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DEAL: For $25 - Add A Second Phone Number To Your Smartphone for life! Use promo code SLASHDOT25. Also, Slashdot's Facebook page has a chat bot now. Message it for stories and more. Check out the new SourceForge HTML5 Internet speed test! × ## Claimed Proof of Riemann Hypothesis345 An anonymous reader writes "Xian-Jin Li claims to have proven the Riemann hypothesis in this preprint on the arXiv." We've mentioned recent advances in the search for a proof but if true, I'm told this is important stuff. Me, I use math to write dirty words on my calculator. This discussion has been archived. No new comments can be posted. #### Claimed Proof of Riemann Hypothesis More Login ## Claimed Proof of Riemann Hypothesis Comments Filter: • #### Dirty Words (Score:5, Funny) on Wednesday July 02, 2008 @11:38AM (#24031621) Homepage Me, I use math to write dirty words on my calculator. Such as 80085? • #### Re:Dirty Words (Score:5, Funny) by Anonymous Coward on Wednesday July 02, 2008 @11:39AM (#24031671) 5318008 • #### Re: (Score:3, Interesting) in portuguese, 50135.50738 (nice breasts). • #### Re:Dirty Words (Score:5, Funny) on Wednesday July 02, 2008 @11:44AM (#24031763) No, you mean 5318008 or for the slashdot crowd, 55378008 • #### Re:Dirty Words (Score:5, Funny) on Wednesday July 02, 2008 @11:56AM (#24031985) No for the slashdot crowd it would be: 58008uÉÉ . Because obviously we all have calculators that support unicode text entry. • #### Re:Dirty Words (Score:5, Funny) on Wednesday July 02, 2008 @11:57AM (#24032019) That would've been a lot cooler if Slashdot supported Unicode. • #### Re: (Score:3, Funny) äOEæ--¥é..."ããï¼ï¼ • #### Re:Dirty Words (Score:5, Funny) on Wednesday July 02, 2008 @12:34PM (#24032637) Homepage At that point, isn't it safe to assume that our calculators can just draw a pair of boobs in 2-bit greyscale? And that we've written apps that simulate what we assume bouncing would look like given our collective lack of experience outside of the pornographic realm? • #### Re: (Score:2, Funny) I had proof of concept Porn on my TI-89 in 2000. • #### Re:Dirty Words (Score:5, Funny) on Wednesday July 02, 2008 @08:56PM (#24038631) Link? Does your project have donation page? • #### Re:Dirty Words (Score:5, Funny) on Wednesday July 02, 2008 @01:23PM (#24033421) Homepage You haven't grafted a color TFT screen to your calculator yet? Who let these guys in? • #### Re:Dirty Words (Score:5, Funny) on Wednesday July 02, 2008 @02:12PM (#24034159) You just gave me the best idea for an iPhone app: Boobies that bounce according to how the phone is bouncing.... • #### Re:Dirty Words (Score:5, Funny) on Wednesday July 02, 2008 @03:16PM (#24035013) Your ideas are intriguing to me and I wish to subscribe to your newsletter. • #### Re:Dirty Words (Score:5, Funny) on Wednesday July 02, 2008 @11:59AM (#24032037) Journal On linux, wouldn't it be ... host:>man 80085 ??? • #### Re: (Score:2, Funny) Newbie... correct spelling is "5318008" and you have to look at the calculator "umop apisdn" Mod me down, I dare you!!! • #### Re: (Score:3, Funny) Nah, if you really want a dirty word, try 71077345... • #### I like to describe my workplace with my calculator (Score:2, Informative) 37047734 • #### Yeah but did they point this out? (Score:5, Funny) on Wednesday July 02, 2008 @11:39AM (#24031645) Journal By using Fourier analysis on number fields, we prove in this paper E. Bombieri's refinement of A. Weil's positivity condition, which implies the Riemann hypothesis for the Riemann zeta function in the spirit of A. Connes' approach to the Riemann hypothesis. Weather permitting of course. (Just looking on the positivity side) • #### Re:Yeah but did they point this out? (Score:5, Funny) on Wednesday July 02, 2008 @12:18PM (#24032393) By using Fourier analysis on number fields, we prove in this paper E. Bombieri's refinement of A. Weil's positivity condition, which implies the Riemann hypothesis for the Riemann zeta function in the spirit of A. Connes' approach to the Riemann hypothesis. Weather permitting of course. (Just looking on the positivity side) I thought you were randomly babbling, but then I RTFA and realized you were just quoting it... • #### Re:Yeah but did they point this out? (Score:5, Funny) on Wednesday July 02, 2008 @01:01PM (#24033039) Homepage Wait... both of you RTFA? We have a new /. record! • #### Re:Yeah but did they point this out? (Score:5, Funny) on Wednesday July 02, 2008 @01:39PM (#24033651) Homepage Not so fast. I read it -2 times. • #### Re:Yeah but did they point this out? (Score:5, Funny) <<imipak> <at> <yahoo.com>> on Wednesday July 02, 2008 @02:11PM (#24034141) Homepage Journal I imagined I read it, so that's +i. • #### Re:Yeah but did they point this out? (Score:5, Funny) on Wednesday July 02, 2008 @06:48PM (#24037537) Homepage Come on, be real. • #### Tried to RTFA (Score:5, Funny) on Wednesday July 02, 2008 @11:39AM (#24031657) Homepage Man, where's Charles Eppes when you need something explained to you in layman's terms? • #### Re:Tried to RTFA (Score:5, Funny) on Wednesday July 02, 2008 @12:00PM (#24032073) Ummm...I think that WAS layman's terms. For you math geeks, try being a history major and looking at all that. It just looks like a cat walked on the keyboard to me... • #### Re:Tried to RTFA (Score:5, Funny) on Wednesday July 02, 2008 @12:21PM (#24032439) Journal Ummm...I think that WAS layman's terms. For you math geeks, try being a history major and looking at all that. It just looks like a cat walked on the keyboard to me... Are you reading slashdot as some kind of anthropological study? • #### Re:Tried to RTFA (Score:5, Informative) on Wednesday July 02, 2008 @12:17PM (#24032369) Homepage Journal The Riemann zeta function is \zeta(s) = \sum_{n=1}^{\infty} \frac{1}{n^{s}} [written for LaTeX], or "the sum of 1/(n^s) as n goes from 0 to infinity (increasing by 1 repeatedly)" [in more human-readable form]. Riemann was interested in the zeros to this function, where s is a complex number. He conjectured that all zeros (aside from those of the form s = -2c, where c is a positive integer) would have to be of the form (1/2) + ki, where k is a constant and i is the square root of -1. This paper is saying that they've found a way to verify this intuition by patching a hole in a previous attempt. Assuming that everything is correct (a big assumption), this would finally solve a long-standing problem (dating back to 1859). Details of the actual solution are a bit heavy. Those actually interested in this sort of number theory might want to start here [amazon.com]. • #### typo (Score:5, Informative) on Wednesday July 02, 2008 @12:24PM (#24032481) Journal The Riemann zeta function is \zeta(s) = \sum_{n=1}^{\infty} \frac{1}{n^{s}} [written for LaTeX], or "the sum of 1/(n^s) as n goes from 0 to infinity (increasing by 1 repeatedly)" [in more human-readable form]. You have a slight typo. Should be: "... as n goes from 1 to infinity ..." • #### Re:typo (Score:5, Funny) on Wednesday July 02, 2008 @02:47PM (#24034641) Journal The Riemann zeta function is \zeta(s) = \sum_{n=1}^{\infty} \frac{1}{n^{s}} [written for LaTeX], or "the sum of 1/(n^s) as n goes from 0 to infinity (increasing by 1 repeatedly)" [in more human-readable form]. You have a slight typo. Should be: "... as n goes from 1 to infinity ..." You have a slight typo. It should be: "You have a slight typo. It should be: ..." • #### Re: (Score:3, Funny) Okay...I would ask WHY this is important, but someone is ponying up a million bucks for the solution. THAT tells me this is important. I'm not sure if I care why... • #### Re:Tried to RTFA (Score:5, Informative) on Wednesday July 02, 2008 @03:00PM (#24034827) It's important because the zeros of the zeta function tell you how the prime numbers are distributed and prime numbers are to number theory as elements are to chemistry, everything you could care about is built out of them. The RH is also related to host of other more esoteric, but no less important conjectures; the truth of a large part of modern mathematics relies on knowing if the RH is true or false. Although it's unlikely to impact the storage capacity of a flash drive any time soon the zeta function shows up in high energy physics and thus does have real world consequences. • #### Re: (Score:3, Interesting) Here's another easy-to-grasp one: public key encryption (think: credit card purchases online) is dependent upon the use of large primes. Large primes are currently not the easiest/fastest to find - what if you knew better where to look for them? • #### Or, in layman's terms... (Score:5, Informative) on Wednesday July 02, 2008 @02:57PM (#24034787) I just finally found a simple explanation of complex numbers, and just heard of this Riemann Hypothesis, so I may be way off, but let me try to put what (I think) I've figured out so far in layman's terms for the rest of the lost souls: Riemann was interested in the zeros to this function, where s is a complex number. He conjectured that all zeros (aside from those of the form s = -2c, where c is a positive integer) would have to be of the form (1/2) + ki, where k is a constant and i is the square root of -1. Basically, 10 trillian calculations have been done involving certain complex numbers, which all show a clear pattern: if you get an answer of 0, the real part of the number given to the function always seems to be 0.5. As yet, no one has proven this, and so, presumably, no one truly understands why that's the case yet. Also, presumably, when we do understand it, we'll have forward (either in a a step or a leap) in our ability to use complex numbers (and the multi-dimensional calculations they represent. • #### Numb3rs (Score:5, Funny) on Wednesday July 02, 2008 @12:28PM (#24032541) Charles Eppes: Imagine you have an infinite number of plot holes, and you want to test how they compare to imaginary numbers. The Riemann Hypothesis states that I can use the zeros in this formula to predict how bullets will bounce off of concrete to a degree of statistical accuracy that it will actually give me the social security number of the guilty shooter. • #### Re:Numb3rs (Score:5, Funny) on Wednesday July 02, 2008 @02:47PM (#24034643) Homepage Dude, you owe me a monitor. Note to self: Do not drink coke while reading /. • #### Re: (Score:3, Funny) It's like 50 football fields laid in line from here to Riemann. Rieman sounds like a place in Germany. • ####$1,000,000 prize to be collected then if true (Score:5, Informative)

on Wednesday July 02, 2008 @11:46AM (#24031779) Homepage

Was reading wikipedia because I have no idea why this is important, but need to know enough to impress my friends (and by that I mean, alienate).

But I noticed this is such a big deal, theres a cool million waiting for the person that proves it. John Nash in "beautiful Mind" tries to prove this one too. Sorry gladiator... not today!

So yeah, Check it out, notice the offer at the end, after all the completely unintelligible mathematicrap:

Riemann hypothesis

The Riemann hypothesis (also called the Riemann zeta-hypothesis), first formulated by Bernhard Riemann in 1859, is one of the most famous and important unsolved problems in mathematics. It has been an open question for almost 150 years, despite attracting concentrated efforts from many outstanding mathematicians. Unlike some other celebrated problems, it is more attractive to professionals in the field than to amateurs.

The Riemann hypothesis (RH) is a conjecture about the distribution of the zeros of the Riemann zeta-function (s). The Riemann zeta-function is defined for all complex numbers s 1. It has zeros at the negative even integers (i.e. at s = 2, s = 4, s = 6, ...). These are called the trivial zeros. The Riemann hypothesis is concerned with the non-trivial zeros, and states that:

The real part of any non-trivial zero of the Riemann zeta function is ½.
Thus the non-trivial zeros should lie on the so-called critical line, ½ + it, where t is a real number and i is the imaginary unit. The Riemann zeta-function along the critical line is sometimes studied in terms of the Z-function, whose real zeros correspond to the zeros of the zeta-function on the critical line.

The Riemann hypothesis is one of the most important open problems of contemporary mathematics, mainly because a large number of deep and important other results have been proven under the condition that it holds. Most mathematicians believe the Riemann hypothesis to be true.[1] A $1,000,000 prize has been offered by the Clay Mathematics Institute for the first correct proof.[2] • #### Re:$1,000,000 prize to be collected then if true (Score:5, Informative)

on Wednesday July 02, 2008 @11:54AM (#24031953) Homepage

Good explanation here too:
http://www.irregularwebcomic.net/1960.html [irregularwebcomic.net]

• #### Re: (Score:2)

That is probably the best explanation I've seen, thanks! And it makes use of LEGO, another plus!
• #### Re: (Score:2)

http://www.irregularwebcomic.net/1960.html

Great! Now how am I supposed to get any work done.
• #### Tough problems (Score:4, Interesting)

on Wednesday July 02, 2008 @11:55AM (#24031975) Homepage
Part of the reason these problems are so tough because to solve them, you have to understand what the problem is first. I studied the Riemann hypothesis in college for a good week and I'm still not sure where you might begin solving it. Like the Navier-Stokes equations (another big problem with a big prize) solving it will probably require the invention of some new mathematics. Its not simply a matter of dividing by 3 and carrying the 2. I don't know about you but I haven't the slightest idea about how to go about inventing new math. That's the realm of Newton and Einstein, and few others.

New math is the only way to go about solving some of these problems.
• #### Re: (Score:3)

New math is the only way to go about solving some of these problems.

You mean like this? [aol.com]

• #### Re:Tough problems (Score:5, Funny)

on Wednesday July 02, 2008 @12:39PM (#24032717) Homepage

...solving it will probably require the invention of some new mathematics. Its not simply a matter of dividing by 3 and carrying the 2.

If you're carrying numbers when dividing, I guess you are inventing new math :-)

• #### Re: (Score:3, Funny)

It's easier to have just one heavy maths function and one trivial maths function than two heavy maths functions, so division is easiest implemented as multiplication with the inverse of one of the two numbers, inverses being relatively trivial in exponential notation. As only computers operate this way, the grandparent poster is obviously an artificial intelligence.
• #### Re:$1,000,000 prize to be collected then if true (Score:4, Insightful) by Anonymous Coward on Wednesday July 02, 2008 @12:03PM (#24032131) The Riemann hypothesis is considered the most important unsolved problem in math. But, considering the source here (random paper on ArXiv by complete unknown), there's no real reason to believe this paper is correct. The number of incorrect proofs to major mathematics problems every year is staggering. • #### Re: (Score:2) John Nash in "Beautiful Mind" tries to prove this one too. One of the things I remember from the book is that he and his wife had a running joke that all babies know the solution to this problem and then forget it when they learn to talk. Maybe Xian-Jin Li had a flashback. • #### Re: (Score:2) Ahh - here's where it came from: Paul Erdos once said all babies (he used to call them epsilons, because babies are really small!) remember the solution for Riemann Hypothesis. The only problem though is that they tend to forget everything once they reach the age of six month. Found that here [wordpress.com] • #### Re:$1,000,000 prize to be collected then if true (Score:4, Funny)

on Wednesday July 02, 2008 @02:02PM (#24034025)

Step 1: Find 5-month old baby.
Step 2: Interrogate baby from step 1, asking questions relevant to the Riemann Hypothesis.
Step 3: Profit!

Progress so far:
Step 1: Complete.
Step 2: Complete. Reply to question consisted of: "Blah gurgle <splursh> gah hwooo naaae".
Step 3: Incomplete, but I have reduced the problem from one of Mathematics to one of Linguistics. I expect results soon.

• #### Re: (Score:2)

Flashbacks to babyhood, that reminds me of another outstanding film, the directors cut to The Butterfly Effect. If you haven't seen it I highly recommend it though it's definitely not for people who cry easily or women who have lost a child!
• #### Re: (Score:3, Funny)

John Nash in "beautiful Mind" tries to prove this one too.

And I would have succeeded if it weren't for these meddling kids! What do you mean you can't see them?!

• #### Reimann? (Score:5, Funny)

on Wednesday July 02, 2008 @11:46AM (#24031783)
Reimann? Like the Noodles right?
• #### Re:Reimann? (Score:5, Funny)

on Wednesday July 02, 2008 @11:54AM (#24031951)
It's not just noodles. Its a way of life.
• #### Hmmm.... (Score:5, Funny)

on Wednesday July 02, 2008 @11:46AM (#24031791) Journal
The only part of it I understood was:

The author is grateful to J.-P. Gabardo, L. de Branges, J. Vaaler, B. Conrey, and D. Cardon who have obtained academic positions in that order for him during his difficult times of finding a job.

Sounds about par for the course for academic hiring, and it sounds like he's still pretty traumatized from it. I hope this works out for him and he can go around flipping off all the hiring committees who turned him down.

• #### Re: (Score:2, Informative)

by Anonymous Coward

It's brutal trying to try to get into academia in a field that doesn't produce money. The sad thing is that departments want to hire more people but there is never any money or open positions and tenured professors hang onto their positions until they die. Things are a little better in physics than math, but not much (I am an experimental physicist).

I had an undergraduate professor tell us endlessly to NOT go into physics, as it would make us miserable careerwise. I'm still in physics, but most of my fri

• #### Re:Hmmm.... (Score:5, Funny)

by Anonymous Coward on Wednesday July 02, 2008 @01:26PM (#24033467)

I had a history professor tell me that if he knew how hard it would be to get to where he was, he never would have been a history major.

Well, that's all in the past now.

• #### Math =  (Score:5, Funny)

on Wednesday July 02, 2008 @11:47AM (#24031805) Homepage
According to the http://en.wikipedia.org/wiki/Riemann_hypothesis [wikipedia.org] wikipedia article, this means $1,000,000 if the proof turns out to be valid. Unfortunately, I didn't understand anything else in that article. • #### Re: (Score:2) He gets a million because a lot of modern mathematics assumes it is true but no-one can (so far) prove it .... It he is correct a lot of mathematicians breathe a huge sigh of relief If someone proves it is false then mathematics collectively panics and a lot of proofs will have to be re-written ... • #### So what? (Score:3, Insightful) on Wednesday July 02, 2008 @11:47AM (#24031815) arXiv has become the repository for junk that couldn't pass peer review. Wake me up when we see a published journal article. • #### Re: (Score:2) Also, the proof of something that complicated is likely so complicated that only the very best minds would even be able to prove that the proof was wrong. • #### Re:So what? (Score:5, Informative) on Wednesday July 02, 2008 @12:14PM (#24032335) I think you misunderstand the scope and purpose of arXiv. arXiv is a repository for *preprints*. By uploading the file to arXiv before submitting it, not only do you ensure that those that can't afford$10,000+ subscription fees can access the article, but you open up your findings to a much wider international audience.

The lack of peer review is not necessarily a liability in this situation

• #### Previous proofs (Score:5, Interesting)

on Wednesday July 02, 2008 @11:48AM (#24031827)
• #### not so fast (Score:5, Informative)

by Anonymous Coward on Wednesday July 02, 2008 @11:49AM (#24031845)

there are "proofs" of the Riemann hypothesis on the arXiv every few weeks. Don't believe it 'til it's vetted.

• #### Re:not so fast (Score:5, Funny)

by Anonymous Coward on Wednesday July 02, 2008 @12:07PM (#24032185)

• #### You mean that... (Score:2)

Simple Simon actually met a Riemann, after all?!

I thought that was just a hypothesis!

• #### The REAL importance is Primes (Score:5, Interesting)

by Anonymous Coward on Wednesday July 02, 2008 @01:13PM (#24033239)

Section two of the wiki article (http://en.wikipedia.org/wiki/Riemann_hypothesis) is the great importance here. If indeed there is a proof of Riemann's Hypothesis, then there is a similar proof of the Generalized Riemann Hypothesis, which is in turn a big step in finding the exact distribution of prime numbers.

Finding the distribution of prime numbers has epic consequences, like breaking most encryption, for starters.

• #### Re:The REAL importance is Primes (Score:5, Informative)

on Wednesday July 02, 2008 @05:26PM (#24036561)
The Riemann Hypothesis and RSA encryption both have to do with prime numbers, but the relationship between the two pretty much ends there. To break RSA you need to know how to factor large numbers quickly. RH, on the other hand, pretains to the distribution of prime numbers. It's pretty unlikely that a proof would make computers any faster at factorizing.

So this begs the question that a lot of people have been asking on this thread: why should you care? There tongue-in-cheek answer is that a solution is worth \$1,000,000. While that response may suffice for non-mathematicians, mathematicians would have another, more important reason to celebrate. RH and its generalization, the Grand Riemann Hypothesis, have an absolutely enormous number of profound impliations in number theory, and it is difficult to overstate how critical a proof of either would be. (The implications are too technical to write about here, but you can read about them in most good survey books on analytic number theory; for example, see section 5.8 of Iwaniec & Kowalski [amazon.com]). A successful proof probably won't affect your life in any meaningful way (unless you work with analytic number theory for a living), but it would be monumental in the world of math - indeed, this is precisely why there's a reward for solving it. If that's not enough for you, just remember that many mathematicians are motivated not by fame or money but by the beauty and elegance of mathematics, and any proof of RH would establish a truly beautiful and amazing result.

Of course, there's also the question: is Li's proof correct? I certainily don't know, and I doubt anyone will for quite some time, but there's an interesting story. Li's Ph.D. adviser was Louis de Branges [nodak.edu] who, as noted on this very website [slashdot.org], claimed to prove RH in 2004. His proof has not been accepted by the mathematical community and is widely considered to be incorrect, in large part because the method he wclaims to use was shown, in a 2000 paper [arxiv.org] co-authored by none other than Xian-Jin Li, to have holes in it.
• #### DOOOOOMED!!!!!!! (Score:2, Funny)

by Anonymous Coward

I can't believe they are brazenly going forward with research into this subject without knowing if it could possibly lead to the creation of a black hole that will swallow the earth.

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