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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
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()?
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.
there are "proofs" of the Riemann hypothesis on the arXiv every few weeks. Don't believe it 'til it's vetted.
Good explanation here too:
http://www.irregularwebcomic.net/1960.html
"The weirdest thing about a mind, is that every answer that you find, is the basis of a brand new cliche" -
http://xkcd.com/113/
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
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?
No. Every number field has its own zeta function. The standard Riemann hypothesis concerns that of the rationals.
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.
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.
"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.
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: ..."
I have no problem with your religion until you decide it's reason to deprive others of the truth.