Mochizuki's proof of the ABC conjecture accepted for publication

Math student here. This whole process reflects very poorly on Mochizuki, IMO. The proper thing to do when claiming to have solved a major open problem is to make yourself available to the mathematical community, for example by giving lectures on your work. Releasing a preprint on your website and expecting other mathematicians to drop what they're doing and devote years of their time to understand your obscure paper just screams of arrogance. Also, publishing your work in a journal where you are the editor isn't a good look; it gives the impression of a conflict of interest. The critique by Scholze et al is the final nail in the coffin as far as I'm concerned.

&gt; Acceptance of the work in Publications of the Research Institute for Mathematical Sciences (RIMS) — a journal of which Mochizuki is chief editor, published by the institute where he works at Kyoto University<p>That&#x27;s exceptionally bad optics.

I mean, I’m enjoying the show, but this changes nothing. Very few people claim to understand the proof and some of the few that do think it’s wrong.<p>Contrast with Wiles, where they _did_ understand it, they _did_ find a gap in his proof and he fixed it to everyone’s satisfaction.

&gt; But one mathematician who prefers to be quoted anonymously says that editors and referees handling these papers might have been in a nearly impossible situation. “If the best mathematicians spend time trying to work out what’s going on and fail, how can one referee on his own have any chance?”<p>I totally disagree. When someone is making extraordinary claims, <i>the burden is on them</i> to go the extra mile to explain their reasoning, none of which Mochizuki has done. The easy decision in this case should be to leave things at the current &quot;default&quot; state unless a higher burden of proof is met.<p>I think it reflects especially poorly that when confronted with criticisms that Mochizuki just waved the criticisms away with what was basically a &quot;you mere mortals misunderstood my greatness&quot;, without taking the effort to engage and explain himself. I&#x27;m not in the math community so could be misunderstanding, but that&#x27;s certainly the sense I got reading this article.

I&#x27;m not a mathematician but coming from the software world if one guy wrote a massive program (I&#x27;m assuming 600 pages is massive) in &quot;an impenetrable, idiosyncratic style&quot; you could virtually guarantee it would not be correct.

The first comment in <a href="https:&#x2F;&#x2F;news.ycombinator.com&#x2F;item?id=15971802" rel="nofollow">https:&#x2F;&#x2F;news.ycombinator.com&#x2F;item?id=15971802</a> (one of <i>many</i> HN posts discussing this ongoing situation) is intriguing.

Previous threads on this:<p><a href="https:&#x2F;&#x2F;hn.algolia.com&#x2F;?dateRange=all&amp;page=0&amp;prefix=true&amp;query=comments%3E1%20abc%20conjecture&amp;sort=byDate&amp;type=story" rel="nofollow">https:&#x2F;&#x2F;hn.algolia.com&#x2F;?dateRange=all&amp;page=0&amp;prefix=true&amp;que...</a><p><a href="https:&#x2F;&#x2F;hn.algolia.com&#x2F;?dateRange=all&amp;page=0&amp;prefix=true&amp;query=comments%3E1%20mochizuki&amp;sort=byDate&amp;type=story" rel="nofollow">https:&#x2F;&#x2F;hn.algolia.com&#x2F;?dateRange=all&amp;page=0&amp;prefix=true&amp;que...</a>

This is Mochizuki&#x27;s informal blog post in Japanese about the current situation.<p><a href="https:&#x2F;&#x2F;plaza.rakuten.co.jp&#x2F;shinichi0329&#x2F;diary&#x2F;202001050000&#x2F;" rel="nofollow">https:&#x2F;&#x2F;plaza.rakuten.co.jp&#x2F;shinichi0329&#x2F;diary&#x2F;202001050000&#x2F;</a><p>Although he had lived in the US for more than a decade and has no problem with the English language, he seem to have a kind of &quot;western culture allergy&quot; that is written in detail in the post below:<p><a href="https:&#x2F;&#x2F;plaza.rakuten.co.jp&#x2F;shinichi0329&#x2F;diary&#x2F;201711210000&#x2F;" rel="nofollow">https:&#x2F;&#x2F;plaza.rakuten.co.jp&#x2F;shinichi0329&#x2F;diary&#x2F;201711210000&#x2F;</a><p>I think the &quot;allergy thing&quot; is the reason he doesn&#x27;t want to follow the ordinary &quot;western approved way&quot; and do a tour in the US.<p>Also I have read somewhere that he is open to mathematical discussions via online or if you visit him in Japan.

For a decent take in support of the publication, see this recent philosophy of mathematics paper:<p><a href="https:&#x2F;&#x2F;www.maths.nottingham.ac.uk&#x2F;plp&#x2F;pmzibf&#x2F;rpp.pdf" rel="nofollow">https:&#x2F;&#x2F;www.maths.nottingham.ac.uk&#x2F;plp&#x2F;pmzibf&#x2F;rpp.pdf</a>

TL;DR: obscure, long &quot;proof&quot; of major conjecture by respected mathematician to be published in a journal he is closely associated with despite several years of scepticism by the wider maths community his attempt is successful.<p>Complicated somewhat by possible language and cultural barriers, and his perceived reluctance to fully engage with his critics or the maths world outside his home country.<p>It&#x27;s an interesting and odd story that has been rumbling on for the last few years.

Excerpt:<p>&quot;The saga began when Mochizuki, a respected number theorist quietly posted his preprints on 30 August 2012 — not on arXiv.org, mathematicians’ preferred repository, but on his own webpage at RIMS. Written in an impenetrable, idiosyncratic style, the papers seemed to entirely consist of mathematical concepts that were completely unfamiliar to the rest of the community —<p><i>“like you might be reading a paper from the future, or from outer space”</i>,<p>wrote Jordan Ellenberg, a number theorist at the University of Wisconsin–Madison, on his blog soon after the papers appeared.&quot;<p>...Which makes it all the more a subject of curiousity -- and worth looking at...

The top 2 math journals are, in many people&#x27;s minds, Annals and Inventiones (i.e. Annals of Mathematics and Inventiones Mathematicae). The fact that this work, which is supposed to be of utmost importance, was not published in one of these two, is not confidence inspiring. That it was published in a journal where the author is chief editor is downright scandalous.

He should have written the proof in Lean or something.

Had we a slick method of formalizing proofs for computer verification, no polemics would be possible.

Maybe try publishing it first, <i>then</i> see if it&#x27;s newsworthy.<p>This isn&#x27;t something you hype like a iPhone.

Once again, this is a rather perfect example of why there is a great need in Math for a universal formal proof language that can be verified by computers.<p>If this existed, the burden of proof would be on Mochizuki to present his proof in a language that can actually be understood by others and by machines.

It seems mathematicians are not aware of code obfuscation. Mochizuki objective is to keep this knowledge in Japan and protect this technological advantage.