5 ms·

Your post feels like a dispatch from bizarro-world. There is a good amount of second-order evidence that the proof is wrong. Further, I skimmed the introductio

Your post feels like a dispatch from bizarro-world. There is a good amount of second-order evidence that the proof is wrong. Further, I skimmed the introduction, and it seems the indicated approach cannot possibly work. My guess is that both authors are senile. (They're quite old.) If you give me decent odds, I'd be happy to bet against you regarding the proof's correctness. Would you take 1:1?

ogogmad 4y ago
The tone of your comment is pretty harsh. What kind of 2nd-order evidence do you see? And why did you learn from the introduction that makes you so sure? It's only an introduction, which might only give you an oversimplified summary of their ideas. Are both of them senile?
- spekcular 4y ago
  Yeah, my guess is that both are senile if they're putting this on the arxiv. Second-order evidence: Old mathematicians (~80). Famous problem. Weird, imprecise writing style. No mention of the proof by mainstream mathematical news sources (breakthroughs are usually accompanied by excited blogging/tweeting). No acknowledgements directed at other mathematicians who have checked or commented on the proof. [deleted argument here; replaced by more precise comment below] My tone is harsh because I think the best thing to do is to quietly ignore it, similar to how the community treated Atiyah's claims of a RH proof at the end of his life.
  - ogogmad 4y ago
    > The argument looks like it's based on large n asymptotics, so even assuming everything works correctly the strongest statement they can hope to show is that the theorem is true for all n > n_0, where n_0 is some large constant. But there is no mention of this fact. The theorem is claimed for all n. Have you seen this comment? https://news.ycombinator.com/item?id=34083099 https://news.ycombinator.com/item?id=34083099
    - spekcular 4y ago
      Yes. How does it bear on what I wrote?
      - eganist 4y ago
        You're claiming: > the argument looks like it's based on large n asymptotics, so even assuming everything works correctly the strongest statement they can hope to show is that the theorem is true for all n > n_0, where n_0 is some large constant. but there is no mention of this fact. the theorem is claimed for all n. They're claiming: > Theorem 7. If there is a map L which cannot be 4-coloured then only an exponentially small fraction of the maps with n edges can be 4-coloured. These claims appear mutually exclusive.
        spekcular 4y ago
        See above clarification about the bad writing.
      - adgjlsfhk1 4y ago
        The point is that if there were a small graph that was a counter-example, then there would be large graph counter-examples (and the percentage of them would increase with graph size), so proving that the 4 color theorem is true for large graphs implies that it is true for all graph sizes.
  - adgjlsfhk1 4y ago
    Some counterpoints: 2 mathematicians greatly increases chances of senility. Blogs/twitter also correlate much stronger with author age than truth of statement. >The argument looks like it's based on large n asymptotics, so even assuming everything works correctly the strongest statement they can hope to show is that the theorem is true for all n > n_0, where n_0 is some large constant. But there is no mention of this fact. The theorem is claimed for all n. This is completely wrong. A proof for all n>n_0 is a proof for all n, since any counter-examples have to exist as subgraphs of arbitrarily large graphs.
    - spekcular 4y ago
      I don't think asymptotic estimates of that form suffice to treat this problem. (Where else in combinatorics has an argument of this form succeeded? What intuitive reason is there to expect it to succeed here?) Specifically I think section 4 is basically nonsense. (I see Sniffnoy has already pointed this out below.) (Re: your comment, Theorem 7 is going to fail below the smallest counterexample, right? This is bad, imprecise writing - a red flag.)
  - blast 4y ago
    > I think the best thing to do is to quietly ignore it If you think that's the best thing to do then why not do it?
  - p1necone 4y ago
    This is a bizarrely hostile attitude to have. Critique their work, not their age.
    - spekcular 4y ago
      It's not bizarre at all. The math community has unfortunately been down this road many times before. When an 80-year-old announces a 7 page proof of a famous problem, the smart money is on the proof being wrong. As the comments elsewhere on this story indicate, this heuristic turned out to be correct. The only new twist is that we have two 80-year-olds this time, not one. To be clear, I don't like this state of affairs. As suggested above, the best course of action seems to be to ignore the posting.
      - JohnHaugeland 4y ago
        It is not appropriate for you to speculate publicly about the mental health of people you've never met. It's so inappropriate that in the field that's actually trained for this, they're disallowed by compact, even with extensive evidence. Please stop.
        Anderkent 4y ago
        >It's so inappropriate that in the field that's actually trained for this, they're disallowed by compact, even with extensive evidence. The field trained for this is not refraining from this because it's hard to get right, but because it undermines the privacy promise they give their clients! not an argument applicable to people who do not have that professional reputation to uphold. Of course you should speculate about mental health of people when it's relevant to the topic - it's a factor heavily shaping many people's behaviour!
  - wikfwikf 4y ago
    * No discussion of how these techniques were developed. * No discussion of why they were not found by other people in the past. * No discussion of how these techniques could be used on other problems. * A lot of calculations which would be left out as trivial by most graph theory papers (for example, calculations about the edge counts of subgraphs)
deleted 4y ago
[deleted]
dang 4y ago
Hey, could you please make your substantive points without swipes and personal attacks? If you know more than others, that's great, but then share some of what you know (without putdowns) so the rest of us can learn. If you don't want to do that, not posting is also a fine option. I have no idea whether the proof is right or wrong, and I'm not so sentimental as to believe that the harsher person is more likely to be wrong. (Besides, naysayers are usually right, just like they are when predicting that any given startup will fail.) However, the HN guidelines (https://news.ycombinator.com/newsguidelines.html https://news.ycombinator.com/newsguidelines.html) ask you not to post like this and that's important too. Other users are making their case against the OP while following the guidelines just fine. Please be more like them.
- AbrahamParangi 4y ago
  I am going to finetune a content moderation model based only on the principle that it should, at all times, ask itself: “what would dang do?” and then do that
- spekcular 4y ago
  Hi Dang, There's no personal attack here. I'm sorry if that comment comes across as curt, but the post I responded is (in my opinion) grossly misleading and deserves pushback. For example, consider the statement: "If the proof has a flaw, the issue will be technical and difficult to uncover," made by someone claiming years of experience as a math professor thinking about this question. This is easily identifiable as wrong, because the purported proof is just 7 pages (actually less than that due to extraneous material) and does not use any particularly technical mathematics (a strong undergraduate major probably knows enough to comprehend what's going on). Indeed, people found the error in (less than) 12 hours after that comment was made. The comment about senility is not a "swipe." It is a very real problem in the mathematics community. Mathematicians get old and are sometimes afflicted by dementia, and this unfortunately can manifest as hopeless attempts at famous problems. Atiyah's "proof" of the Riemann Hypothesis right before his death is perhaps the most well known example, but there are others that (thankfully) aren't disseminated publicly. In the pre-internet age, journal editors were able to make such things quietly disappear. But now we have the arxiv. This is valuable context for understanding why two mathematicians with distinguished publication histories might be posting an incorrect proof, which had not been provided by other comments. That being said, I will endeavor to phrase such comments more carefully in the future. Thank you for your message.
kazinator 4y ago
Their LaTeX compiled, though.

ogogmad 4y ago

The tone of your comment is pretty harsh. What kind of 2nd-order evidence do you see? And why did you learn from the introduction that makes you so sure? It's only an introduction, which might only give you an oversimplified summary of their ideas. Are both of them senile?

spekcular 4y ago
Yeah, my guess is that both are senile if they're putting this on the arxiv. Second-order evidence: Old mathematicians (~80). Famous problem. Weird, imprecise writing style. No mention of the proof by mainstream mathematical news sources (breakthroughs are usually accompanied by excited blogging/tweeting). No acknowledgements directed at other mathematicians who have checked or commented on the proof. [deleted argument here; replaced by more precise comment below] My tone is harsh because I think the best thing to do is to quietly ignore it, similar to how the community treated Atiyah's claims of a RH proof at the end of his life.
- ogogmad 4y ago
  > The argument looks like it's based on large n asymptotics, so even assuming everything works correctly the strongest statement they can hope to show is that the theorem is true for all n > n_0, where n_0 is some large constant. But there is no mention of this fact. The theorem is claimed for all n. Have you seen this comment? https://news.ycombinator.com/item?id=34083099 https://news.ycombinator.com/item?id=34083099
  - spekcular 4y ago
    Yes. How does it bear on what I wrote?
    - eganist 4y ago
      You're claiming: > the argument looks like it's based on large n asymptotics, so even assuming everything works correctly the strongest statement they can hope to show is that the theorem is true for all n > n_0, where n_0 is some large constant. but there is no mention of this fact. the theorem is claimed for all n. They're claiming: > Theorem 7. If there is a map L which cannot be 4-coloured then only an exponentially small fraction of the maps with n edges can be 4-coloured. These claims appear mutually exclusive.
      - spekcular 4y ago
        See above clarification about the bad writing.
    - adgjlsfhk1 4y ago
      The point is that if there were a small graph that was a counter-example, then there would be large graph counter-examples (and the percentage of them would increase with graph size), so proving that the 4 color theorem is true for large graphs implies that it is true for all graph sizes.
- adgjlsfhk1 4y ago
  Some counterpoints: 2 mathematicians greatly increases chances of senility. Blogs/twitter also correlate much stronger with author age than truth of statement. >The argument looks like it's based on large n asymptotics, so even assuming everything works correctly the strongest statement they can hope to show is that the theorem is true for all n > n_0, where n_0 is some large constant. But there is no mention of this fact. The theorem is claimed for all n. This is completely wrong. A proof for all n>n_0 is a proof for all n, since any counter-examples have to exist as subgraphs of arbitrarily large graphs.
  - spekcular 4y ago
    I don't think asymptotic estimates of that form suffice to treat this problem. (Where else in combinatorics has an argument of this form succeeded? What intuitive reason is there to expect it to succeed here?) Specifically I think section 4 is basically nonsense. (I see Sniffnoy has already pointed this out below.) (Re: your comment, Theorem 7 is going to fail below the smallest counterexample, right? This is bad, imprecise writing - a red flag.)
- blast 4y ago
  > I think the best thing to do is to quietly ignore it If you think that's the best thing to do then why not do it?
- p1necone 4y ago
  This is a bizarrely hostile attitude to have. Critique their work, not their age.
  - spekcular 4y ago
    It's not bizarre at all. The math community has unfortunately been down this road many times before. When an 80-year-old announces a 7 page proof of a famous problem, the smart money is on the proof being wrong. As the comments elsewhere on this story indicate, this heuristic turned out to be correct. The only new twist is that we have two 80-year-olds this time, not one. To be clear, I don't like this state of affairs. As suggested above, the best course of action seems to be to ignore the posting.
    - JohnHaugeland 4y ago
      It is not appropriate for you to speculate publicly about the mental health of people you've never met. It's so inappropriate that in the field that's actually trained for this, they're disallowed by compact, even with extensive evidence. Please stop.
      - Anderkent 4y ago
        >It's so inappropriate that in the field that's actually trained for this, they're disallowed by compact, even with extensive evidence. The field trained for this is not refraining from this because it's hard to get right, but because it undermines the privacy promise they give their clients! not an argument applicable to people who do not have that professional reputation to uphold. Of course you should speculate about mental health of people when it's relevant to the topic - it's a factor heavily shaping many people's behaviour!
- wikfwikf 4y ago
  * No discussion of how these techniques were developed. * No discussion of why they were not found by other people in the past. * No discussion of how these techniques could be used on other problems. * A lot of calculations which would be left out as trivial by most graph theory papers (for example, calculations about the edge counts of subgraphs)

deleted 4y ago

[deleted]

dang 4y ago

Hey, could you please make your substantive points without swipes and personal attacks? If you know more than others, that's great, but then share some of what you know (without putdowns) so the rest of us can learn. If you don't want to do that, not posting is also a fine option. I have no idea whether the proof is right or wrong, and I'm not so sentimental as to believe that the harsher person is more likely to be wrong. (Besides, naysayers are usually right, just like they are when predicting that any given startup will fail.) However, the HN guidelines (https://news.ycombinator.com/newsguidelines.html https://news.ycombinator.com/newsguidelines.html) ask you not to post like this and that's important too. Other users are making their case against the OP while following the guidelines just fine. Please be more like them.

AbrahamParangi 4y ago
I am going to finetune a content moderation model based only on the principle that it should, at all times, ask itself: “what would dang do?” and then do that
spekcular 4y ago
Hi Dang, There's no personal attack here. I'm sorry if that comment comes across as curt, but the post I responded is (in my opinion) grossly misleading and deserves pushback. For example, consider the statement: "If the proof has a flaw, the issue will be technical and difficult to uncover," made by someone claiming years of experience as a math professor thinking about this question. This is easily identifiable as wrong, because the purported proof is just 7 pages (actually less than that due to extraneous material) and does not use any particularly technical mathematics (a strong undergraduate major probably knows enough to comprehend what's going on). Indeed, people found the error in (less than) 12 hours after that comment was made. The comment about senility is not a "swipe." It is a very real problem in the mathematics community. Mathematicians get old and are sometimes afflicted by dementia, and this unfortunately can manifest as hopeless attempts at famous problems. Atiyah's "proof" of the Riemann Hypothesis right before his death is perhaps the most well known example, but there are others that (thankfully) aren't disseminated publicly. In the pre-internet age, journal editors were able to make such things quietly disappear. But now we have the arxiv. This is valuable context for understanding why two mathematicians with distinguished publication histories might be posting an incorrect proof, which had not been provided by other comments. That being said, I will endeavor to phrase such comments more carefully in the future. Thank you for your message.

kazinator 4y ago

Their LaTeX compiled, though.