Has the Riemann Hypothesis Finally Been Proven?

[devious_]

Apparently someone thinks they might have proved the Riemann Hypothesis. What do you think?

http://www.aronpalmer.com/riemann_proof.htm

 

[mathman]

I think the proof should be submitted to a reputable math journal and refereed. If it is correct, the author will become very famous.

 

[Treadstone 71]

The author would be a millionaire AND gain instantaneous immortality.

 

[quasar987]

And the women, ô, the women!

 

[aronp]

I must say how polite everyone is here, I had expected to be slammed. Would love to get it refereed but finding it quite difficult, I might as well send a stock tip to the journals as this for the interest I get. All of which is totally understandable, I am sure I wouldn't behave much differently, but if anyone has any ideas on how to proceed they would be very welcome. Even any feedback on whether its clearly rubbish so that at least I can stop making a fool of myself.
Thanks,
Aron.

 

[HallsofIvy]

I don't understand. Send it to a journal and it WILL be refereed. That's what journals do. Of course, they are not in the business of fixing mistakes for you- you might well get back a message saying "No, thank you we're not interested"- which means "No, this is not a valid proof".

 

[matt grime]

Actually, a rejection from a journal does not mean that the proof is incorrect, and acceptance in a journal does not mean the proof is correct either. The referee process is to ensure that the result is not obviously false, satisfies the criteria of the journal's acceptance policy and that it is original work as far as it is reasonably possible to tell.

Some referees do take it as part of their job to make sure the proof is actually correct, and they will certainly make sure it is not obviously false. This is why the conditions for getting a Clay prize are not merely that the result is published in a high-profile journal, but that it stands 18 months of scrutiny after publication without any (serious, ie fatal) errors in the proof being found.

A quick scan of the result makes me instantly sceptical.

I see no explanation of what the 'real positive continuous decreasing function' that is used is to determine something about the zeta function actually is.

One simple line, after the theory, which states: let f=? then we see that... would make all the difference, plus a proof that the f so used actually satisfies the criteria given would be required.

 

[mathwonk]

matt is right. refereeing is a difficult, time consuming, anonymous, and essentially thankless job. I received a lengthy and difficult paper some time back that I had no time to review, but a few months later I received it back again with a personal apeal from the editor, since no one else could be found to review it either.

I accepted but said it woiuld take a long time. 7 months later or mroe I received a followup appeal from the editor, but i was still checking laboriously, every detail in the terse arguments, and every reference of the sort " this proved in my [300 page] paper", with no specific page citation.

It was very impressive, but the logic was not clear. When I finished after one year, and laid it all out clearly, there was a big gap in the argument. He had simply assumed some other author, whose work he used, had proved an if and only if statement where in fact that author only proved an "only if" statement.


I sent it back with a favorable review but pointing out the gap. A couple weeks later the author sent back a revised version with a "completed" version of the other authiors work.

I did not have time to c=verify this so just let it go.


There is no guarantee from em that the mpaper is correct, and indeed I am very rare in even checking as far as I do the correctness of authors's works.

Matt is giving you valuable free advice here. If you cannot get your work refereed it is probably because it is not clearly enough written to make it possible to review without great effort, and that effort is not justified in the case of a theorem whose proof from anyone is so difficult that it is likely to be wrong.

 

[aronp]

Thanks to all for spending time on this and the advice.
The function is detailed here
http://www.aronpalmer.com/some_more_on_last_stage_of_riema.htm
Will pursue with journals.

 

[devious_]

Good luck!

 

[aronp]

Thanks, realize odds are against me.
Does anyone have any ideas who I should approach in order to get this published. I am new to all of this.

 

[matt grime]

So when I said you merely ought to state: let f=something, why have you not said what f is equal to in any clear or concise way. I scanned taht page.I didn't see the word zeta at any point. Perhaps I was just being too quick.

 

[quasar987]

Therefore the two sided Laplace transform of our function does indeed represent a product form of the Zeta function.

:p

-----------

 

[aronp]

Well I am sure if you missed it others will miss it. I have tried to make it clearer at the bottom of here
http://www.aronpalmer.com/riemann_proof.htm
Better?

 

[aronp]

And I have added more detail regarding
quasar987's comments.

 

[matt grime]

You did not say you'd altered the original page, merely gave a new link.

Well, the obvious counter example is: let f(t)=0, this satisfies all the criteria you place on f (at least the only ones you give), and by your 'proof' you're saying that the laplace transform of the zero function (which is the zero function) is never zero (in the right half plane).

 

[aronp]

0 is excluded because the integral of f(t) from 0 to Infinity is 0 and part of the proof requires this to be non zero. I originally had a comment pointing this out but I removed it because I thought it didn't help, obviously I was wrong.

 

[matt grime]

You cannot require something to be a condition in the proof if it is not met or deduced from the hypotheses. What else do you add into the proof that is not in the hypotheses (which are not clearly stated; I guessed that the first three things you wrote were all that was required).

 

[Treadstone 71]

This is just me talking here, but if you gave it a duller title, something other than "PROOF OF RIEMANN HYPOTHESIS", it might not provoke instant skepticism.

 

[aronp]

f(t)=0 is the only continuous function I excluded and didn't mention.
I expexcted instant skepticism, and so far have found everything on this board very constructive, but would really like to find a referee/publisher. So far (7 days),no one has pointed out an obvious mistake (in fact no-one has said anything at all) and this is the only board its been posted on (not by me, blame devious :-) ).
Hopefullly my next post will be more extreme (one way or the other).
Thanks,
Aron

 

[matt grime]

Your presentation isn't up to standard to be published, and is the reason why I've not gone through it to check whether it is correct or not. It isn't clear from what you've written (to me) what you're doing, and I have no interest to figure out what you are trying to do. That is probably why you've got no response, not because there are no problems. Sorry, but honest explanation of why there is no response is probably best.

 

[aronp]

Apologies that I am posting again pretty sure people are getting fed up at this stage.
I certainly didn't take no response to mean no problems and I certainly accept it wasn't a great presentation. Have tidied it up and improved it here.
http://www.aronpalmer.com/rproofv2.pdf
and actually never called it at proof of RH, just a proposed proof, I know the odds are against me, but the first bit and the last bit I would bet my house on, just the bit from the one sided laplace to the two sided laplace is what I am worried about.

 

[devious_]

Any progress?

 

[aronp]

Well thanks for asking. Short answer not really, its with a publisher, but I am beginning to realize how frustratingly slow that process is going to be.
The proof is in a lot better state now, much neater easier to follow and a lot gaps filled in. As far as I am aware only one person has gone through it and he thinks its "probably right" (after spending quite a while pointing out typo's and weak areas) and has become an ardent helper. Apart from being too short no-one has pointed out a flaw with the approach.
I did get good advice from this board, thanks, and I now realize how poor the original presentation was so apologies to those who tried to wade through it.


Aron.
http://www.aronpalmer.com/rproofv2.pdf

 

[aronp]

Okay guys, devious was right, the inevitable flaw has emerged, right at the end I can prove that the one sided laplace cannot be expressed in the product form required. Think it may not be fatal, but its not trivial either.
Apologies.
Thanks for all your help.