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Prominent Mathematicians Rebuke Recent Riemann Hypothesis Proof
Bryan writes "Xian-Jin Li's purported proof of the Riemann Hypothesis (reported on recently) has been rebuked by Fields Medalist Terence Tao. Fortunately, Dr. Li's proof fails alongside a respectable graveyard of previous attempts." Relatedly, jim.shilliday writes "The proof cites and appears to be based in part on the work of the leading French theorist Alain Connes. A few hours ago, Connes posted a comment on his blog stating that the purported proof is so badly flawed that he stopped reading it."
From the summary:
Fortunately, Dr. Li's proof fails alongside a respectable graveyard of previous attempts
Why? I'm probably missing something obvious, I'm not even a mathematician to start with, but...
I mean, we (the world) do want to prove it right (or wrong) one day or another, don't we?
I have to ask, I know for mathematicians this is a big deal and all, but what are the piratical applications for this?
-Ours is the wisdom of Solomon, the magic of Merlyn, the fall of Icaris.
The "proof" is that of Theorem 7.3 page 29 in Li's paper, but I stopped reading it when I saw that he is extending the test function h from ideles to adeles by 0 outside ideles and then using Fourier transform (see page 31). This cannot work and ideles form a set of measure 0 inside adeles (unlike what happens when one only deals with finitely many places).
The proof, and the rebuke, only proved my theory that there is a distinct surge in advil usage when something like this is posted on /. or digged.
Feed the need: Digitaladdiction.net
Well duh this is what we have been saying - this is a preprint and is likely to have errors. Whether or not they can be repaired is open to question.
Wiles' proof of Fermat's last theorem took a long time to go through the review and repair process. And there was at least one pretty hard problem that had to be fixed.
Slashdot's "journalistic" process really suxors when it comes to this sort of stuff.
Oh come on, you were almost there! How about:
"Renowned Researchers Rebuke Recent Riemann Reasoning"
The submitter used stronger language to describe the comment than the comment itself. Connes just said "The 'proof' is that of Theorem 7.3 page 29 in Li's paper, but I stopped reading it when I saw that he is extending the test function h from ideles to adeles by 0 outside ideles and then using Fourier transform (see page 31). This cannot work... "
I'm not sure, but the way I read that is the quote is saying that the mathematician whose work was the basis for the proof started to read it and he (the mathematician) stopped reading.
From the link pointing to Connes blog ...
Of course, I don't understand anything in the above other than "I stopped reading". Meaning, "your work was so wrong on page 2, pages 3 and up are irrelevant".
Cheers
Lost at C:>. Found at C.
My husband is a mathematician, and he gets emails weekly from crackpots claiming to have disproved the proof of Fermat's Last Theorem or having proven the Riemann hypothesis or whatever. You can submit anything to the ArXiv, this shouldn't have even been news in the first place until it was confirmed.
Warning: Apple/Nintendo fangirl. Likes her electronics cute & cuddly. May be rabid.
Yeah, the AC is a member of a previously uncontacted Amazon tribe, you insensitive clod!
Warning: Apple/Nintendo fangirl. Likes her electronics cute & cuddly. May be rabid.
Yes, why don't you tell the Fields medalist how to make himself look good? I'm sure he needs your help desperately. Jeebus, you know that a Fields medal is objectively harder to get than a damned Nobel prize, right?
He did critique the 'proof' objectively. The claim was that by looking at the function on a certain domain ("ideles" whatever those are), one could look out from there and see how it would have to behave elsewhere ("adeles"). However, the "ideles" aren't big enough to give a good viewpoint of what's going on (i.e. the function at the ideles is not necessarily representative of the rest of the function). If you only look at multiples of 2pi, you could "prove" that sin(x)==0. Just because you or I couldn't notice the obvious problem in the RH proof, doesn't mean that it doesn't merit quick dismissal. Sometimes obvious mistakes are made in math (some would say that only obvious mistakes are made - but they are only obvious once they are pointed out).
"They were pure niggers." – Noam Chomsky
If you are quite certain of that, then you are also quite wrong.
A better translation would be 'FAIL!'
Having been through the peer review process with my work many times I'm familiar with this sort of thing, believe me, the statement in the original comment is nasty if your the author.
I can see why the submitter edited it, because people unfamiliar with the peer review process probably wouldn't get what a kick in the teeth the sentence is.
A learning experience is one of those things that say, 'You know that thing you just did? Don't do that.' - D. Adams
When someone has a 40-page purported proof of a famous difficult theorem, any mathematician will stop reading it after the first blatant error. It is up to the author to fix his own mistakes, and before they do so the whole thing is worthless.
Why? Li is stating "I base my proof on X". Connes says "I see you've based your proof on X. I'm quite content that X doesn't work." Game over. If the fundamental assumption is wrong, what is gained from going on? If you read a paper that started "assume the square root of 9 was 3.1", do you *really* need to read all of it before you decide "this fellow might be off track."?
What? Fail.
Just wanted to point out that Professor Connes is also a Fields medalist (1982).
I guess it is a testament to Xian-Jin Li excellent reputation and the importance of the topic that these two mathematical superstars took the time to look at his proof.
The proof was a legitimate effort by a non-crackpot, but the ideas in it were well known to specialists in the field and were generally understood to not be powerful enough to crack the problem. So the errors were found fairly quickly. Scott Aaronson's post Ten Signs that a claimed mathematical breakthrough is wrong item #10 may be helpful in understanding what happened.
Yes it will. It's electric.
"Rebuke"is not a technical word and is certainly not what happened.
The whole thing was a bit more polite than the way it has been descibed here - as anyone who follows the link will find, at least.
When you come to the point in the paper where the author divides by zero, there's generally not much point in continuing on.
Who modded the parent "Troll"? I disagree with the parent, but I see absolutely no reason to call him "troll". I think people tend to assume bad faith, even when good faith is possible and often the most likely possibility.
"Oh, tough talk for someone with only one Fields medal!" -- Wernstrom (to Farnsworth)
I suffer from attention surplus disorder.
me too.
Three o'clock is always too late or too early for anything you want to do. - Jean-Paul Sartre
Actually, factoring prime numbers is not NP complete, as it has already been proven to be in P on Quantum computers. So, if factoring were NP-complete, then we could very happily say that P=NP.
Li's already posted revisions since the original two that were up when this first appeared here. I wonder if those being critical have read the most recent version.
I didn't mean to suggest that Connes disapproved of the proof, just that he found a problem that he believed was a deal-breaker and therefore saw no reason to read on. As others have noted, the proof's author has since revised it, apparently in response to the comments by Profs Tao and Connes.
Jim Shilliday
Yeah, this is becoming a real problem with the preprint journals. Media groups like New Scientist will run a hyped-up story on some "ground-breaking new development" which will have propagated through the blog echo-chamber before other scientists have even had a chance to review it. It's not enough for the media to completely butcher the science they do present, now they have to present results which haven't even had cursory review. It's no wonder the public doesn't trust science considering what is is being presented to them.
It also creates unnecessary drama within the science community by means of the Leonardo DiCaprio affect - the more people hype a star the more everyone else hates them. The author of these papers are usually legitimate scientists who just made an honest mistake, whose only crime was submitting their preprint to ArXiv just like thousands of other scientists. But now they are suddenly being framed as "genius underdog" / "cocky attention whore" by the media and scientists.
The only reason that the preprint journals exist is as a loophole to get around normal journals posting rules. I'm really hoping that preprint journals will fade away as more reviewed papers are published for free X months after their journal publication date.
I think Connes was refuting the proof which is a more neutral term than rebuke (which means telling off).
Interestingly enough, this rebuke has also disproved what is known as the "Reindeer Effect"
Particle Physicist: There is either a black sheep in Scotland or there is a stationary black sheep somewhere but I cannot say with certainty that there is a stationary black sheep in Scotland and, for that matter, I'm not really sure Scotland exists.
Biologist: A sheep in Scotland is expressing the "black" phenotype.
Geneticist: Color? Boring, solved problem. Ask me why he is antisocial.
Evolutionary Geneticist: I know why there are black sheep.
Creationist: No he doesn't!
Philosopher: They're both right.
Computer Scientist: black_sheep++
C Programmer: q++
Perl Programmer: $_[$&]++
PHP Programmer: I'm busy looking for how to increase count of variable by one, but haven't found the answer on Google, and will eventually use a system call to execute the Perl guy's solution*
Liberal Arts Major: Its a sheep of color, people.
* You would laugh less at this if *you* were the guy trying to read through and analyze 125 pages of outsourced PHP which uses this "solution" 30 times, invariably calling code that has already been used for Perl golf practice, with sparse comments written only in Japanese.
Help poke pirates in the eyepatch, arr.
A proof is a chain of deductions, if one link in the chain fails catastrophically the entire chain is invalid. That's what happened here.
Justice is the sheep getting arrested while an impartial judge declares the vote void.
I read some of the comments after I posted my first comment. I particularly point out one where the one who posted claims to be working partime for a Mathematical Journal. His comments that a Crank sents one page material on a weekly basis. He may be a crank but I don't subscribe to the fact that one page paper writen in some format is always a requirement for Mathematical publication. It implies that a person who does the hard part of the work also has to have the skill of a 'glorified stenographer or Secratary' to make his or her work published for others to scrutny. Such comments are illfounded. A page or many pages doesn't make any difference to me as long as the contents are valueble. Mathew Cherian
Please check on httpp://www.riemann.co.in for my proof for Riemann Hypothesis. I believe it has meaning in the Engineering and Physical Sciences. May be some times in the Bhor Atomic Models etc; It is for other field specialists to figure out how this phenomenon is associated with their field. Mathew Cherian