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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
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.
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.
So... Einstein would have been banned from theoretical physics using your rules. His original theory of Special Relativity was wrong in some cases, so we got "general" relativity as a correction... With your rules we would have banned him.
I wouldn't be too quick to "ban" anybody, unless they *should* have known better or they obviously violated the rules of math with their work and tried to hide it. You punish willful deception (those who are lying and know it), but mistakes and oversights are part of the human experience and why we have peer reviews. If you get found to have made mistakes or overlooked something, your reputation will suffer but you should be allowed to correct and proceed.
"File to fit, pound to insert, paint to match" - Aircraft Maintenance 101
Famous Russian Troll error, unable to incorporate THE and A into the language.
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.
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?...
Why is this voted up!?!?
General Relativity was not a correction to Special Relativity. They're about completely different things! Special Relativity is about the speed of light being a constant in all reference frames and the implications of that. General Relativity is about how mass distorts spacetime giving rise to gravity.
I agree with your point that bans are bad, but stop trying to sound smart using Einstein as an example until you learn more about him, OK?
Special Relativity is about the speed of light being a constant in all reference frames and the implications of that.
If you actually read Einstein's original paper on special relativity, you'll find that it's about electrodynamics.
sub f{($f)=@_;print"$f(q{$f});";}f(q{sub f{($f)=@_;print"$f(q{$f});";}f});
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
This is not a published paper. It is being reviewed now to determine whether it should be published. That's partially why peer-review exists in the first place. Mochizuki just made his opus available to other mathematicians so that they can determine whether it makes sense to them. That's how research works.
"What lies behind us, and what lies before us are tiny matters compared to what lies within us." Ralph Waldo Emerson
On the one hand, I would like to give Peter and Jacok a big round of applause for taking the time to understand and publish the error in the original publication (shoveling stool). On the other hand, even though it is still possible that there may be a solution if Mochizuki was really that confident to have claimed to have the solution instead of asking for review, then given what I know about Japanese culture I would be more worried that Mochizuki is heading towards Aokigahara right about now than the possibility that he could be somehow "banned" from submitting a PDF to the interwebz.
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.
If you actually read Einstein's original journals, you'll find that it's about the subjugation of the working class.
Ban is too strong. Right: +10 points, wrong: -2
Slashdot, fix the reply notifications... You won't get away with it...
...and everyone wrong here should be banned on slashdot?
Slashdot, fix the reply notifications... You won't get away with it...
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...
Have NBC and CBS confirmed it?
How about CNN?
All of it or none of it?
FTFY
"Nine times out of ten, starting a fire is not the best way to solve the problem." - my wife
re quote "So... Einstein would have been banned from theoretical physics using your rules. His original theory of Special Relativity was wrong in some cases, so we got "general" relativity as a correction... With your rules we would have banned him." no theoretical physics is what it says on the tin theoretical , you could come up with a theory that the universe is just a magnified representation of a bacteria that resides in the gut , and it would still be valid theoretical physics , then its up to scientists to ether prove or disprove the theory , if proven it becomes science fact if not then try again , that's how theoretical physics works , but for science to say its this or that then you would be banned for giving false or inacurate results that you declared as facts not theory
You have just created the best incentive ever to NOT say that something is wrong even if you're 99.9% sure it is.
-=This sig has nothing to do with my comment. Move along now=-
...and everyone wrong here should be banned on slashdot?
*tumbleweed*
To have a right to do a thing is not at all the same as to be right in doing it
I could live with that, if folks where actually keeping score.
Personally, I'd give points for coming up with a theory and trying to prove it correct without resorting to deception, even if you are eventually shown to be wrong. Such things happen, folks propose ideas which turn out to be bad all the time; it's part of the process. My issue is when folks propose bad ideas, then insist they must be true and resort to lying and deception to gain notoriety. If you are honestly trying, great, if you are not being honest about the idea's problems, then that's bad.
So, being credited with coming up with a theory that proves true is good for positive points based on the importance of the theory. If you propose a theory that turns out to be false, then that's neither good or bad. If you propose a theory and make grandiose claims in the press then use your notoriety to bury competing theories or those who are pointing out flaws in your theory, THEN I'm likely to be done with believing your claims until independently verified.
"File to fit, pound to insert, paint to match" - Aircraft Maintenance 101
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?
If you come up with an idea and it's wrong, you're banned from Ideas.
*BANNED*