7 ms·

Riemann Hypothesis Disproved?

18 points by Quant10 4y ago

Quant10 4y ago
Not a math major, but this paper is claiming that the RH is false. Is the claim (proof) valid ?
- gus_massa 4y ago
  Math major here, but it's not my area. so I have to guess Note that it's not a "per review paper", it's just a PFD shared somewhere, a "preprint" if you like a formal word. It looks short (4 pages) and looks quite readable, so I guess that if you wait a week or two it will be a major new IF true. My guess is it's false. It looks like the author made a similar claim two years ago and it's now fixing some details. With a loooooooooooooooooooong proof that is possible because only the author can understood it good enough to fix it, but with a proof that is so short a minor error would have been fixed soon.
  - pwdisswordfish9 4y ago
    It looks like the author made the opposite claim three years ago: http://math.ahu.edu.cn/_upload/article/files/85/03/f191ded54991a45d0dde5f53576e/d0cea4af-90b4-4e99-b8ce-47ffb111328f.pdf http://math.ahu.edu.cn/_upload/article/files/85/03/f191ded54...
    - gus_massa 4y ago
      I'm not going to blame anyone because I make this all the time. Sometimes the poof that something is true or false are very similar. In this case the difference is if some value is 1/2 or 3/4. Anyway, my coworkers find the error before we publish it.
    - kklisura 4y ago
      Someone reviewed that specific paper here [1]. [1] https://web.archive.org/web/20220128195023/https://motls.blogspot.com/2019/10/some-fun-with-proof-of-riemann.html https://web.archive.org/web/20220128195023/https://motls.blo...
      - Quant10 4y ago
        This was a review of the author's earlier paper of 2018, in which they were actually claiming a proof of the RH. On their arXiv page: https://arxiv.org/abs/2006.12546 https://arxiv.org/abs/2006.12546, the author states that "though all my previous proposed (dis)proofs were flawed, i think the flaws pointed me towards the right direction..."
  - oblvious-earth 4y ago
    This is actually the 19th version of the paper the author has published in just over 2 years: https://arxiv.org/abs/2006.12546 https://arxiv.org/abs/2006.12546 Being such a short paper if people in this field thought it was close to actually disproving the Riemann Hypothesis likely another mathematician could takes the proofs concept, fix it, publish it, and have it peer reviewed to snipe the claim of disproving the Riemann Hypothesis.
    - gus_massa 4y ago
      Fully agree. I guess there is still some honor and the other person would invite the original author as an author of the fixed paper, but it looks very snipable.
      - Quant10 4y ago
        If there are no significant improvements to the paper by the "second" author, such acts of "sniping" might be treated by the math community as academic theft, and the second author might not get any credit at all. If anything, their reputation might be seriously damaged. This is exactly what happened with Perelman's proof of the Poincare conjecture: https://www.newyorker.com/magazine/2006/08/28/manifold-destiny https://www.newyorker.com/magazine/2006/08/28/manifold-desti...
        oblvious-earth 4y ago
        Perelman and all the surrounding controversy is the most extreme examples in modern times and I feel the mathematical community has got much more accepting of group contributions in the last 2 decades. But yes, if the proof is only missing easy plug-able gaps then likely a mathematician would reach out to the author so they could co-author the paper. Anything else would be rude. I was more meaning in the case where the proof has some insight but not apply it in a way that actually disproves the Riemann Hypothesis.
- mjreacher 4y ago
  No and this post will hopefully be flagged soon. A quick Google search of the author would also show that they have published several similar proofs before [0] which were also wrong. [0]: https://arxiv.org/abs/2006.12546 https://arxiv.org/abs/2006.12546
  - Quant10 4y ago
    If anyone is going to solve the RH, it would be after numerous failed attempts.
    - gus_massa 4y ago
      Most people wait until they are almost sure that the proof is correct before publishing it, with a few informal reviews of coworkers. It's strange that he posted so many versions. Is this [v19] version the final correct one or he is going to post a fix in a few weeks?
      - Quant10 4y ago
        I wouldn't know. But from the author's arXiv statement [1] that ..though all of my previous (dis)proofs were flawed, i think the flaws pointed me towards the right direction..." it seems they are quite confident in the current version. [1] https://arxiv.org/abs/2006.12546 https://arxiv.org/abs/2006.12546
        gus_massa 4y ago
        I've read that, but looking at the previous history I'd wait a month before reading it in case the author finds yet another error. (Unless you are a specialist in the subject.)
        Quant10 4y ago
        I'm a physics major, unfortunately. But i have taken some basic courses in number theory & analysis. As far as i can tell, the argument looks interesting (can't find any serious fault in it). However, i can't say anything conclusive. Maybe someone else will.
gerikson 4y ago
Betteridge's law of headlines says: no.
- t6jvcereio 4y ago
  That's not how maths work. Please keep the memes at the door, doesn't help the quality of the conversation
  - majou 4y ago
    It's less a meme and more a decent rule of thumb.
    - t6jvcereio 4y ago
      It's a literal meme, and the fact you think is a decent rule of thumb tells me you never studied maths. Meme: an idea, behavior, style, or usage that spreads from person to person within a culture
azeirah 4y ago
I don't know any math, but I did quickly check who this author is. He's some guy with no credentials, graduated as an accountant. Clearly has a knack for math and is not terrible at it (mathoverflow), but otherwise has no social credit supporting his credibility (twitter, LinkedIn). Doesn't mean he's necessarily wrong, maybe he got it. It's not impossible that he's some kind of contemporary Ramanujan, but yeah.. unlikely.
- bitL 4y ago
  "He's some guy with no credentials, working at the Swiss Patent Office in Bern. Clearly has a knack for physics and is not terrible at it (physics teaching diploma), but otherwise has no social credit supporting his credibility (Nature, Knowledge)."
- kklisura 4y ago
  Someone did a review of his previous work on Riemann hypothesis [1]. Not into this field, but apparently that blog is being run by someone credible [2]. I have found a link to [1] via this forum [3]. [1] https://web.archive.org/web/20220128195023/https://motls.blogspot.com/2019/10/some-fun-with-proof-of-riemann.html https://web.archive.org/web/20220128195023/https://motls.blo... [2] https://en.wikipedia.org/wiki/Lubo%C5%A1_Motl https://en.wikipedia.org/wiki/Lubo%C5%A1_Motl [3] https://www.scienceforums.net/topic/124368-has-the-riemann-hypothesis-has-been-proved-here/ https://www.scienceforums.net/topic/124368-has-the-riemann-h...
  - Quant10 4y ago
    This was a review of the author's earlier paper of 2018, in which they were actually claiming a proof of RH. On their arXiv page: https://arxiv.org/abs/2006.12546 https://arxiv.org/abs/2006.12546, the author states that "though all my previous proposed (dis)proofs were flawed, i think the flaws pointed me towards the right direction."
- throwoutway 4y ago
  HavkerNews likes to appeal to authority and elitism
t6jvcereio 4y ago
The Riemann hypothesis is that the zeta function has all its (nontrivial) zeros with real part 1/2. To disprove this you need only to present a single zero with real part != 1/2. So what's that number you found then? No need to write a paper, just show me the number. I'm not even going to bother opening the link.
- sebzim4500 4y ago
  This result is almost certainly bullshit, but there is nothing wrong in principle with a non constructive proof. Sometimes it is much easier to prove a counterexample exists than to demonstrate that a specific number is a counterexample. Here's the canonical example of this: We want to show that there exists irrational numbers a, b s.t. a^b is rational (with b != 0). If sqrt(2) ^ sqrt(2) is rational then we are done. Otherwise, (sqrt(2) ^ sqrt(2)) ^ sqrt(2) = 2 so that is a counterexample. In this case, it is possible to prove that sqrt(2) ^ sqrt(2) is irrational, but this requires much more work.
  - twiceaday 4y ago
    Suppose sqrt(2)=a/b, a reduced rational. Then 2b*b=a*a, so a is even. But the right side has two a's therefore two 2's, so b is even. Contradiction!
    - etothepii 4y ago
      You proved sqrt(2) is irrational not sqrt(2)^sqrt(2)
      - twiceaday 4y ago
        d'oh!
- contravariant 4y ago
  Hmm, while it is in all likelihood not true it doesn't look like your average crackpot and it doesn't look like the proof was posted in bad faith. Whether you want to put a lot of effort into it is your call but it's still interesting to see what kind of approach they chose.

18 points by Quant10 4y ago

Quant10 4y ago

Not a math major, but this paper is claiming that the RH is false. Is the claim (proof) valid ?

gus_massa 4y ago
Math major here, but it's not my area. so I have to guess Note that it's not a "per review paper", it's just a PFD shared somewhere, a "preprint" if you like a formal word. It looks short (4 pages) and looks quite readable, so I guess that if you wait a week or two it will be a major new IF true. My guess is it's false. It looks like the author made a similar claim two years ago and it's now fixing some details. With a loooooooooooooooooooong proof that is possible because only the author can understood it good enough to fix it, but with a proof that is so short a minor error would have been fixed soon.
- pwdisswordfish9 4y ago
  It looks like the author made the opposite claim three years ago: http://math.ahu.edu.cn/_upload/article/files/85/03/f191ded54991a45d0dde5f53576e/d0cea4af-90b4-4e99-b8ce-47ffb111328f.pdf http://math.ahu.edu.cn/_upload/article/files/85/03/f191ded54...
  - gus_massa 4y ago
    I'm not going to blame anyone because I make this all the time. Sometimes the poof that something is true or false are very similar. In this case the difference is if some value is 1/2 or 3/4. Anyway, my coworkers find the error before we publish it.
  - kklisura 4y ago
    Someone reviewed that specific paper here [1]. [1] https://web.archive.org/web/20220128195023/https://motls.blogspot.com/2019/10/some-fun-with-proof-of-riemann.html https://web.archive.org/web/20220128195023/https://motls.blo...
    - Quant10 4y ago
      This was a review of the author's earlier paper of 2018, in which they were actually claiming a proof of the RH. On their arXiv page: https://arxiv.org/abs/2006.12546 https://arxiv.org/abs/2006.12546, the author states that "though all my previous proposed (dis)proofs were flawed, i think the flaws pointed me towards the right direction..."
- oblvious-earth 4y ago
  This is actually the 19th version of the paper the author has published in just over 2 years: https://arxiv.org/abs/2006.12546 https://arxiv.org/abs/2006.12546 Being such a short paper if people in this field thought it was close to actually disproving the Riemann Hypothesis likely another mathematician could takes the proofs concept, fix it, publish it, and have it peer reviewed to snipe the claim of disproving the Riemann Hypothesis.
  - gus_massa 4y ago
    Fully agree. I guess there is still some honor and the other person would invite the original author as an author of the fixed paper, but it looks very snipable.
    - Quant10 4y ago
      If there are no significant improvements to the paper by the "second" author, such acts of "sniping" might be treated by the math community as academic theft, and the second author might not get any credit at all. If anything, their reputation might be seriously damaged. This is exactly what happened with Perelman's proof of the Poincare conjecture: https://www.newyorker.com/magazine/2006/08/28/manifold-destiny https://www.newyorker.com/magazine/2006/08/28/manifold-desti...
      - oblvious-earth 4y ago
        Perelman and all the surrounding controversy is the most extreme examples in modern times and I feel the mathematical community has got much more accepting of group contributions in the last 2 decades. But yes, if the proof is only missing easy plug-able gaps then likely a mathematician would reach out to the author so they could co-author the paper. Anything else would be rude. I was more meaning in the case where the proof has some insight but not apply it in a way that actually disproves the Riemann Hypothesis.
mjreacher 4y ago
No and this post will hopefully be flagged soon. A quick Google search of the author would also show that they have published several similar proofs before [0] which were also wrong. [0]: https://arxiv.org/abs/2006.12546 https://arxiv.org/abs/2006.12546
- Quant10 4y ago
  If anyone is going to solve the RH, it would be after numerous failed attempts.
  - gus_massa 4y ago
    Most people wait until they are almost sure that the proof is correct before publishing it, with a few informal reviews of coworkers. It's strange that he posted so many versions. Is this [v19] version the final correct one or he is going to post a fix in a few weeks?
    - Quant10 4y ago
      I wouldn't know. But from the author's arXiv statement [1] that ..though all of my previous (dis)proofs were flawed, i think the flaws pointed me towards the right direction..." it seems they are quite confident in the current version. [1] https://arxiv.org/abs/2006.12546 https://arxiv.org/abs/2006.12546
      - gus_massa 4y ago
        I've read that, but looking at the previous history I'd wait a month before reading it in case the author finds yet another error. (Unless you are a specialist in the subject.)
        Quant10 4y ago
        I'm a physics major, unfortunately. But i have taken some basic courses in number theory & analysis. As far as i can tell, the argument looks interesting (can't find any serious fault in it). However, i can't say anything conclusive. Maybe someone else will.

gerikson 4y ago

Betteridge's law of headlines says: no.

t6jvcereio 4y ago
That's not how maths work. Please keep the memes at the door, doesn't help the quality of the conversation
- majou 4y ago
  It's less a meme and more a decent rule of thumb.
  - t6jvcereio 4y ago
    It's a literal meme, and the fact you think is a decent rule of thumb tells me you never studied maths. Meme: an idea, behavior, style, or usage that spreads from person to person within a culture

azeirah 4y ago

I don't know any math, but I did quickly check who this author is. He's some guy with no credentials, graduated as an accountant. Clearly has a knack for math and is not terrible at it (mathoverflow), but otherwise has no social credit supporting his credibility (twitter, LinkedIn). Doesn't mean he's necessarily wrong, maybe he got it. It's not impossible that he's some kind of contemporary Ramanujan, but yeah.. unlikely.

bitL 4y ago
"He's some guy with no credentials, working at the Swiss Patent Office in Bern. Clearly has a knack for physics and is not terrible at it (physics teaching diploma), but otherwise has no social credit supporting his credibility (Nature, Knowledge)."
kklisura 4y ago
Someone did a review of his previous work on Riemann hypothesis [1]. Not into this field, but apparently that blog is being run by someone credible [2]. I have found a link to [1] via this forum [3]. [1] https://web.archive.org/web/20220128195023/https://motls.blogspot.com/2019/10/some-fun-with-proof-of-riemann.html https://web.archive.org/web/20220128195023/https://motls.blo... [2] https://en.wikipedia.org/wiki/Lubo%C5%A1_Motl https://en.wikipedia.org/wiki/Lubo%C5%A1_Motl [3] https://www.scienceforums.net/topic/124368-has-the-riemann-hypothesis-has-been-proved-here/ https://www.scienceforums.net/topic/124368-has-the-riemann-h...
- Quant10 4y ago
  This was a review of the author's earlier paper of 2018, in which they were actually claiming a proof of RH. On their arXiv page: https://arxiv.org/abs/2006.12546 https://arxiv.org/abs/2006.12546, the author states that "though all my previous proposed (dis)proofs were flawed, i think the flaws pointed me towards the right direction."
throwoutway 4y ago
HavkerNews likes to appeal to authority and elitism

t6jvcereio 4y ago

The Riemann hypothesis is that the zeta function has all its (nontrivial) zeros with real part 1/2. To disprove this you need only to present a single zero with real part != 1/2. So what's that number you found then? No need to write a paper, just show me the number. I'm not even going to bother opening the link.

sebzim4500 4y ago
This result is almost certainly bullshit, but there is nothing wrong in principle with a non constructive proof. Sometimes it is much easier to prove a counterexample exists than to demonstrate that a specific number is a counterexample. Here's the canonical example of this: We want to show that there exists irrational numbers a, b s.t. a^b is rational (with b != 0). If sqrt(2) ^ sqrt(2) is rational then we are done. Otherwise, (sqrt(2) ^ sqrt(2)) ^ sqrt(2) = 2 so that is a counterexample. In this case, it is possible to prove that sqrt(2) ^ sqrt(2) is irrational, but this requires much more work.
- twiceaday 4y ago
  Suppose sqrt(2)=a/b, a reduced rational. Then 2b*b=a*a, so a is even. But the right side has two a's therefore two 2's, so b is even. Contradiction!
  - etothepii 4y ago
    You proved sqrt(2) is irrational not sqrt(2)^sqrt(2)
    - twiceaday 4y ago
      d'oh!
contravariant 4y ago
Hmm, while it is in all likelihood not true it doesn't look like your average crackpot and it doesn't look like the proof was posted in bad faith. Whether you want to put a lot of effort into it is your call but it's still interesting to see what kind of approach they chose.