’s a very good argument that this is a topic anyone with any sense should be ignoring, but I just can’t resist linking to the latest in the abc saga, the REPORT ON THE RECENT SERIES OF PREPRINTS BY K. JOSHI posted yesterday by Mochizuki. To summarize the situation before yesterday, virtually all experts in this subject have long ago
Just a reminder that the abc conjecture is still a conjecture, there is no known valid proof (don’t believe what you might read in an EMS journal). For more about why one attempted proof doesn’t work, see here and here. For extensive background on this, you could start at this blog posting and work backwards, to the first announcement of a claimed proof back in 2012. By 2018 Scholze and Stix had s
Davide Castelvecchi at Nature has the story this morning of a press conference held earlier today at Kyoto University to announce the publication by Publications of the Research Institute for Mathematical Sciences (RIMS) of Mochizuki’s purported proof of the abc conjecture. This is very odd. As the Nature subheadline explains, “some experts say author Shinichi Mochizuki failed to fix fatal flaw”.
As discussed here a couple months ago, Peter Scholze and Jakob Stix believe they have found a serious problem with Mochizuki’s claimed proof of the abc conjecture, and traveled to Kyoto in March to discuss it with him. Their write-up is now available here. Mochizuki has made public his response to this, creating a web-page available here. There’s also an updated version of Ivan Fesenko’s take on t
I’ve seen reports today (see here and here) that indicate that Mochizui’s IUT papers, which are supposed to contain a proof of the abc conjecture, have been accepted by the journal Publications of the RIMS. Some of the sources for this are in Japanese (e.g. this and this) and Google Translate has its limitations, so perhaps Japanese speaking readers can let us know if this is a misunderstanding. I
This spring I’ve been teaching a course aimed at math graduate students, starting with quantum mechanics and trying to get to an explanation of the Standard Model by the end of the semester. Course notes for the first half of the course are available here, but still quite preliminary, in particular I need to do a lot of work on section 9.4 and add material to chapter 10. Hoping to get to this tomo
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