## Claimed Proof of Riemann Hypothesis 345

Posted
by
CmdrTaco

from the two-scoops-of-math-please dept.

from the two-scoops-of-math-please dept.

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.
## Dirty Words (Score:5, Funny)

Me, I use math to write dirty words on my calculator.Such as 80085?

## Re:Dirty Words (Score:5, Funny)

5318008

## Re: (Score:3, Interesting)

## Re:Dirty Words (Score:5, Funny)

5318008or for the slashdot crowd,55378008## Re:Dirty Words (Score:5, Funny)

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)

That would've been a lot cooler if Slashdot supported Unicode.

## Re: (Score:3, Funny)

äOEæ--¥é..."ããï¼ï¼

## Re:Dirty Words (Score:5, Funny)

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)

Does your project have donation page?

## Re:Dirty Words (Score:5, Funny)

You haven't grafted a color TFT screen to your calculator yet?

Who let these guys in?

## Re: (Score:3, Funny)

## Re:Dirty Words (Score:5, Funny)

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)

## Re:Dirty Words (Score:5, Funny)

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)

reallywant a dirty word, try 71077345...## Re: (Score:2, Funny)

## Re:Try this. (Score:5, Funny)

your mother?

## Re:Dirty Words (Score:5, Funny)

## I like to describe my workplace with my calculator (Score:2, Informative)

## Wrong (Score:5, Funny)

"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.

## Yeah but did they point this out? (Score:5, Funny)

## Re:Yeah but did they point this out? (Score:5, Funny)

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)

bothof you RTFA?We have a new

## Re:Yeah but did they point this out? (Score:5, Funny)

Not so fast. I read it -2 times.

## Re:Yeah but did they point this out? (Score:5, Funny)

## Re:Yeah but did they point this out? (Score:5, Funny)

Come on, be real.

## Tried to RTFA (Score:5, Funny)

Man, where's Charles Eppes when you need something explained to you in layman's terms?

## Re:Tried to RTFA (Score:5, Funny)

## Re:Tried to RTFA (Score:5, Funny)

Ummm...I think that WAS layman's terms. For you math geeks, try being a

history majorand 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, Funny)

Thus, archaeologists are as anal about their 1 meter units (or even smaller units) as chemists are about their titrations (or whatever chemists do).

Last time I tried to get anal with my 1 meter unit, I damned near killed someone.

## Re:Tried to RTFA (Score:5, Informative)

\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

bigassumption), this would finally solve a long-standing problem (dating back to 1859).Details of the actual solution

area bit heavy. Those actually interested in this sort of number theory might want to start here [amazon.com].## typo (Score:5, Informative)

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)

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)

## Re:Tried to RTFA (Score:5, Informative)

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)

## Or, in layman's terms... (Score:5, Informative)

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 trilliancalculations 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.## Re: (Score:3, Funny)

Or a 'variable' as it is also known.

## Numb3rs (Score:5, Funny)

## Re:Numb3rs (Score:5, Funny)

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)

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)

Good explanation here too:

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

## Re: (Score:2)

## Re: (Score:2)

http://www.irregularwebcomic.net/1960.htmlGreat! Now how am I supposed to get any work done.

## Tough problems (Score:4, Interesting)

isfirst. 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)

You mean like this? [aol.com]

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

...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 :-)

areinventing new math## Re: (Score:3, Funny)

## Re: (Score:3, Funny)

I carry something else to

avoidreproducing.A clipboard?

## Re: (Score:3, Informative)

## Re:$1,000,000 prize to be collected then if true (Score:4, Insightful)

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)

Found that here [wordpress.com]

## Re:$1,000,000 prize to be collected then if true (Score:4, Funny)

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)

## Re: (Score:3, Funny)

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

## Re:$1,000,000 prize to be collected then if true (Score:5, Funny)

## Re:$1,000,000 prize to be collected then if true (Score:5, Informative)

No. Every number field has its own zeta function. The standard Riemann hypothesis concerns that of the rationals.

## Re: (Score:3, Funny)

Do you even know, what a number field is

It's where they grow new numbers, right?

PS: Do you, even, know: how to use correct punctuation?1!?!?!?

## Re: (Score:3, Informative)

## Reimann? (Score:5, Funny)

## Re:Reimann? (Score:5, Funny)

## Hmmm.... (Score:5, Funny)

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)

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)

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)

## 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)

## 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)

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

## Re: (Score:3, Insightful)

Just look at the above threads.

## Previous proofs (Score:5, Interesting)

## not so fast (Score:5, Informative)

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)

Yeah. arXiv once published my paper that shows cases where P = NP; I proved it conclusively for the cases where P = 0 and/or N = 1, but so far I haven't gotten my $1,000,000.00 check from the Clay Math Institute.

## Re:not so fast (Score:4, Funny)

They sent you your checks for cases where you are equal to 0.

Someone beat you to the "1" part.

## Re: (Score:2, Interesting)

## Re: (Score:3, Interesting)

## Dolly Parton (Score:2)

6922251x8=55378008

## Oblig. (Score:5, Funny)

## Apology for the Re (Score:2)

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 [purdue.edu] :-)

-Hack

PS: Does anyone find it STRANGE that the guy who can solve this problem has issues finding a job?

WTF?

## Re: (Score:2, Interesting)

I doubt too many Maths faculties in the world have people working full-time on the Riemann Hypotheses.

Of course I echo your sentiments that

## Re: (Score:2)

Interestingly, DeBranges was Xian-Jin Li's advisor:

http://www.genealogy.math.ndsu.nodak.edu/id.php?id=16641 [nodak.edu]

## 1134 (Score:2)

hEll

## 53188008? (Score:2)

## His Advisor Also Claimed Proof (Score:2, Interesting)

## 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)

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)

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)

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.

## Re: (Score:2)

The version I learnt as a kid: There was a girl of 13, who had a bust of 84. She wanted to make it 45, so she went to the doctor. 0, he said. Take these pills 2 times a day - instead she took them four. Of course, she ended up...

## Re: (Score:2)

Does that make me the only person who remembered how "boobless" is spelt and just typed 55318008 into the calculator when they wanted something to snigger at?

## Re: (Score:3, Funny)

Solving the energy crisis is easy.

Use less energy.

Kthxbye.

## Re: (Score:3, Interesting)

it has huge effects on prime number distributionPrime 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.

## Re:The continuum hypothesis will be next... (Score:4, Insightful)

First Fermat, now this. Is nothing sacred?!Money. Not much else these days.

## Re:The continuum hypothesis will be next... (Score:5, Insightful)

The Continuum Hypothesis is known to be neither provable nor disprovable in the standard axiomatic set theory ZF, enriched with the axiom of choice (ZFC). So I wouldn't really count on someone settling that one either way any time soon. Of course one could come up with a new set of axioms for the set theory and *then* prove or disprove CH but you would be hardpressed to find anyone showing interest in that result. After all, I could just add CH or not(CH) to ZFC and trivially prove or disprove it. So anything in that line first needs to even define what a sensible problem is.

For those who have no clue what I said above:

Continuum hypothesis:There is no set strictly larger than the set of natural numbers and at the same time strictly smaller than the set of real numbers. The size of a set in relation to other is defined in terms of mapping. Positive integers are the same number as even numbers because you can define a bijection between the two. Reals are strictly more than naturals.ZF:Set theory made axiomatic. Few axioms (like empty set exists, supersets are larger than original sets etc) that you need to believe and most of the set theory believed to follow.Axiom of Choice:Given a set of sets, one can make a set containing one element from each set. Looks obviously true but in some equivalent but different sounding formulations looks obviously false. Known to be independent to ZF.Y Independent to axioms X:Believing that Y is true does not yield contradiction together with X unless X itself yield contradictions. Same holds for believing that Y is false.PS: Apologies for not including links. I am feeling lazy. Wikipedia has nice articles about all of the above. Articles on ZF, CH or Axiom of Choice are the place to start for a fun reading.

## Re: (Score:2)

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.

## Re: (Score:3, Insightful)