Has the Riemann hypothesis been proven?

In summary, there are rumors that Sir Atiyah has claimed to have proof of the Riemann hypothesis, which he will present at a talk next week. However, there has been little buzz about this and some are skeptical due to Sir Atiyah's age and the sensational nature of the claim. The talk will be livestreamed and if the proof is correct, it could have a significant impact on mathematics. There are also discussions about previous failed attempts to prove the Riemann hypothesis.
  • #1
nrqed
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I am very baffled.

I have heard through the grapevine that the Riemann hypothesis has been proven. My first reaction was of course to dismiss it as yet another failed attempt by someone who was not careful or by a crackpot, or some type of April's fool joke made a few months late.But what I read was this is a claim made by none other than Sir Atiyah himself and that he is planning to give a talk next week. So *if* the statement is true that it is a claim made by Atiyah, then it is of course an extremely serious and possibly correct solution.

But I thought the web would be buzzing with this, especially here. So does anyone know more about this??
 
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  • #2
Sir Atiyah is 89 years old, so with all necessary respect for this great mathematician, I'd be cautious.
 
  • #3
fresh_42 said:
Sir Atiyah is 89 years old, so with all necessary respect for this great mathematician, I'd be cautious.
I know and it was indeed part of the reason for my skepticism.
 
  • #4
Google news found nothing, and a local magazine which usually publishes those news as soon as they are on the news teleprinter neither. Example: "Super Earth in the constellation Eridanus - Is this the home planet of Mr Spock?" - just to support that they would have written about it.
 
  • #5
fresh_42 said:
Google news found nothing, and a local magazine which usually publishes those news as soon as they are on the news teleprinter neither. Example: "Super Earth in the constellation Eridanus - Is this the home planet of Mr Spock?" - just to support that they would have written about it.
Ah, ok. Thank you. That would explain the near silence...
 
  • #6
Here is part of the abstract
For every proof of a famous theorem there are usually several attempts that turn out to be flawed. So let's see. He will present what he has, then hundreds of mathematicians will check every step. The most likely result is a critical mistake somewhere, a good result is some gaps that can be fixed in the following year(s), a great result is a full proof, and the best possible result is a full proof that leads to insights way beyond the Riemann hypothesis.

Livestream here, probably
September 25.
https://www.heidelberg-laureate-forum.org/event_2018/. I guess it is one of the "hot topics", starting 13:30 (11:30 UTC) and 15:30 (13:30 UTC).
 
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  • #7
Would be interesting to see, whether this would affect the (theoretical) decoding of RSA and therewith has consequences for NP.
 
  • #8
I caught wind of this announcement with half an ear and wanted to look up on it.
Found this . Among other news, the candidate solution for the abc conjecture is determined to be flawed.

As for Sir Atiyah's proposition. He is an aged man - I can't help but be skeptical, especially considering the sensational claim that it is a 'simple proof' within our 'mainstream technique' with a 'radically new approach'. I mean, that has to set off some alarms, right? On the other hand, it would be astonishing beyond any sensible description if a nearly 90 year old person presents correct proof for one of the most elusive problems.

Exciting, for sure.
 
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  • #9
mfb said:
Here is part of the abstract
For every proof of a famous theorem there are usually several attempts that turn out to be flawed. So let's see. He will present what he has, then hundreds of mathematicians will check every step. The most likely result is a critical mistake somewhere, a good result is some gaps that can be fixed in the following year(s), a great result is a full proof, and the best possible result is a full proof that leads to insights way beyond the Riemann hypothesis.

Livestream here, probably
September 25.
https://www.heidelberg-laureate-forum.org/event_2018/. I guess it is one of the "hot topics", starting 13:30 (11:30 UTC) and 15:30 (13:30 UTC).
Thanks for the links. But what I heard was that the talk would be on Monday at 9:30, the very first talk.

I live in Canada but I will probably get up in the middle of the night to watch this, if it is streamed live. It might be a storm in a glass of water (as we say in French), but if it turns out to be correct, it will be one of the most important, if not the most important, event in pure math in a century, in my humble opinion. I think it would have more profound impact on math than the proof of Fermat's last theorem. Something on par with the discovery of the Higgs (although this might be comparing oranges and apples).
 
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  • #10
Is the talk really going to happen? How credible are the sources? It isn't that hard to fake an abstract and a talk announcement.
 
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  • #12
mfb said:
Yes it is going to happen
https://www.heidelberg-laureate-forum.org/social-media/
If Atiyah's idea will be proven correct, whether on the first draft or even after major additional contributions by others doesn't matter, then I will have to add him to the list I associate with Heidelberg. Beside military information and the inevitable tun, there is only Mark Twain on the list.
 
  • #13
Personally I just filed it away as interesting - but likely wrong. If it is correct I am 100% certain Terry Tao will discuss it in his blog - that's when I will take notice and try to understand at least some of the details.

Thanks
Bill
 
  • #14
Hardy sent a postcard to a friend, when he was on a boat trip, claiming that he had a proof of the Riemann hypothesis. The idea being that the boat won't sink, surely god would not allow him to get the same fame as Fermat. So, does anyone know if Atiyah is traveling this weekend? :wink:
 
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  • #15
martinbn said:
So, does anyone know if Atiyah is traveling this weekend? :wink:
To Heidelberg, I guess.
 
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  • #16
While talking about RH, I'm probably very late to the party with this (Polson, June 2018), but does anyone know if this has received some criticism? Can't find any specifics other than the article itself.
 
  • #17
martinbn said:
Hardy sent a postcard to a friend, when he was on a boat trip, claiming that he had a proof of the Riemann hypothesis. The idea being that the boat won't sink, surely god would not allow him to get the same fame as Fermat. So, does anyone know if Atiyah is traveling this weekend? :wink:

The flaw in Hardy's argument was, of course, that God could simply have disposed of the postcard.
 
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  • #18
nuuskur said:
While talking about RH, I'm probably very late to the party with this (Polson, June 2018), but does anyone know if this has received some criticism? Can't find any specifics other than the article itself.
I assume there are several reasons for the apparently disregard of the publication, one could be

On Hilbert’s 8th problem
Article in Brazilian Journal of Probability and Statistics
32(3):670-678 · August 2018 with 4 Reads
DOI: 10.1214/18-BJPS392

or at least has similar causes. Polson submitted 15(!) versions to arxiv.org. My personal impression is, that he enforced his personal area of expertise on the problem regardless of its suitability. And a continuation argument of a family of expectation values as main step of he proof doesn't sound very trustful. On a quick view I could see a lot of computations to make the problem fit into his stochastic language, but I couldn't see, where some truth is generated. Especially at the crucial point, where he claims
Finally, the Laplace transform, ##E(exp(−sH^\xi_{\frac{1}{2}}))##, of a GGC distribution, is analytic in the whole complex plane cut along the negative real axis, and, in particular, it cannot have any singularities in that cut plane.
there is neither a reference to a location within his paper nor to someone else's. I would start here to look for a flaw. The arxiv.org paper doesn't quote the publication above, neither does it have any endorsements: https://arxiv.org/abs/1708.02653

Here's his other paper which is a follow up of his argument on: https://arxiv.org/abs/1806.07964 (6 versions, 0 endorsements), and at least he cites, where the expectation value comes from, however, again without mention of its analycity.

But I want to explicitly state, that the above is a personal opinion and easily could be wrong. In any case, there seems to be more proofs around than I thought: here's another one by Frank Stenger: https://arxiv.org/abs/1708.01209 (Aug. 17 - Feb. 18) and one, which even covers the GRH, too, by Vladimir Blinovsky https://arxiv.org/abs/1703.03827 (Mar. 17 - Aug. 18)
 
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  • #19
mfb said:
To Heidelberg, I guess.
Let's hope he will travel the last 100 km from the airport to the city by train and not by car!
 
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  • #22
I'm always somewhat weary of computer demonstrations of real numbers and infinite series, given the mantissa issue.

But yeah, that doesn't sound too good at all.
 
  • #24
I just made a thread, "Atiyah's arithmetic physics", for discussing the physical aspect of his current ideas (which may in fact be the dominant aspect).
 
  • #25
mitchell porter said:
I just made a thread, "Atiyah's arithmetic physics", for discussing the physical aspect of his current ideas (which may in fact be the dominant aspect).
Are you sure we shouldn't merge the two threads? IMO they are too closely related to justify two of them.
 
  • #26
If it wasn't for the name of the author I would say crackpot after the first two sentences and not bother any further.
 
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  • #27
fresh_42 said:
Are you sure we shouldn't merge the two threads? IMO they are too closely related to justify two of them.
Atiyah's Arithmetic physics - while directly mentioned as a result of his talk/paper - is a physical theory, while the topic of this thread is the discussion of (the event of) Atiyah's purported proof of the RH.

That should be enough to justify a discussion on that physics topic alone... however for the moment, whether that physical theory exists or not seems to be all dependent upon his proof being correct, which is obviously what this thread is about.
 
  • #28
martinbn said:
If it wasn't for the name of the author I would say crackpot after the first two sentences and not bother any further.
I remember a guest lecture from Konrad Zuse in the late 80's. The whole auditorium was packed and everybody wanted to hear some of those stories from the past. Instead, he spoke about his current scientific work which was, sad to say this, neither interesting nor relevant. The entire event was quite embarrassing in the end.

Some people on the internet blamed the organization for allowing this to happen. Well, I had to think about the fact that we allow some persons even far more critical access to highly dangerous weapons without any checks on their mental status. I guess the reason is a similar one: nobody in town dares to tell the king that his new clothes don't exist and he stands there naked.
 
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  • #29
Auto-Didact said:
I'm always somewhat weary of computer demonstrations of real numbers and infinite series, given the mantissa issue.

But yeah, that doesn't sound too good at all.
The integral has an exact solution and it is trivial to check the quick convergence of the series. If the value would differ at the 10th decimal place: Sure, who knows how reliable that is. But it is off by a factor of 1000. This is not a rounding issue. The formula is completely wrong.
 
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  • #30
nrqed said:
I am very baffled.

But what I read was this is a claim made by none other than Sir Atiyah himself and that he is planning to give a talk next week. So *if* the statement is true that it is a claim made by Atiyah, then it is of course an extremely serious and probably correct solution.

But I thought the web would be buzzing with this, especially here. So does anyone know more about this??
What happened with checking a proof for its contents and not its author?!
 
  • #31
MathematicalPhysicist said:
What happened with checking a proof for its contents and not its author?!
Quod licet jovis non licet bovis.
 
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  • #32
fresh_42 said:
Quod licet jovis non licet bovis.
Bullshit! Everyone should be scrutinized for their work and not for who they are.
 
  • #33
MathematicalPhysicist said:
Bullshit! Everyone should be scrutinized for their work and not for who they are.
Of course, and in this case the author has done a lot of important work over the decades.
 
  • #34
MathematicalPhysicist said:
Bullshit! Everyone should be scrutinized for their work and not for who they are.
That's not how the world works, despite the French revolutions. And it isn't b.s. If Atiyah writes a proof and you do for the same theorem, guess which one I will read!
 
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  • #35
fresh_42 said:
Quod licet jovis non licet bovis.
Capital letters please when naming a deity :cool:
 
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