It's worth noting that one of the authors of the cited paper [1] (Nick Polson) is infamous for claiming (incorrectly) a proof of the Riemann hypothesis [2].
This case is somewhat strange because he's not the usual mathematical crank; he's actually a quite well-recognized economics researcher who is clearly mathematically competent. But for some reason he persists. (If you search his name, you can find his YouTube channel where he lectures on his RH work...)
"A Hadamard factorization of the Riemann Xi-function is constructed to characterize the zeros of the zeta function."
Like, dude, you are claiming to solve a Millennium problem, you're gonna have to put a little more effort into explaining, ya know, the breakthrough...
We care about the Riemann Hypothesis not for the theorem itself, but because the methods used to solve it will surely be revolutionary and it's those methods that are important, not the theorem.
That's what makes it a Millennium problem. So a paper like this immediately shows the author doesn't even understand why the problem is important, let alone its solution.
> Like, dude, you are claiming to solve a Millennium problem, you're gonna have to put a little more effort into explaining, ya know, the breakthrough...
In the abstract? If papers needed to cover everything in the abstract they would need to have an abstract for the abstract and they you’d just end up complaining about the abstract abstract not being complete…
It's odd that people can't work on something in which they're interested and talk about it publicly without being labeled a "crank".
Sorry, there's nothing holy about the Riemann Hypothesis; anyone can add their input to the problem, especially on ArXiV and/or YouTube. You know, that's how discussions can start, and sometimes people want to discuss things with others.
It seems like you might think only certain people should work on these special problems, and only if they do it correctly according to you.
Your comment is just an ad hominem, so why don't you tell us why you're actually mentioning this? Do you think the math is wrong in the relevant material from the article because of his RH-related musings on ArXiV, or do you have an anti-RH-researcher bias that you want to share with the world? Are you just hating on someone?
It's not the discussion that makes you a crank. It's publishing a paper claiming you have solved something that you haven't even begun to understand. It's bypassing peer review. It's ignoring all the literature out there and claiming that is somehow a virtue.
You have an interesting idea? Go ahead, please share it! But it's not productive to just start with "Look everybody, I solved it!"
It just wastes everyone's time. For example, this paper. It would take a lot of time to sit down and work through the math until I find a specific error in it. But the barren abstract and reference sections strongly suggest that would be a huge waste of my time and energy.
Mochizuki pulled this stunt with the ABC conjecture. Wasted YEARS of mathematicians' time just to arrive at the conclusion it was all elaborate mathematical smoke and mirrors. The guy is an egotistical asshole with a messiah complex, and managed to burn a lot of PhD students by chasing his red herring. Not cool.
I think a lot of people don't appreciate how open mathematicians are, in general, to work "outside the field" - it's especially baked into the DNA through lessons like e.g. Ramanujan.
This guy though, knows what the right way to present the idea would be, but for some reason (ego? knowing it's weak/broken? pique?) chose not to.
Further, in certain cases (P =? NP is one I know of) it has been proven that certain types[0] of proofs cannot possibly work -- and yet people keep offering "proofs" of those bound-to-be-wrong types.
[0] Not sure if 'types' is the right word? Using it colloquially. Maybe 'classes' would be more accurate?
It's subtle, because some of the impossibility proofs are effectively saying that any real proof needs to be somehow sensitive to whether it's in an imaginary universe with oracles, so they can _fail_ in them!
It really is mind-bending stuff -- I have only the vaguest idea of how these proofs could work, but you summarized it beautifully.
As an aside, this is also perhaps also one of the best motivating examples of the idea of "oracles" in math. ("Ok, assume we can do $IMPOSSIBLE_THING... now what?" :) )
> It's not the discussion that makes you a crank. It's publishing a paper claiming you have solved something that you haven't even begun to understand. It's bypassing peer review. It's ignoring all the literature out there and claiming that is somehow a virtue.
You've effectively said that people can't post things on ArXiV unless they're up to your unstated standards; otherwise, they're just "cranks".
Also, no one is "bypassing peer review" by posting on ArXiV and/or YouTube, nor have I seen anyone claim "a virtue" of any sort. Where are you getting all this? From the abstracts?
> It just wastes everyone's time. For example, this paper. It would take a lot of time to sit down and work through the math until I find a specific error in it. But the barren abstract and reference sections strongly suggest that would be a huge waste of my time and energy.
Well, since you've now admitted that you haven't read his work, it seems like everything you said earlier really must be coming from the abstracts alone.
> It just wastes everyone's time. For example, this paper. It would take a lot of time to sit down and work through the math until I find a specific error in it. But the barren abstract and reference sections strongly suggest that would be a huge waste of my time and energy.
Who's time is wasted? The random people who volunteer to read his ArXiV submissions and/or YouTube videos? Really, the only waste of time I've seen is your ad hominem comment in a HN post that isn't even about the author you're blatantly criticizing.
> Mochizuki pulled this stunt with the ABC conjecture. Wasted YEARS of mathematicians' time just to arrive at the conclusion it was all elaborate mathematical smoke and mirrors. The guy is an egotistical asshole with a messiah complex, and managed to burn a lot of PhD students by chasing his red herring. Not cool.
And that's why we must all attack Mochizuki whenever we see his name, right? Do you know Nick? Is he egotistical? Does he have a messiah complex? Are you just going on a tangent now? Are you just math trolling?
Not trolling, I am serious. It took Peter freakin Scholze to finally settle the debate over Mochizuki's work. What came out of it? What else could Scholze have been working on instead of spending time finding the incredibly subtle gaps in logic that he used to construct his false theory?
What Mochizuki did was wrong is because he was utterly uncooperative with the mathematics community, he would answer questions only with more papers that never addressed the concerns being raised, and he was offended that so much scrutiny was applied.
Has Nick made an effort to educate people on the incredible breakthrough he has made? How many lectures has he given on it? Any conference videos on YouTube? Because I'll watch them. Mochi is an extreme example, so I'm sure he's not trying to do anything wrong. He should just retract the paper and keep working on it. An interested volunteer can tell him what is specifically wrong, and that's all that needs to happen.
> It is bad practice to post incorrect results and not retract them when this is pointed out.
And it's good practice to take shots at people whenever you see their name?
Also, no, there's no "practice" that says you can't keep a mistake posted on ArXiV or YouTube. That just sounds like something you've made up to justify attacking someone.
Peer review isn't a great modern invention. It's better to publish things out in the open and allow discussion of them. If we perform code reviews out in the open and it has proven exceptionally successful then I don't see why we wouldn't encourage the same for scientific research. The fact that peer reviews happen in private makes the whole process opaque to outsiders, and it simply creates artificial barriers.
If you have valid criticisms of something, you can make them in public and help everyone involved grow.
Unfortunately, if you aren't already part of the in-crowd, getting peer review at all can be very difficult, if you have any type of unorthodox idea. Because, you guessed it, you get labelled as a "crank", so why bother wasting time reviewing your paper?
He has continued to update the paper (as recently as last year), it has not been retracted, and he appears to maintain the proof is correct on his YouTube channel.
We all make mistakes, and no one would really care if he admitted this. What makes the case notable is that he has enough mathematical training that he should be able recognize the proof is wrong. Especially after the errors are uncovered by others and communicated to him. Continuing to assert the proof is correct after errors have been found is bizarre.
> He has continued to update the paper (as recently as last year), it has not been retracted, and he appears to maintain the proof is correct on his YouTube channel.
You know that ArXiV and YouTube aren't considered "journals" and don't have a similar requirement for "retractions". It sounds like you think he should hide his shame; otherwise he deserves your attacks.
> We all make mistakes, and no one would really care if he admitted this. What makes the case notable is that he has enough mathematical training that he should really be able recognize his proof is wrong, especially after the errors are uncovered by others. Continuing to assert the proof is correct after errors have been found is bizarre.
People probably shouldn't, and don't, care because he's not affecting them in any way with his RH-related ArXiV and YouTube musing.
More importantly, where are there people showing him how his proof is wrong, and where is he outright denying their points/proofs? It seems like I'm missing a link or two, because I haven't seen any of these things, yet you're referring to them as though they're apparent and damning.
My guess is that he simply doesn't get feedback about this stuff, and he probably doesn't even care that much, because this is just a set of ideas with which he likes to work. I've seen no signs of a charged or "high stakes" math community engagement, and definitely not the kind that deserves these unwarranted personal criticisms.
You know that ArXiV and YouTube aren't considered "journals" and don't have a similar requirement for "retractions".
My guess is that he simply doesn't get feedback about this stuff, and he probably doesn't even care that much, because this is just a set of ideas with which he likes to work.
Having every right to be a jackass doesn't make you not a jackass.
I believe knowingly disseminating incorrect results is wrong. This is a violation of fundamental academic standards; we would not tolerate it in any other scientific field. Do you disagree?
Arxiv's submission policy says: "Submissions to arXiv should be topical and refereeable scientific contributions that follow accepted standards of scholarly communication." (https://arxiv.org/help/submit)
It against the prevailing norms of scholarly communication to publish results with serious errors known to the author.
I agree YouTube does not have this policy. I still find incorrectly claiming a proof of RH on YouTube distasteful, for similar reasons.
I personally know a mathematician who has pointed out the mistakes to him. But also, Polson good enough at math himself that he should be aware of these points. I would criticize him just the same if he knowingly published false economics results.
> Arxiv's submission policy says: "Submissions to arXiv should be topical and refereeable scientific contributions that follow accepted standards of scholarly communication." (https://arxiv.org/help/submit)
If you're implying that he violated ArXiV's submission policy, then you're going to need to stretch the definitions of those words a bit, as you attempted to do.
> I agree YouTube does not have this policy. I still find incorrectly claiming a proof of RH on YouTube distasteful, for similar reasons.
I get that you have all these personal opinions/takes, but ArXiV and YouTube don't appear to be justifying them.
> I personally know a mathematician who has pointed out the mistakes to him. But also, Polson good enough at math himself that he should be aware of these points. I would criticize him just the same if he knowingly published false economics results.
OK, so where did they post these discussions with Nick so that we can all clearly see that he's a bad or stupid person, as you're implying? Your comments assume that this is all common knowledge or apparent, but it isn't.
Are we just supposed to take your word for it? Well, I happen to know Nick, and, from my experiences with him, I have no reason to believe any of the things you're saying and/or implying.
I don't think Nick Polson is a bad or stupid person. I never said this. In fact, as I said above, I believe he is quite mathematically competent. But even competent people make mistakes.
Norms of scholarly communication are not a personal opinion.
You have also curiously avoided my question about whether it is improper to knowingly disseminate incorrect results.
This case is somewhat strange because he's not the usual mathematical crank; he's actually a quite well-recognized economics researcher who is clearly mathematically competent. But for some reason he persists. (If you search his name, you can find his YouTube channel where he lectures on his RH work...)
[1] https://arxiv.org/abs/2208.09563
[2] https://arxiv.org/abs/1708.02653.