## Prominent Mathematicians Rebuke Recent Riemann Hypothesis Proof 172

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."*
## Why "fortunately"? (Score:5, Interesting)

From the summary:

Fortunately, Dr. Li's proof fails alongside a respectable graveyard of previous attemptsWhy? 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?

## Re:Why "fortunately"? (Score:5, Informative)

I guess they mean that there's no shame in having failed, since many other respectable attempts also failed.

## Re: (Score:2, Informative)

Li did respectable work once and has made a large faux pas in his handling of this affair, but it is now over. Let's focus on something far more interesting if we're talking about the Riemann Hypothesis - a wonderful (translation of a) transcript of an interview with Atle Selberg [ams.org], which makes fascinating reading.

## Re:Why "fortunately"? (Score:5, Insightful)

They're just being polite by pointing out there's no shame in failing to prove the Riemann Hypothesis, since it has frustrated the attempts of many a prominent mathematician so far.

## Re: (Score:3, Interesting)

## Re:Why "fortunately"? (Score:5, Insightful)

Having said that, Li is no crank. I had not heard of him, but that's no surprise since I'm not a number theorist. But he has published several refereed papers in this area, has a position at BYU, and really ought to have known better than to explode on the scene like this.

I've gotten communications from genuine crackpots, wanting my comments on their work. Early in my career, I wrote back, gently pointing out the mistake. To my horror, friends then received slightly modified but still absurd drafts, listing me as a collaborator! Li is a real mathematician, probably with poor social skills, and a bad proof.

## Re:Why "fortunately"? (Score:4, Informative)

Are you sure about that? Getting a paper onto arxiv.org doesn't seem to be that hard, and there's lots of ways to find out about it (RSS feed, etc.). He may not have had any reason to believe that he'd get this sort of attention, as he may have thought everyone involved would simply assume that it wasn't worth much, not having been peer reviewed.

While I love the free and open flow of information that arxiv represents, this is hardly the first time that something has been posted on there and subsequently blown out of proportion. The Internet at large doesn't seem to really understand arxiv.org, that just because someone's got a fancy LaTeX paper up claiming some wild thing doesn't mean it's credible. A paper on arxiv.org shouldn't even be understood as being endorsed by the author, let alone "science". I always love when somebody backs up their argument about physics with a link to arxiv.org, it's like a red flag that it's time to just pack it in, you're not going to get through to this person, because they only understand the trappings of science, not the actual process.

## Re:Why "fortunately"? (Score:4, Interesting)

...with a link to arxiv.org, it's like a red flag...

An even redder flag is a link to New Scientist as if its some peer reviewed source. NS references arxiv.org heavily no matter how stupid the claims (aka Zero Point Energy).

## Re: (Score:2)

## Re:Why "fortunately"? (Score:5, Informative)

I believe you're mixing this up with another hard problem that hasn't been proven yet. You're thinking about the NP = P [wikipedia.org] problem. The difference is that here we don't know what will be the outcome, whereas for the RH most people assume it's true. Having a proof for this wouldn't really change anything (apart from validating large parts of mathematics that assume it is true)

## Re: (Score:3, Interesting)

## Re: (Score:2)

You, however, make a strong claim:

There's basically no chance whatsoever that the eventual proof will involve a faster way to factor numbers.

Do you have a reference?

## Re: (Score:3, Informative)

I am a mathematician, and there's no reference for this claim, but RH is a problem in analytic number theory and none of the credible work on it (meaning not by random crackpots) uses anything involving factoring. Why would an algorithm to factor numbers have any use at all, especially since this isn't something that can be proven computationally anyway?

The best we've done algorithmically by assuming the Riemann hypothesis is come up with faster algorithms to test primality (like an unconditional Miller-Ra

## Re: (Score:2)

Worse, there are actually counter-examples -- although they are a curiosity only, being slower than the more widely used and known algorithms.

I hope he's

nota mathematician, because it's rather bad form to claim opinion as fact in that field.## Re: (Score:2)

## Re: (Score:3, Insightful)

For the record, most people don't know what P or NP is ;)

## Re: (Score:2)

You meant "factoring

INTOprimes", of course. Your typo is a common one, but people tend to be extremely unforgiving about that one, since idiots who don't know squat about the subject (such as Bush) have famously made it, too, presumably without understanding how fantastically ludicrous the phrase is. (I'm sure in your case it was merely a slip; I'm just saying...)As for its complexity, you mig

## Re:Why "fortunately"? (Score:5, Funny)

[..] lead to the undermining of current encryption methods, which depend on the difficulty of factoring large prime numbers.That's a trivial problem.

All prime numbers have two factors: 1 and itself.

Goodbye encryption :-)

## Re: (Score:2)

## Re:Why "fortunately"? (Score:5, Informative)

One possible explanation for your understanding (which in my understanding, is wrong), is the Miller-Rabin primality test algorithm.

The primality problem (telling whether a number is prime), although hard, was never proved to be NP-complete.

The Miller-Rabin primality test is a (actually, the 1st and possibly the only) polynomial deterministic algorithm that is based on the Riemann hypothesis (polinomial deterministic meaning "fast and accurate"). Proving RH would prove that Miller-Rabin is exact and therefore shown that primality testing is in P.

http://en.wikipedia.org/wiki/Miller-Rabin_primality_test [wikipedia.org]

Unfortunately, algorithm freaks were faster than math freaks (well, the algorithm freaks involved were math freaks too) and a new algorithm called AKS was developed that did everything Miller-Rabin did without relying on the Riemann Hypothesis.

http://en.wikipedia.org/wiki/AKS_primality_test [wikipedia.org]

So, to this day, we know primality testing is polynomial. The _real_ problem in cryptography is prime *factoring* (if it's not prime, then find 2 numbers that when multiplied produce the original number). Although it is not know whether that problem is P or NP-complete or both, it is believed to be outside NP because it is much harder than plain primality testing.

http://en.wikipedia.org/wiki/Integer_factorization [wikipedia.org]

## Re: (Score:2)

I think you mean that it's outside P. It's obviously in NP, since we can verify any possible factorisation in polynomial time.

## Re: (Score:2)

Indeed, I meant NP-complete both times. Thanks for pointing it out.

## Re: (Score:2)

not at all.## Re: (Score:2)

If by 'this', you mean the original Riemann zeta hypothesis, yes, there are literally thousands of mathematical proofs which are 'conditioned by Riemann' that is, they assumed the Riemann hypothesis was true so they could do the rest of the math.

Jim Holt, writing in the essay compilation "Year Million" (ed. Damien Broderick), has said that the Reimann hypothesis was so central to further mathematical progress that its truth just had to be assumed, implying that large numbers of mathema

## what does it all mean, Basil? (Score:2, Funny)

## Re:what does it all mean, Basil? (Score:5, Funny)

## Re:what does it all mean, Basil? (Score:5, Informative)

There are a lot of results based on assuming the conjecture is true, including a variety of factoring and root finding algorithms that are computationally very useful.

Until it is proven you really don't know if these algorithms are giving correct answers.

This is why it is so important and has a big prize associated to it.

## Re: (Score:2)

The conjecture doesn't affect whether the answers are correct - that's easy enough to verify (even, despite several follow-ups, if the algorithm claims values/factors are prime - even before it was shown that primality testing is in P, there were known ways to prove a value was prime, showing that PRIMES is in NP).

However, it does affect the running time analysis. There are several algorithms that have a run-time analysis that says something like "Assuming the Riemann Hypothesis, the running time is ...."

S

## Re: (Score:3, Insightful)

Unless it says the number is prime (you have to trust there are no factors) or gives factors that aren't primes.

## Re:what does it all mean, Basil? (Score:4, Interesting)

Since the work based on the assumption that the hypothesis is true is in itself valuable, it will still be used.

It's just that a proof, if found, will elevate who-ever finds it to the status of mathematical superstar.

Consider this, we are still finding proof of various of Einstein's theories, but work based on his has been of real value for decades.

Here's another example that makes me sound all clever because I know it.

Newtons equations, and his entire body of work, completely failed to explain how it is that the moon can orbit the earth while the earth orbits the sun, and we *still* don't have the equation to explain that bugger.

There are specific n-body solutions, I've written one myself, but a solution for the general case? Nope, never been done.

Louis Pasteur spent most of his life on that particular problem, as have many other prominent scientists, all to no avail. We found a use for Newtons work regardless, and Einstein extended it successfully, even with that glaring hole.

## Re:what does it all mean, Basil? (Score:5, Insightful)

You are mixing the basic tenants of physics and mathematics, not a good thing to do. Science is a mix of inductive and deductive logic, math has a higher standard and doesn't admit inductive proofs.

Three guys were vacationing in Scotland. One was an astronomer, one a physicist and one a mathematician.

In their travels they chance on a black sheep grazing in a field.

Astronomer: All sheep in Scotland are black

Physicist: Some sheep in Scotland are black

Mathematician: There is one sheep in a field in Scotland that is black on at least one side.

## Re: (Score:2)

## Re: (Score:3, Insightful)

Mathematician: There is one sheep in a field in Scotland that is black on at least one side.

I thought he was going to say all sheep in Scotland are grey?

Anyhow, what's with there's no inductive proof in Mathematics? There are many many inductive proofs, even at high-school you write "proof by induction" quite a lot. Google it, all the top hits are mathematical.

http://en.wikipedia.org/wiki/Mathematical_induction [wikipedia.org]

## Re: (Score:2)

Yes you are right - I should have been more clear about the difference between induction in the context of science vs. math.

An inductive proof in math is the process of proving A is true for all members of B by first proving that A is true for one member of B and then proving that if A is true for one member of B is it is true for other members of B instead. Mathematicians call it an inductive proof however it is proven for all possible existing cases using deductive logic.

In science induction is the concep

## Re: (Score:3, Informative)

Inductive is a philosophical term, the inference of new facts based on previously known ones. In Physics, this means using experimental data in order to make general assumptions about the universe.

In mathematics, we use the term tongue-in-cheek, to refer to a particular and useful consequence of the least-element axiom. It resembles inductive reasoning, but it is indeed quite more rigorous.

## Some more variations of black sheep counting (Score:2)

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.

Compu

## Re: (Score:3, Informative)

Addressing the latter first, Newton's equations describe to a very high degree of accuracy (perfectly, in the limit of ignoring relativistic and other high-order corrections) the interaction of any arbitrarily large number of bodies. The fact that we cannot solve these equations is in no way

## Re:what does it all mean, Basil? (Score:4, Informative)

Nope. We can do calculations that involve n-bodies, of which obviously 3-body is part, but they involve using the 2-body solution of Newton for all unique pairs in a simulation.

A separate general three body solution probably does exist, but no-ones found it.

If found, it would quite possibly revolutionise n-body modelling, and prove useful to space science (if, and only if, it sped up calculations), but I doubt astronomers would care much.

## Re: (Score:2)

If your interested my specific solution resides in this software (of my own creation).

http://code.google.com/p/nmod/ [google.com]

## Re: (Score:2)

No its not trivial to check that. Factorizing a 1024 bit number you really really want to get it right in the first go, if the algorithm isn't proven you can only hope whatever you get returned is correct.

## Re: (Score:2)

potentialbut not guaranteed factor of N, it takes merely one trial division to see if it was an actual factor or not.You're probably mixing it up with probablistic primality tests, although even there "you can only hope" is not how we proceed in practice. Further details widely available via google.

## Re: (Score:2)

Ok, so you use this algorithm, checked the results and find the result is wrong. Guess what!! YOU HAVE JUST WON $1,000,000 because you have proved the Reinmann Conjecture is wrong. But that won't help you very much if you are using it to calculate a re-entry trajectory.

Up until then though all that code you have put in your systems is worthless, a waste of time and is probably generating false alarms due to bugs every now and then.

Nah, it really is much better to have the proof.

## Re: (Score:2)

Ok, so you use this algorithm, checked the results and find the result is wrong. Guess what!! YOU HAVE JUST WON $1,000,000 because you have proved the Reinmann Conjecture is wrong. But that won't help you very much if you are using it to calculate a re-entry trajectory.If you won the $1,000,000, you could easily just

hiresomeone whocancalculate the re-entry trajectory if disproving the Riemann conjecture doesn't help.Of course the ultimate would be to demonstrate the proof or disproof of the Riemann conj

## Re: (Score:2)

If you are in the vehicle that is re-entering you aren't going to care about the prize nor have time to hire anyone.

## Re: (Score:2)

I had to go look it up after you asked... apparently to mathematicians, there are plenty of practical applications. See http://en.wikipedia.org/wiki/Riemann_hypothesis [wikipedia.org] for a few examples. Neither of them made sense to me yet, and I've already had coffee. If they are looking for one example where this theory is not true, and offering a million bucks, someone is sure to put a couple yellow dog games console clusters together and find out soon enough. (either that or prove Doom is written by zombies who don't

## I don't know about you all... (Score:5, Funny)

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).## Re: (Score:2)

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).## Re:I don't know about you all... (Score:5, Insightful)

It's called "Proof by Intimidation":

using the formula:

[ some formula ]

it is trivial to see that:

[ some other formula out of nowhere ]

therefore, combining the above, we can arrive at the easily obtained answer:

[ some MATLAB result ]

Don't forget, it works both ways; the people marking your assignment don't want to admit that they can't see the so-called "trivial" derivation.

## Re: (Score:2)

I know a paper that uses that approach. "And it is obvious that the inverse operation may be be accomplished by departitioning the spectrum...."

A colleague and I actually looked into the "obvious" problem and found some pretty powerful results that the author of that paper is going to be kicking himself for missing.

## Re: (Score:2)

I agree that's the beauty of science... I don't think the situation I described was quite the same though.

I was pointing out that because the guy used the "proof by intimidation" approach (I love that term) instead of actually properly working out the theory himself, he missed all the elegance that was waiting to be discovered.

## Re: (Score:2)

I agree. And on the occasion that it does work, it's because of a grader's laziness, not pride. And I would think that the chance of pissing off a grader will be higher than the chance of getting away with this.

## Re: (Score:2)

And I would think that the chance of pissing off a grader will be higher than the chance of getting away with this.

Yes, you are right. When I was a grader, when someone said things like "it is easy to show" or "trivial", I took a point off for every step skipped.

## Re: (Score:2)

Well, it's sort of like gambling. At times, I think I'm just missing one step in an otherwise complete proof. And I'll write "I can't get this step", or "We see that...", depending on how honest I'm feeling. But what if it really is a trivial step that I just can't see because I'm so short on sleep? In this situation, I could see an advantage in bluffing. Not that it's nice to do so--a student grader might frustratedly try to see whether the claim really was true, while a teacher would know at a glance and

## Re: (Score:2)

## Re:I don't know about you all... (Score:5, Insightful)

Use the "Star Trek" filter:

he is extending the test function h from [ tech ] to [ tech2 ] by [ tech 3 ] and then using Fourier transform ... This cannot work and [ tech ] form a set of measure 0 [ tech 4 ] (unlike what happens when one only deals with finitely many places).When he moved from one set to another and did the Fourier transform, he forgot that he ended up with an empty set instead of a finite number of points because that's apparently a property of whatever the hell he was talking about.

## Re:I don't know about you all... (Score:4, Informative)

## Re: (Score:2, Insightful)

No shit. I took a minor in math, really loved and grokked things, up to a certain level. Beyond that I suddenly have no fscking clue what they're even talking about. When looking at similar levels of, say, biology, I at least have a faint idea of what it's about. High-level math is weird.

## Re: (Score:3, Interesting)

This is not all that bad.

Probably many slashdotters are familiar with the discrete Fourier transform (used in JPEG encoding, incidentally). The DFT for sequences of length n fits together nicely with the DFT for longer sequences whose length is a multiple of n. If you try to put all these DFTs for sequences of different length together in a certain way and combine them with the continuous Fourier transform, you end up with something called the adelic Fourier transform. (That's a little bit different

## Re: (Score:2)

Well kinda sorta he had a function h valid for integers, and he wanted it to be valid for all rational numbers, so he just defined it as 0 everywhere else.

I remember the example from my university math class about function defined in exactly that way. The question was if it is possible to calculate an integral of the function. The conclusion was that it is impossible, because of something I forgot, but it is related to definition of the integral, which requires some very basic kind of continuity and this function lacks such feature. (I guess that some limes must exist, and it does not exist here as it always go 1 to 0 unpredictably.)

Then he took a continuous and not a discrete Fourier transform of the resulting function, maybe getting an infinite series of coefficients that diverge. Of course keep in mind that I'm just talking out of my ass.

Since the definition of Fo

## Ow my head (Score:5, Funny)

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.

## Re: (Score:3, Funny)

I stopped reading when I saw that he is using Advil, this cannot work when it is well established that Excedrin is the preferred migraine reliever.

## Preprint, not a reviewed paper (Score:5, Insightful)

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.

## Re:Preprint, not a reviewed paper (Score:5, Funny)

Slashdot's "journalistic" process really suxors when it comes to this sort of stuff.Wel of course it does. Slashdot is journal

ology, not journalonomy.## Re: (Score:3, Interesting)

The comments made by Tao and Connes are the sort of comments one would make if the paper was irrevocably flawed. For instance, Tao notes that "the decomposition claimed in equation (6.9) ... is, in fact, impossible; it would endow the function h ... with an extremely strong dilation symmetry which it does not actually obey. It seems that the author was relying on this symmetry ..."

In more simple terms: Partway into the paper the author proved something that is definitely false; he then relied on this false

## Preprints are not ideal. (Score:3, Insightful)

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 bein

## Lazy title selection (Score:5, Funny)

"Renowned Researchers Rebuke Recent Riemann Reasoning"

## Re: (Score:2)

-1 Alliteration;)

## Re: (Score:2)

## So many errors (Score:1)

## Re: (Score:3, Funny)

## What a shock... (Score:5, Interesting)

## Re:What a shock... (Score:5, Interesting)

I work part-time for a couple of mathematics research journals and we do get the occasional crank submission. There's one guy who's been sending us, on average, a 'paper' every week or so for the past few years: typically a single, badly-written page of gibberish (we're talking Time Cube [wikipedia.org] standard lunacy here) which is clearly not the work of someone who's ever seen a real mathematics paper. We've never responded to him, or even acknowledged any of his submissions (helpfully he prints his return address on the back of the envelope, so these days they go straight in the bin, unopened and unread) and yet he still keeps sending them in.

The arXiv also tends to get its fair share of crank submissions, usually elementary attempted (but trivially broken) proofs of things like the Goldbach Conjecture, Fermat's Last Theorem and the like - I'm assuming that the really mad stuff is filtered out by the moderators.

In contrast, at a quick glance to my nonspecialist eyes (I'm a knot theorist) Xian-Jin Li's preprint looks like a genuine (if flawed) attempt by a serious, qualified mathematician who specialises in the relevant area. Fair play to him for trying, though. I'm also not sure I'd characterise Terence Tao or Alain Connes' refutations as 'rebukes' - they looked more like dispassionate analyses of the paper's flaws to me, the sort of discussion you'd expect from the peer-refereeing process.

## Re: (Score:2)

(I'm a knot theorist)So how is work coming on the time cube knot ?

## Re: (Score:2)

IANAM, but I love to read about it. Maybe you can answer this for me, since you are a knot expert. ;-)

I've read that you can't have knots in 4-space, so how do 4-dimensional beings tie their shoes?

## Re: (Score:2)

I've read that you can't have knots in 4-space, so how do 4-dimensional beings tie their shoes?Velcro, but unfortunately there are eight pieces to a velcro set there. (The proof of this is, of course, trivial, per novakyu (636495)). All sentient creatures in 4-space must therefore have at least a pair of hyper-thumbs (thumbs cubed), and not just supra-thumbs (thumbs squared), QED.

## Re: (Score:2)

I've read some of Rudy Rucker's stuff, but don't recall if I've read that one. I'll have to look it up. I just discovered "Dimensions", the movie made by some French mathematicians with POV-Ray, which I've used since the early 90's. The movie is really cool and talks about geometry, particularly in regards to 4-space, and of course is very visual (we're talking eye candy). The coolest part was that my kids loved it. They sat with rapt attention while this movie is demonstrating geometry proofs and show

## Re: (Score:2)

This person is obviously a lawyer. He is preparing you for the real and very important letter that he is obliged by law to send you but really does not want you to read before it is too late.

## Re: (Score:3, Funny)

## Re: (Score:3, Funny)

See if she weighs the same as a duck?

## Prof Connes also a Fields medalist (Score:5, Informative)

Just wanted to point out that Professor Connes is also a Fields medalist (1982) [wikipedia.org].

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.

## Re: (Score:2)

Note that I could have refuted this proof, but who would have believed me?

So what papers have you published?

Li lost his honnor and should seppuku himself to preserve it.

Wrong nationality. Plus you spelled honor wrong. Failure all around.

## Re: (Score:2)

You spelt honour incorrectly as well

I use American spelling, not British.

but 'wrong' is your real failure here

I don't even know what this means.

## Re: (Score:2)

I believe the correct way to put it would have been "Plus you spelled honour wrongly". Consider if you used the word 'incorrect' instead of 'wrong' - "Plus you spelled honour incorrect" is wrong - it should be "Plus you spelled honour incorrectly".

## Re: (Score:2)

"spelled honor wrong" is perfectly correct, idiomatic American English. I did some quick searches to back this up:

http://www.usingenglish.com/forum/ask-teacher/101-wrong-wrongly-spelled-spelt.html [usingenglish.com]

http://dictionary.reference.com/search?q=wrong [reference.com]

See the many examples of "wrong" used as an adverb in the dictionary reference. I think it's clear that the original poster is used to British English, and it sounds like you are too.

## there was no rebuke (Score:5, Insightful)

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 [scottaaronson.com] item #10 may be helpful in understanding what happened.

## Re: (Score:2)

Like if I tell you my plan for making a 1000 mpg car, and it turns out to depend fundamentally on steel being lighter than air. This dependence might be subtle enough that neither of us realized it at first, so I'm not necessarily a crackpot for coming up with such a plan.I thought i was the only one who made those mundane mistakes.

## Re: (Score:3, Interesting)

## Re: (Score:2)

Like if I tell you my plan for making a 1000 mpg car, and it turns out to depend fundamentally on steel being lighter than air. This dependence might be subtle enough that neither of us realized it at first, so I'm not necessarily a crackpot for coming up with such a plan.

Your post makes a good point, but this is the worst car analogy I've ever seen on Slashdot :)

## Sensational (Score:2)

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.

## Refute, not rebuke (Score:2)

I think Connes was refuting the proof which is a more neutral term than rebuke (which means telling off).

## Re:Not Making Yourself Look Good Here (Score:5, Insightful)

## Re: (Score:2)

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 ...

## Re: (Score:2)

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

nastyif 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.

## Re:Not Making Yourself Look Good Here (Score:5, Insightful)

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).

## Re: (Score:2)

## Re:Not Making Yourself Look Good Here (Score:5, Insightful)

## Re: (Score:2)

When you come to the point in the paper where the author divides by zero, there's generally not much point in continuing on.

## Absurd moderation (Score:2)

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.

## Re: (Score:2)

## Re: (Score:2)