Talk:Riemann hypothesis/Archive 1

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I have archived this discussion because it is off topic. - Taxman ^Talk 16:44, 8 November 2005 (UTC)

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My experiences with the "proofs" of RH are, that using the functional equations as the kernel of the proof leads us to a "dead end". Means: for the real part of the argument of RH unequal 0.5 we get an undefined situation, and we like to think that this "undefined" is a proof. But it isn't. W.Aschauer

in my proof i view (a) from equation 60 till the end as a parameter,(a<0.5),this leads me to a contradiction,yet in the same token,(a=0.5),does not lead to any contradiction.the matter here is not a matter of experience,rather it is false or true,be or not to be.obvious things cannot be negated qualitatively.my proof is exact.fayez fok al adeh.

Experiences are very useful to avoid repeating the same mistakes. And juggling with "indefinite", "unbounded" and "0" can bring a lot of them.

However, one of the best tests of a proof is to use the argumentation for similar problems ! A math professor told me about functions related to Riemann Zeta function, e.g. Davenport-Heilbronn Zeta function, which have more or less the same functional equation, but they have zeroes on the right side of the critical line "real part of s = 1/2". There are informations with Titchmarsh, 'The theory of the Riemann zeta-function', chapter 10.25 .

Example of Dirichlet series with zeroes off the critical line: http://www.emis.de/journals/DM/v82/art8.pdf

If a proof is able to distiguish between the zeroes on and off the critical line of the different Zeta functions, then it's possible that we have got a new knowledge about such functions. The math professor I mentioned above had told me that we need a new cognition. Maybe it's based on the Euler Product.

Kind regards, W.Aschauer

it is not always true that similar problems give the same insight.a very sriking example is kummer's attempt in 1847 to prove that unique factorization applies to algebraic numbers.to his astonishment the number 23 violated the rule.this forced him to rescue unique factorization by introducing ideal factors. with best regards.fayez fok al adeh.

it is not always true that similar problems give the same insight.a very striking example is kummer's attempt in 1847 to prove that unique factorization applies to algebraic numbers.to his astonishment the number 23 violated the rule.this forced him to rescue unique factorization by introducing ideal factors. with best regards.fayez fok al adeh.

... not always true, that's right. But it's enough, if it's only one time right, e.g. with RH. Only a try can show how it is. And your Kummer example show's us, that such a try is the flexibility which we need to get new ideas.

To use the proof for similar problems creates a better abstraction of each step. If a proof is mainly based on the functional equation, and we have a lot of such functions with very similar equations, then we will see, how the proof distinguishes between the functions. There must be a characteristic of the Riemann Zeta function, which all the other Zeta functions with zeroes off the critical line don't have. I don't know any proof which fulfill this condition completely.

Because of this a lot of the proofs are nothing else than other forms of the RH.

Good luck with the extend of your proof ! W.Aschauer

above are unsigned comments from various IP addresses, circa August 2, 2005

this reminds me by galois theory.what are the characteristics of the second,third,and fourth degree equations so that they can be solved by radicals?yet higher degree equations cannot.by the way we can arrive at galois conclusion using variational calculus and group theory(refer to the book theory of groups by kurosh vol 1).now the problem is what is special about numbers five and beyond?is the solvability of a group that matters here or some hidden properties of numbers.we still have galois theory,although many meta-mathematical ideas can be put forward.fayez fok al adeh

above are unsigned comments from various IP addresses, circa August 3, 2005

Is the proof of Fayez Fok Al Adeh correct?

At 18th of March 2005 Dr. Fayez Fok Al Adeh presented a proof for Riemann Hypothesis at [1]

I have checked the proof and found some errors [2] I wonder, if some other people confirm those errors I have found.

Kaufmann Friedrich 11:36, 17 October 2005 (UTC)

Fayez Fok Al Adeh:my proof is exact and correct

Mr. Kaufmann is confused between single and double integrals.He does not notice that the variables in the double integral are seperated in the inequality. After seperating the real and imaginary variables after equation 9 ,the proof deals only with the real field,yet Mr. Kaufmann discusses the imaginary part again. [As for the next sentences, please remember WP:NPA --Army1987 17:39, 17 October 2005 (UTC)] In brief the comments of Mr. Kaufmann are not based on the objective scientific attitude,rather they are rooted in some sort of discriminaion. I suggest Mr. Kaufmann learns some mathematics and morals.Best regards to him.

Under our policy, we cannot use original research in Wikipedia, anyway. We are not the people you need to convince. Charles Matthews 18:19, 17 October 2005 (UTC)

Scientific attidude?

Hello Dr. Fayez Fok Al Adeh, thank you for your scientific based comments. Perhaps some other good mathematicians have an opinion to my paper too. I would be glad to hear other opinions too.

Kaufmann Friedrich 12:15, 17 October 2005 (UTC)

Fayez Fok Al Adeh:Another proposed proof

Please be kind enough to refer in this same page to the comments describing my proof under the title :Another proposed proof.Here are some of the descriptions:ugly,nasty,broken,no proof,dull,mis-application,non-sense,no-good,junk.What do you say about these descriptions? What do you say about comments which have nothing to do with the a given scientific paper? I am eager to know your response. Best regards.Mr. Charles Matthews

Fayez Fok Al Adeh:response to Mr. Kaufmann

Dear Mr. Kaufmann Please note that equation(6) implies the two real integrals (12) and (13) which have distinct variables,although they follow from equation (6).This means that your notice about the product of two imaginary parts is not correct,since you return to the begining,ignoring the following manipulations.You jump back to the essential part of the problem that 0<a<1 which I mention at the begining of my paper.This also replies your last comment:why not consider a=1 and a=0.your comments about equation (47) say nothing,because the integral is bounded,but what I aim at is to prove that in this special case the integrand is bounded and deduce the corresponding values or value of a.As regarding the double integral you did not notice that the variables are seperated.Your comments are totally wrong.Best regards. Fayez Fok Al Adeh

More precise description of an error in the proof of Fayez Fok Al Adeh

Since some mathematicians have problems with my paper [3] concerning the errors in Fayez Fok Al Adeh proof for Riemann Hypothesis, I have worked out a paper to show the comment 1.) each step which lead to a contradiction precisely [4]. I hope that this comment is clearer now. Kaufmann Friedrich 11:49, 19 October 2005 (UTC)

Fayez Fok Al Adeh:A second response to Mr.kaufmann

In my proof,I go on from equations (12) and (13) through a long sequence of hard manipulations and deductions to prove at last that a=0.5.Mr.Kaufmann stops at these equations.Stopping at these equations does not take us beyond the essential assumption 0<a<1. The content of the work of Mr.Kaufmann resembles manipulating tautologies in mathematics.Best regards.

Don't you both think that this discussion doesn't belong here?--Army1987 14:56, 19 October 2005 (UTC)

You are right it makes no sense to discuss further. Every time anyone finds an argument against the proof of Dr. Fayez Fok Al Adeh, he will be personally attacked concerning his mathematical knowledge. It makes no sense to convince Dr. Fayez Fok Al Adeh concerning errors in his proof, because he believes absolutely that it is "correct and exact". Perhaps someday he will be the only one who believes that. Kaufmann Friedrich 18:37, 19 October 2005 (UTC)

I agree that this is not the place to discuss such detail,but still ask Mr. Kaufmann to answer my lateset comments.Fayez Fok Al Adeh.

A typical "Dead End" of a lot of proofs.

I am not a mathematican, but it's indeed clear, that this "proof" of Fayez Fok Al Adeh is in a very typical way wrong. I don't know, what is wrong or not wrong in his paper till point (75), but it looks at least strange. After (75) it's absolute wrong, because the argumentation there is as follows: a=lim(x->0)(0.5+x) => it's allowed to set a=0.5+x before the lim for the whole expression (80), ((1/a)-2)/x^(1-a)) , is calculated. Means, a relation between a und x is set, which hasn't existed before. The Independency of a and x was given up without any proof of it's unimportance. And such a proof has to include the correctness of lim(a->0.5)(x->0)... = lim(x->0)(a->0.5)... . Point (80) shows, that the sequence, first a->0.5 and second x->0 or first x->0 and second a->0.5 is important because of different results. Because of this, the Independency has to be kept. Another example: Let us set x=((1/a)-2)^(1/(1-a)) , thus we have a=0.5 <=> x=0 , but point (80) has with this condition the result 1 on the contrary to 0 in the paper at point (81). We can get any result, which we like to have: 0 or 1 or infinit. Or whatever. We only need to change the relation between x and a.

This "dead end" is very typical for all "proof"s, which are based on the functional equation of the Riemann Zeta function !

From: Winfried Aschauer (29.Oct.2005)

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==Independency is Maintained==

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Independency is maintained

In limiting processes,it is immaterial what symbol we use to approach the limit.This symbol is not an argument.We can not break the proof at a point,as Mr. Kaufmann did,and return to the begining.We get a tautology.Fayez Fok Al Adeh

The "dead end" 0/0 .

a/b is not defined, when a->0 and b->0 are independent of each other. The definition - and therefore the value - of a/b depends on the relation between a and b. In a lot of proofs of the RH, maybe more than 90%, we have such or similar problems.

Winfried Aschauer (8th Nov.2005)

Another proposed proof

I'm moving this off the page to here instead. Does anyone know if this has been seen or reviewed by the rest of the mathematical community?

On 18 March 2005, Fayez Fok Al Adeh, the President of the syrian Cosmological Society, published on the Site of "The general Science Journal" an astonishing simple proof of the Riemann Hypothesis.(A Link to the proof). But a proof of such an hypothesis must be very critical verified.

I read/skimmed it. Its ugly and nasty and broken. Its no proof at all. Its 10 pages long. Pages 1-7 (equations 1-49) are very simple, freshman-calculus manipulations of simple integrals. Rather tediously dull. Lets assume these manipulations are correct (although I spotted an error/typo on page 2.) But then equation 50 starts getting strange and equation 56 is just plain bizarre. After 7 pages of freshman calculus, there's a sudden (mis-?)application of a variational principle of some kind, without any ado or explanation, as if it were just some more basic calculus. Equations 57, 58 and so on don't follow, don't make sense, and nothig after that is any good, although the manipulations continue in the same freshman-calc type of presentation. Its junk. linas 00:21, 15 Jun 2005 (UTC)

another proposed proof how to prove the riemann hypothesis i read the comments about my proof the commentator said that he skimmed the proof yet he described the proof as ugly nasty broken no proof at all ado junk and he asks for a timinig to apply a certain mathematical topic i admire his high morals and distinguished scientific attitude fayez fok al adeh (anonymous User:212.31.117.130 User contributions 10:35, 15 July 2005)

If you are who you say you are, I suggest that you re-write the paper, and explain very very carefully what formula 50 through 58 mean, how they should be interpreted, and why the manipulations you are making are valid. The problem was that formulas 50 and onwards make a number of unjustified and very strange manipulations. linas 14:44, 18 July 2005 (UTC)

Again about another proposed proof of the Riemann Hypothesis:How to prove the Riemann Hypothesis.My proof is exact.We can talk calmly putting aside your descriptions of the proof(nasty ugly...etc).Please read it again and refer to any book on variational calculus.From equation 50 to 59 (a) is considered as a fixed exponent(a=0.5).But from equation 60 onward it is a parameter(a<0.5).Author Fayez Fok Al Adeh —Preceding unsigned comment added by 213.178.224.227 (talk • contribs) 18:16, July 18, 2005

The Fayez al-Adeh proof is flawed due to elementary mistakes (wishful thinking). There is a very simple explanation of one of the major flaws posted at:

http://www.wbabin.net/comments/sfarti3.pdf

a slightly different one:

http://www.wbabin.net/comments/sfarti5.pdf

The proof is 10 pages long, the counterproof is 2 lines!!! The 1m prize is safe, no challenge from this one.

Fayez Fok Al Adeh

Please refer to my proof of the Riemann hypothesis.it appeared in "the General Science journal" on March 18th 2005.The address of the Journal on the web is www.wbabin.net

Found your paper, but I am not qualified to judge its merit. As far as style goes, a paragraph or two at the beginning explaining your proof strategy would help readers to understand which direction your algebraic manipulations are taking, and where the key points of the proof are. Splitting out preliminary results into lemmas, which you can then use in your main proof, would also make the structure of your proof clearer to the reader. The General Science Journal does not appear to be a refereed journal - has your paper been published by a refereed journal, or has it been reviewed independently by an established mathematician in this field ? Unless your paper has passed this type of peer review, I am afraid no one is likely to give it much credence. Gandalf61 11:04, 22 September 2005 (UTC)

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A comment can be seen under [5] (W.Aschauer)

The Fayez "proof" is fatally flawed due to elementary mistakes (wishful thinking). While the original proof doodles on 10 long pages, the counterproof is 2 lines !!! For a simple disproof see:

http://www.wbabin.net/comments/sfarti3.pdf

or, a newer one:

http://www.wbabin.net/comments/sfarti5.pdf

FAYEZ FOK AL ADEH

please see my last comment to Dr.Sfarti in the "General Science Journal"where I show that his few lines are wrong.Also in a previous comment I show that his epistemological interpretation of superluminal velocities is wrong.

Assessment comment

The comment(s) below were originally left at Talk:Riemann hypothesis/Comments, and are posted here for posterity. Following several discussions in past years, these subpages are now deprecated. The comments may be irrelevant or outdated; if so, please feel free to remove this section.

Some suggestions for improvements are here. Jakob.scholbach (talk) 15:59, 20 October 2008 (UTC)

Last edited at 15:59, 20 October 2008 (UTC). Substituted at 06:33, 7 May 2016 (UTC)