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Claimed Proof of Riemann Hypothesis
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.
Me, I use math to write dirty words on my calculator.
Such as 80085?
Summation 2
37047734
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)
Man, where's Charles Eppes when you need something explained to you in layman's terms?
Do daemons dream of electric sleep()?
but it was 222 small. So she took 51 pills, 8 times a day, and ended up...
Do you even lift?
These aren't the 'roids you're looking for.
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]
There's nothing Intelligent about Intelligent Design.
Reimann? Like the Noodles right?
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.
What I'm listening to now on Pandora...
According to the http://en.wikipedia.org/wiki/Riemann_hypothesis 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.
arXiv has become the repository for junk that couldn't pass peer review. Wake me up when we see a published journal article.
http://secamlocal.ex.ac.uk/people/staff/mrwatkin/zeta/RHproofs.htm
there are "proofs" of the Riemann hypothesis on the arXiv every few weeks. Don't believe it 'til it's vetted.
Dolly Parton was 69 lbs over weight. The doctor said that's 222 much! You need to lose 51 x 8 days. That left her:
6922251x8=55378008
First Fermat, now this. Is nothing sacred?!
This is seriously disappointing news though. I've always appreciated the romance of such "theories", and now there's one less in the world. That and my planned deal with the devil to save my soul has now hit the rocks.
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.
Even those who arrange and design shrubberies are under considerable economic stress at this period in history.
http://xkcd.com/113/
Ok, so many have tried, all have failed.
It may take a decade to test the assertions that this so called proof attempts to demonstrate.
Perhaps we could give the guy a consolation prize, wait for the work to be "proven" wrong and then off course, issue an Apology:
http://www.math.purdue.edu/~branges/apology.pdf :-)
-Hack
PS: Does anyone find it STRANGE that the guy who can solve this problem has issues finding a job?
WTF?
Got Geometrodynamics? Awe, too hard to figure out? Too bad.
hEll
Solving the energy crisis is easy.
Use less energy.
Kthxbye.
That reminds me.
Actually, if he really did successfully prove this, not only does this make him a rich man, but it has huge effects on prime number distribution (if I recall correctly) and related cryptography. I'm not an expert on the subject (Very far from it. I'm a CS major, not a Math major.) but this is what I remember hearing about it. If I'm wrong, please correct me.
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 ..."
Bantam Dominique roosters crow a four-note song. Once you've heard it as "Happy BIRTHday" you can't NOT hear it that way
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.
your mother?
If you tried, you'd miss by 1/2.
Weaselmancer
rediculous.
Thats ok, the article doesnt say anything either...
In its entirety:
A proof of the Riemann hypothesis
Xian-Jin Li
(Submitted on 1 Jul 2008 (v1), last revised 2 Jul 2008 (this version, v2))
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. Subjects: Number Theory (math.NT)
MSC classes: 11M26
Cite as: arXiv:0807.0090v2 [math.NT]
Submission history
From: Xian-Jin Li [view email]
[v1] Tue, 1 Jul 2008 19:43:13 GMT (20kb)
[v2] Wed, 2 Jul 2008 11:05:52 GMT (20kb)
So Unless you are some encyclopedia of theorems and proofs, you will have to look it all up anyways.
So... could someone explain this theorem in simple(r) terms, please?
This guys advisor, according to the Math Genealogy Project, is Louis deBranges. DeBranges also claimed to have proven this a few years back, but his proof was not accepted (for reasons unknown to me). The $1M might still be safe.
it has huge effects on prime number distribution
Prime numbers are distributed in pretty much the same way as they were before the proof.
The proof is mathematics for the sake of mathematics. The Riemann Hypothesis has been accepted as true true for over a hundred years, so practical applications that derive from it already exist.
Simple Simon actually met a Riemann, after all?!
I thought that was just a hypothesis!
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.
The Music of the Primes, by Marcus du Sautoy is, as far as I know, the best account not only of the great intricacies of the Theorem but also of the amazing quest for an explanation of the hidden structure of numbers.
You may also find interesting the book's website (warning: cool web design)
Dawkins Revisited: A person is shit's way of making more shit -- Steve Barnett, anthropologist.
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.
Tired?
even the Abstract is completely indecipherable.
You mean this?
http://arxiv.org/PS_cache/arxiv/pdf/0807/0807.0090v2.pdf
The links are right on the side for downloading in various formats.
Doogie tried solving this in Numb3rs as well.
Did anyone else see the typo in his paper? So close...
7h3$3 4r3n'7 7h3 Ðr01Ð$ ¥0 4r3 £00|{1n9 f0r. M0v3 4£0n9. --OB1
It's quite simple (the hypothesis) with basic college-level mathematics. You just need to understand complex numbers and sums of series.
That's why it's a nice puzzle.
Compare with Fermat's last theorem, even simpler, yet the proof is only 10 year old and very complicated.
The only one that's relatively simpler and yet unproven is 3x+1, AKA Collatz' conjecture, read it up, it's fascinating.
"hellhole - nice."
No, it's elohlleh, pronounced "elO'-heh-luh", which in the Primitive Quendian proto-language used by the early Elves after their awakening by Eru Ilúvatar, roughly translates to "a dreary, oppressive, or unpleasant place".
Totally different.
America's lack of knowledge in the sciences?
If the fucktards won't pick up a book, what can this guy do about it? For that matter what are YOU doing about it? Nothing? That's what I thought.
I thought it was just German noodles.
Dude, you owe me a monitor.
Note to self: Do not drink coke while reading /.
Do daemons dream of electric sleep()?
For those who get excited about Millennium problem "solutions" on arXiv.org, there's also what I interpret as an attempt to solve Navier-Stokes posted recently: http://arxiv.org/abs/0806.4902 Have fun finding the first error!
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:
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.
This paper is only for the "rational number field" thus does not encompass all possible number fields and the technique, while believed to be generalizable, may not be. So even if this proof pans out, the way I read it, for the time being it is a partial proof and would need to be generalized, before the hypothesis could be considered proven.
Second should he really be using language such as "I feel" to describe his thoughts on the possibility on this generalization.
To avoid the complication of writings, I only considered the rational number
field in this paper. But, I feel that techniques of this paper can be adopted to
any algebraic number field without much difficulty to give a proof of the Riemann
hypothesis for Dedeking zeta functions.
Shop smart, Shop S-Mart.
Is there no gossip among mathematicians whether this proof is worth careful review? I can't see any comments from anyone who is versed in this subject.
Unfortunately, there isn't room here in the margin to post it....
A $1,000,000 prize has been offered by the Clay Mathematics Institute for the first correct proof. http://en.wikipedia.org/wiki/Riemann_hypothesis
1. It's not been accepted as true.
2. "Maths for the sake of maths" is called mathematics. Otherwise it's, I don't know, creationism or something.
is a constant, then
is also a constant.
Thats a pretty strong statement. P vs NP might have something to say about that (especially if a functional P=NP solution emerged)
It's the only one I know.
Dolly Parton went to her doctor. She complained that her breasts were too large and she wanted breast reduction surgery. The doctor measured her chest. "69 inches!" (enter 69) "that's too too too big!" (enter 222) "Five times a day take one of these pills" (enter 51) and after eight days (multiply by 8) you will be (result 55378008)... and turn the calculator over.
Great fun when you're 9 years old...
The Renaissance was stimulated by the Cartesian Philosophy . . .
Interesting, as Descartes was born in 1596, and the Renaissance started much earlier. Yes, that's nitpicking, but if you want me to read a 40-page PDF, you should get such things correct.
At last, I'll know what to put in the captcha on rapidshare :o
No, but I did throw granola at a deaf person once
It's not a question of simplicity. It takes several pages of symbolic logic just to prove 1 + 1 = 2. Mathematicians have been trying to prove RH for about 150 years. Fermat's Last Theorem took twice that to prove, despite being MUCH simpler, and the proof required mathematical tools which didn't even exist in Fermat's day. Plus if RH isn't true, virtually the whole of mathematics comes crashing down about our ears, because there are several critical parts of it which can't be true if RH isn't! Someone mentioned encryption and factorisation of prime numbers, but I think they misunderstood what they've read about RH. The problem with trying to crack encryption lies in trying to determine which prime numbers were used to encrypt the message; prime numbers are hard to generate and verify because as yet there does not exist any method other than brute force to determine if a given number even IS prime, i.e. you have to divide it by all prime numbers smaller than its square root. When you're talking about 60-digit primes, the number of possibilities for public and private key pairs is...well, I don't know what it is offhand, but it's bloody large! But proving RH would indirectly give mathematicians a method of deriving primes WITHOUT checking for possible factors - if RH is true and the given number lies on the critical line, then it's prime. Generating primes would then be a simple matter of plugging the right values into the Riemann zeta function. So untold trillions of years of work with a supercomputer are reduced to maybe a few hours with a PC. Which means public key encryption will be rendered useless once RH is proved. Not that the mathematicians will care about that! :)
Ah well, not quite right. But let g0(x)=x works, because there's no integrability condition. Thm 8.6 then falls apart because h0 is no longer in L^2(C), or V(h) is not an operator, take your pick.
"The ability to delude yourself may be an important survival tool" - Jane Wagner -
You'd have to be crazy to bet that this proof is correct. That said (I'm not a mathematician, but): First, Li's proof at least claims to build on approaches that are, for number theory, reasonably mainstream. He cites the big guns. Second, he's not a delusional crank -- he's had number theory papers published in peer-reviewed journals. The math community will probably take him seriously. Finally, the best news - his paper is only forty pages long, so the few people who are capable of evaluating the proof won't feel that they have to devote the rest of their careers to it. Chances are that we will hear fairly soon whether or not the proof is valid. There's been a raft of comments here about the significance of a proof -- one short answer is that there are hundreds, maybe thousands, of mathematical theorems that start "Assuming the Riemann Hypothesis...."
Jim Shilliday
Unless I missed something, this conjecture does not have the sweeping consequences you allude to; unlike P=NP.
Don't be dense. Here's his point:
The poster to whom you replied suggested that a paper claiming a proof posted on an unreviewed preprint server probably wasn't a good reason to get excited. He's absolutely correct.
Patrick Doyle
I mod down every jackass who puts his moderation policy in his sig. Oh, wait a sec....
Nevermind, I'm quite off there.
"The ability to delude yourself may be an important survival tool" - Jane Wagner -
Wikipedia is accurate (citation needed)
Fields medal winner, and expert in the field,
Alain Connes sees a problem with the attempted
proof.
http://noncommutativegeometry.blogspot.com/2008/06/fun-day-two.html?showComment=1215071400000#c8876982000013974667
What is also interesting to know is that one can generate and calculate primes in a simple and straighforward manner using previous obtained results and primes through a prime number generating function :
"Calculate Primes"
by Prof James M. McCanney, (c)2006,2007
http://www.calculateprimes.com/
Alain Connes, a leading French mathematician whose work forms part of the foundation of Li's claimed proof, believes that the proof is flawed -- so much so that he stopped reading it. Here's his comment (on his blog): http://noncommutativegeometry.blogspot.com/2008/06/fun-day-two.html?showComment=1215071400000#c8876982000013974667 Li will have to respond to this. Expect fireworks.
Jim Shilliday
Prof. Li has posted a fourth version of his proof on arxiv: http://arxiv.org/abs/0807.0090v4. According to this comment on Connes's blog http://noncommutativegeometry.blogspot.com/2008/06/fun-day-two.html?showComment=1215144000000#c3090911722072092520, Li has made changes to the equations that Tao and Connes identified as problematic. The saga continues.
Jim Shilliday
Actually, proving the negative is always quite easy - you just have to state a case under which the hypothesis is not true. Since no one has been able to do that so far, the broad-based assumption is that it must be true. Proving the positive - that it is true and why it is true - is, as always, the hard part.