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I'm surprised and worried by the fact that the question about Collatz conjecture stays opened.

Let me explain myself. There were many cases, when different people couldn't agree whether some particular question is ontopic/subjective/... and should be closed — and it's ok, there always is some «gray area». But in this particular case even supporters of the question say (to quote TonyK): «You are right -- it's not really a question. But to delete it because of that?» and «I am frankly surprised that a mathematician would object to this post simply because it violates the posting rules. Like you're a zombie or something.».

And this (especially when the corresponding comment is highly-upvoted) really worries me. Do we still agree that math.SE shouldn't become another Reddit but stay a place for asking and answering mathematical questions?..

Upd. I mean, there can be exceptions of rules, of course. But in each such case there should be some important reason for this. «Every rule can be broken, but no rule may be ignored.»

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  • $\begingroup$ ("Important" -- as in, say, mathoverflow.net/questions/63221/…) $\endgroup$ – Grigory M Jun 3 '11 at 18:58
  • $\begingroup$ I suggest, downvoter(s) explain, what policy they think should be used. $\endgroup$ – Grigory M Jun 3 '11 at 19:01
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    $\begingroup$ Grigory, I think you're being very dogmatic. It's a perfectly mathematical question - does paper X make sense? $\endgroup$ – Yuval Filmus Jun 3 '11 at 19:14
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    $\begingroup$ @Yuval: "Please explain Grothendieck's Grand Theory" is also perfectly mathematical, but is too broad. The question is whether it is on-topic on math.se. $\endgroup$ – Aryabhata Jun 3 '11 at 19:20
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    $\begingroup$ @Yuval Probably, I wasn't clear enough: there are two distinct questions: (a) is OP a real question, and (b) should we close it if it isn't. I very well may be wrong about (a), it can be discussed. But when (b) is not even discussed -- when it's stated that answer is obviously "no" -- it surprises and worries me. $\endgroup$ – Grigory M Jun 3 '11 at 19:22
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    $\begingroup$ @Yuval I agree that the question is mathematical, but this is not the right place to ask it. An editor usually chooses a referee very carefully. The referee needs to be an expert in the field and should ideally have spent time thinking about this or similar problems. My point is that an answer like "yes, the paper is correct" on Math.SE would mean very little and can certainly not be regarded as definitive. $\endgroup$ – Alex B. Jun 4 '11 at 3:23
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    $\begingroup$ By the way, we might be getting some publicity on the way, having been linked to in two blogs, so far. $\endgroup$ – Yuval Filmus Jun 5 '11 at 0:04
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I agree with you. Such "questions" need to be closed, no matter how important or interesting the result, or credible the author. As the proponents themselves agreed, it is not a real question.

I even opened a new meta thread about whether preprints in general are on-topic. There is even an answer with proposed policy there.

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I was going to wait and see what happened. I don't think it's a great idea either, but I've been trying to be lax about these things.

Edit: TonyK asks

How would math.SE be a better place for closing such posts?

It would be more focused on what it's good at doing. Discussing preprints claiming to resolve big open problems is an iffy business, best left to the experts. Emotions can run high (as they are in danger of doing even now!) and a mathematician's work might get slandered for no good reason. There are lots of reasons to avoid such touchy subjects.

Nevertheless, again, I am willing to wait and see what happens. If the discussion takes an unsavory turn it will promptly be shut down.

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I agree that the question as it stands ("What do mathematicians think, right or wrong?") is not appropriate for Math.SE. Clearly this will not have a short, simple answer: the question is essentially asking someone to review the paper.

Discussion of whether the result is correct would certainly be desirable and interesting, but this site is not the place for it. That's better for a blog. If someone were to ask "Where is this work being discussed", that would IMHO be an appropriate question, which could be easily answered with a link.

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    $\begingroup$ Let's agree to disagree about the last part: I don't think that math.SE is a good place for collecting links to external resources. (But, at least, this is a policy that I can understand.) $\endgroup$ – Grigory M Jun 3 '11 at 19:32
  • $\begingroup$ surely there are existing meta.math.se questions discussing whether it is appropriate to post a math.se question saying "please review this math paper -- is it valid? is it correct?" $\endgroup$ – Jeff Atwood Jun 5 '11 at 17:54
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Let me repeat myself: I was thrilled to see this post. I didn't know about it until I saw it here on math.SE. And there are so many posts that don't thrill me! (I know I am not alone in this.) How would math.SE be a better place for closing such posts?

If you must close posts that don't satisfy the rules, at least close only the boring ones.

Updated to add: Aryabattha's criteria (should I capitalise that?) include:

GOOD: This new paper claiming a big result is beyond my ken to read. Before I invest the time to learn all this stuff and try to read it, I am curious: have there been any technical rebuttals or discussions of it?

Answer: We can answer your question here.

The OP about which this whole controversy rages asks:

What does mathematicians say of this proof, right or wrong?

Perhaps Aryabattha can explain where the OP slipped up here. It seems to me that the OP's question is a direct paraphrase of Aryabattha's Criterion.

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    $\begingroup$ I believe I can restate the question more mathematically, as follows: How does the author prove Theorem 4.17 on page 12? $\endgroup$ – Yuval Filmus Jun 3 '11 at 19:57
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    $\begingroup$ @Tony: Please read the proposed: meta.math.stackexchange.com/questions/2290/…. (And also read the comment again, I edited it, perhaps you missed the edit). $\endgroup$ – Aryabhata Jun 3 '11 at 19:57
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    $\begingroup$ @Tony: Sigh... You have proven yet again that it is not worth the time, having a constructive discussion with you. Goodbye. $\endgroup$ – Aryabhata Jun 3 '11 at 20:03
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    $\begingroup$ Whether you are thrilled or not is irrelevant to whether this is an on-topic question. $\endgroup$ – Qiaochu Yuan Jun 3 '11 at 20:04
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    $\begingroup$ @Yuval: An answer to that is please read the paper. Is there a specific step you don't understand? $\endgroup$ – Aryabhata Jun 3 '11 at 20:05
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    $\begingroup$ @TonyK: if you cannot behave reasonably in this conversation your comments will be deleted. Cut it out. $\endgroup$ – Qiaochu Yuan Jun 3 '11 at 20:11
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    $\begingroup$ @Aryabhatta: I've just read the paper. The step I don't understand is the proof of Theorem 4.17 on page 12 (the proof itself constitutes the bottom half of page 11). Note that the theorem doesn't state "the Collatz conjecture is true". See my answer to the original question. $\endgroup$ – Yuval Filmus Jun 3 '11 at 20:14
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    $\begingroup$ @TonyK: why would I be a moderator if I didn't think the rules were there for a reason? Again, whether you are thrilled or not is irrelevant to whether this is an on-topic question. There's plenty of space for thrilling discussions on the blogosphere. $\endgroup$ – Qiaochu Yuan Jun 3 '11 at 20:16
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    $\begingroup$ @TonyK: there are lots of questions that are mathematically interesting that should be closed. Questions that are too discussion-y, questions that are too subjective and/or argmentative, questions that are too broad... $\endgroup$ – Qiaochu Yuan Jun 3 '11 at 20:39
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    $\begingroup$ @TonyK: that wasn't meant to an exhaustive list. I already described reasons that I'm not a fan of this question in my answer. $\endgroup$ – Qiaochu Yuan Jun 3 '11 at 21:06
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    $\begingroup$ One can formulate a concrete question as follows: (i) Is my description correct? (ii) How is the claim proved? This could prompt a discussion, which doesn't really fit in math.SE. So I'm no longer sure what the best course of action is. $\endgroup$ – Yuval Filmus Jun 3 '11 at 21:23
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    $\begingroup$ @TonyK: Please calm down. Aryabattha's worries are very reasonable, and while you might not agree with them, there's no reason to be uncivilized. There's no vendetta against you, rather the community has a different opinion than you. Acting like you do will certainly keep them away from trying to understand your view on matters. $\endgroup$ – Yuval Filmus Jun 3 '11 at 22:19
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    $\begingroup$ As for my view, I lean toward Aryabattha's, though on the other hand I was very pleased to hear about this paper via this site. Perhaps we need a "news blog" associated with math.se, just as we have a chat service. $\endgroup$ – Yuval Filmus Jun 3 '11 at 22:21
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    $\begingroup$ @TonyK: It's not bizarre at all, Aryabattha was trying to understand whether I had some meaningful mathematical answer in mind. $\endgroup$ – Yuval Filmus Jun 3 '11 at 23:08
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    $\begingroup$ @Yuval, @TonyK: I feel like someone should mention (as Aryabhatta seems too polite to do so himself) that you have been misspelling his handle in your latest few comments. $\endgroup$ – Rahul Jun 4 '11 at 5:02

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