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Titans of Mathematics Clash Over Epic Proof of ABC Conjecture (quantamagazine.org)
Two mathematicians have found what they say is a hole at the heart of a proof that has convulsed the mathematics community for nearly six years. Quanta Magazine: In a report [PDF] posted online Thursday, Peter Scholze of the University of Bonn and Jakob Stix of Goethe University Frankfurt describe what Stix calls a "serious, unfixable gap" within a mammoth series of papers by Shinichi Mochizuki, a mathematician at Kyoto University who is renowned for his brilliance. Posted online in 2012, Mochizuki's papers supposedly prove the abc conjecture, one of the most far-reaching problems in number theory. Despite multiple conferences dedicated to explicating Mochizuki's proof, number theorists have struggled to come to grips with its underlying ideas. His series of papers, which total more than 500 pages, are written in an impenetrable style, and refer back to a further 500 pages or so of previous work by Mochizuki, creating what one mathematician, Brian Conrad of Stanford University, has called "a sense of infinite regress."
Between 12 and 18 mathematicians who have studied the proof in depth believe it is correct, wrote Ivan Fesenko of the University of Nottingham in an email. But only mathematicians in "Mochizuki's orbit" have vouched for the proof's correctness, Conrad commented in a blog discussion last December. "There is nobody else out there who has been willing to say even off the record that they are confident the proof is complete." Nevertheless, wrote Frank Calegari of the University of Chicago in a December blog post, "mathematicians are very loath to claim that there is a problem with Mochizuki's argument because they can't point to any definitive error." That has now changed. In their report, Scholze and Stix argue that a line of reasoning near the end of the proof of "Corollary 3.12" in Mochizuki's third of four papers is fundamentally flawed. The corollary is central to Mochizuki's proposed abc proof. "I think the abc conjecture is still open," Scholze said. "Anybody has a chance of proving it."
Between 12 and 18 mathematicians who have studied the proof in depth believe it is correct, wrote Ivan Fesenko of the University of Nottingham in an email. But only mathematicians in "Mochizuki's orbit" have vouched for the proof's correctness, Conrad commented in a blog discussion last December. "There is nobody else out there who has been willing to say even off the record that they are confident the proof is complete." Nevertheless, wrote Frank Calegari of the University of Chicago in a December blog post, "mathematicians are very loath to claim that there is a problem with Mochizuki's argument because they can't point to any definitive error." That has now changed. In their report, Scholze and Stix argue that a line of reasoning near the end of the proof of "Corollary 3.12" in Mochizuki's third of four papers is fundamentally flawed. The corollary is central to Mochizuki's proposed abc proof. "I think the abc conjecture is still open," Scholze said. "Anybody has a chance of proving it."
I guess it isn't as easy as 1,2,3...
I thought theorem checking was one of the applications that AI was being touted for. Just doing a quick check, there seems to be a large number of articles (like this one, which goes back a bit: http://www.dtic.mil/dtic/tr/fu...) written about this very topic.
Rather that rely on a limited number of mathematicians, all of whom seem to know Professor Mochizuki, how about running his proof through these AI tools to see if they can validate the proof?
Mimetics Inc. Twitter
Let's start defining some stakes.
If you come up with a proof and it's wrong, you're banned from Math.
If you say a proof is wrong and it turns out you are wrong, you're banned from Math.
Solving challenging problems can earn you "Unbanned from Math" cards, but they must be incredibly challenging.
That's true even for simple things: you look at the Pythagorean theorem and at some point the proof of the theory "clicks" somewhere inside you and you say yes this is true. A genius friend at the university argued with his mathematics professor on some advanced course as he didn't give my friend the full credit on some very complicated proof, and he said "see here, colleague" (they call all students "colleague"), "the mistake is you wrote this orientation here is clockwise but it's counter-clockwise". The student said "no it is clockwise." The professor looked back at the paper and asked (aware of the student's genius and reputation) "why is it clockwise?" And the friend said "But it must be!" And the professor looked again and said "yeah, you're right, it is."
Understanding what the abc conjecture states takes effort. Proving it...
A reminder of just how different a real mathematician's mind is from the rest of us.
I live in Cleveland, and not everyone is like that woman you are talking about. Butt heads are butt heads, no matter where they live. And no matter what party they align themselves with. Sick of the politics on this site, stfu idiot. Oh, and moron. I am a republican. You are as bad as the liberal trolls on this web site. There are no differences.
Anonymous comments are as pathetic as the anonymous "sources" that contaminate gutless journalism from the New York Time
I USE
D
Famous Russian Troll error, unable to incorporate THE and A into the language.
I've been vaguely following this since word first came out in 2012. You can find some technical explanations over at https://mathoverflow.net/questions/106560/philosophy-behind-mochizukis-work-on-the-abc-conjecture . A slightly less technical article, but still aimed at a STEM audience can be found in the second quanta magazine link.
Anyways, for anyone else skeptical, I would follow up this article with the blog post at https://galoisrepresentations.wordpress.com/2017/12/17/the-abc-conjecture-has-still-not-been-proved/ and pay attention to Terry Tao's comment at the bottom (read his whole comment, but mostly the last paragraph):
> 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. 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.
Mochizuki is obviously a talented mathematician: "Mathematicians are very loath to claim that there is a problem with Mochizuki’s argument because they can’t point to any definitive error. " (from the galoisrepresentations blog above). But it's been more than six years now, and the more time passes without being accepted for publication makes me more and more skeptical.
I think technically they are FCC 1984 phones (Reagan phones) but who cares, those who keep beating that drum are already dead for the most part.
500 pages for a conjecture proof and a big waste of time is useless.
Why? Because it is very probable to commit an errata and to dispose all its heavy works to the trash.
I've new incomplete theories "To Do" that are also math-heavy.
I need time to learn Common Lisp for making a symbolic calculator as Maxima. I argue that it is full of parentheses but i need made the learned lesson.
Seriously, how is this relevant to anyone on the planet besides the author himself, and the 10 other people who've read his work.
https://www.youtube.com/watch?...
"You punish willful deception (those who are lying and know it)" - AND YET YOU BOBBY CONSTANTLY GIVE TRUMP 4,229+ PASSES? He's the fucking President and you have no problem backing up his constant lies. Not once have you.
https://www.washingtonpost.com/news/fact-checker/wp/2018/08/01/president-trump-has-made-4229-false-or-misleading-claims-in-558-days/
You want to back anti-science bullshitters and reference Einstein, what he would have said or done? Fuck you prison-hard in the butt with treason sauce, you spineless coward! Stand up for the truth or sit on Putin's cock. DECIDE.
I think the title here is misleading. Outside of Mochizuki's friends (and perhaps even including them), every mathematician involved has had serious doubts about this purported proof since the beginning. That's simply because the papers are written very different than the usual math paper ---- that is to say, leaving very many things not explained or explained poorly.
"What lies behind us, and what lies before us are tiny matters compared to what lies within us." Ralph Waldo Emerson
In their report, Scholze and Stix argue that a line of reasoning near the end of the proof of "Corollary 3.12" in Mochizuki's third of four papers is fundamentally flawed.
I am definitely incapable of reading Mochzuki's proof, but it would have been interesting if the article had cited the line in question.
What is it with Japan and supposedly brilliant mathematicians and refusing to collaborate with outsiders? I thought that died when the Earth Simulator lost the top spot
Well, to comprehend page 500 you have first to understand the 499 previous pages, which is why the flaw "near the end" is hard to spot.
Slashdot, fix the reply notifications... You won't get away with it...
The last page of the linked pdf explains where the issue is. It's kind of a combination of a few previous steps.
Have NBC and CBS confirmed it?
How about CNN?
What good would it be? Scholze and Stix already stripped down the alleged proof extremely in their outline, so much so that they keep apologizing for it. As I understand it, they left out everything that was not directly connected to the error they spotted. I don't think it can be further condensed than in their PDF. Or rather, the only possible way to further condense it is to simply say "they found an error".
This Scholze guy is merely a filthy fellow Millenial. Slashdot taught me those are all useless underachieving lazy cunts. So what is it?
So, if in a statement (theorem) nobody spots an error, it's considered proven and true? I wonder how many such theorems are out there in which we have faith?
It's always Corollary 3.12 isn't it? Every single time.
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