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.

Dirty Words

Me, I use math to write dirty words on my calculator.

Such as 80085?

Re:Dirty Words

5318008

Re:Dirty Words

No, you mean 5318008 or for the slashdot crowd, 55378008

Re:Dirty Words

No for the slashdot crowd it would be: 58008uÉÉ . Because obviously we all have calculators that support unicode text entry.

Re:Dirty Words

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

Re:Dirty Words

On linux, wouldn't it be ...

host:>man 80085

???

Yeah but did they point this out?

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?

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...

Tried to RTFA

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

Re:Tried to RTFA

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

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

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

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 ..."

Numb3rs

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.

$1,000,000 prize to be collected then if true

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

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

Reimann?

Reimann? Like the Noodles right?

Re:Reimann?

It's not just noodles. Its a way of life.

Hmmm....

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.

Math = $$

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.

Previous proofs

http://secamlocal.ex.ac.uk/people/staff/mrwatkin/zeta/RHproofs.htm [ex.ac.uk]

not so fast

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

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.

Oblig.

http://xkcd.com/113/ [xkcd.com]

Re:So what?

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