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I thought of doing a question series with the aim of understanding a paper. I would like to do it so that even undergraduates could understand. The motivation is of course that I want to understand it myself. But in order to provide context for very specific questions which may only possible to answer when reading the paper, I thought it would be better to work through that paper completely via Math.SE, with links to the question before/after and all that. Of course I would self-answer questions that I can answer but think others reading the question-series/paper may not be able to. If someone doesn't understand another part of the paper that isn't yet covered by the series, the community can seamlessly integrate that question into the series.

I'm asking in general, but the concrete example that spawned it and that would be my question-series is Cahit's "Spiral Chains: The Proofs of Tait’s and Tutte’s Three-Edge-Coloring Conjectures" paper, which implies the Four Color Theorem without need of a computer.

I'm excited to see what the community thinks about this :)


EDIT: Some thoughts have been collected and I would make my idea more precise by formulating the following guidelines:

  • The paper shouldn't be new. Brand-new research can be discussed over at MathOverflow, according to their guidelines. I think a paper should be at least a year old.
  • If it is a preprint, it should be at least several years old, say five, so that the author had a reasonable amount of time to work out errors and submit it to a journal.
  • A question series is not to be done to prove the correctness or incorrectness of the paper for whatever reasons. It is to be done to make the paper accessible to a wider range of audience and explain intermediate steps.
  • If during the question series the paper does indeed admits a seemingly weakness, then we, as a scientific community, will accept this discovery without making a big ruckus.
  • In general, if you think a question series is done about a dubious paper or dubious author, you can raise your concern, but in a civilized manner (no shaming, no name-calling including "nut", "crank" etc.). A question series is not a place for judging, critiquing, or refereeing the preprint or published article itself.
  • If you want to start a question series on your own, be sure to invest energy into it. You shall not make the first entry for the series and expect the community to do the rest, a question series is no workaround for "Please explain paper X to me!" being too broad.
  • Generally every question of the question series has to fit the MSE standards by itself, as usual.
  • To avoid the concept of question series getting abused by so-called rep-farmers step-by-step explaining simple papers (probably leading to banning this format), entries of the question series are generally to be asked as Community Wiki questions. Exceptions are usually those questions not originally related to the series but who fit completely into the paper at some point. (E.g. the existing series does not answer a question someone studying it has, that person asks a question and this question gets incorporated into the series.)
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    $\begingroup$ This sounds worthwhile to me. $\endgroup$ – hardmath May 10 '18 at 5:43
  • $\begingroup$ @PeterTaylor Sorry for the confusion. No, I was thinking and trying to convey the idea that the opposite way would be better. Because, for example, if I were to ask a question like "does an $x$ with $\mathscr{E}(x)$ really exists, what the author sees as trivial", where $\mathscr{E}(x)$ is highly dependent on constructions in the paper, I may have to explain the paper to the point anyway or hope someone reads and understands it for me. $\endgroup$ – SK19 May 10 '18 at 10:09
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    $\begingroup$ I'm concerned by the use of the verb "discussion". While a paper, preferably one with open-access as in the case mentioned, can motivate Questions about the related proofs, generalizations, historical literature, etc., the goal will still be definitive Answers rather than a discussion in which "all opinions are welcome". $\endgroup$ – hardmath May 11 '18 at 20:08
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    $\begingroup$ @hardmath I meant that in a general way, it was just about pointing those kind of questions ("Questions about the related proofs, generalizations, historical literature, etc.") in the direction of MO. I lack a better word. $\endgroup$ – SK19 May 11 '18 at 20:20
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    $\begingroup$ I'm not terribly enthusiastic about the idea; just as I'm not terribly enthusiastic about the posting of a series of questions to understand a selected text. This would make for a great chat-room, though!! $\endgroup$ – Namaste May 11 '18 at 20:55
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    $\begingroup$ @hardmath I've got the same concern, hence my recommendation that this take place in dedicated chat rooms. (BTW: discussion is a noun. Discuss is a verb, with "to discuss" being the infinitive. But whether we talk of discussions, or discussing vs. asking and answering, I think you have a great point. $\endgroup$ – Namaste May 11 '18 at 21:00
  • $\begingroup$ The questions should stand on their own. If every question is on topic by itself, then also a series of questions is on topic. $\endgroup$ – Trilarion May 23 '18 at 12:45
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Sounds like a great idea!

I once asked a question about a paper that could only be understood by those who knew the paper. The question was received well, so there does not appear to be a problem with asking questions very specific to certain papers.

However for the purpose of making the paper "understandable" for a wide audience, I believe the most important thing to keep in mind while doing this would be that the questions must be mostly self-contained: They should of course refer to the paper but they also should contain all relevant facts that are required to understand what the question is about.

For example if the goal of the question is to understand the proof of a lemma, the text of the question should itself contain the assertion and the proof, not merely refer to its position in the paper. However, if the proof needs previous results from that paper these would be only refered to. - Quoting other results from the paper would be a good means of linking the related questions.

Bottomline: If the questions will make sense as per the general rules for questions and the project does not in principle deviate from the SE concept, I cannot imagine there would be a problem.

Good luck, looking forward to see the results!

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You have left out some important aspects; see Human checkable proof of the Four Color Theorem?

Summary: Cahit is a genuine mathematician, but he has never gotten this particular material into publishable form.

Related MO post found by hardmath: Spencer-Brown's claimed proof of the four color theorem

I agree with the apparent MO stance on incomplete/preliminary research announcements.

From the link Martin found, I like Kevin Buzzard's discussion of this.

Under the circumstances, that the proof in question has never appeared in a peer reviewed journal, I would be against a large scale use of, for example, this website, for the purpose of discussing these arxiv posts.

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    $\begingroup$ I'm afraid I don't get the point you're making. What's behind the link that I missed? Counter-Link!. In this particular case it has been over 10 years since the preprint, are you saying that an intense discussion of the paper could do damage to him? For example, when a mistake in the reasoning is found? Or that he would be no longer able to submit it to a proper journal? Please elaborate. $\endgroup$ – SK19 May 10 '18 at 21:59
  • $\begingroup$ Btw, I'm almost expecting something will turn up under close examination. But I think the mathematical community can only learn from that. $\endgroup$ – SK19 May 10 '18 at 22:00
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    $\begingroup$ Thanks for the edit. I've search MathOverflow's Help Center and Meta for "preliminary" and "incomplete", but I couldn't find any policy like you said. Please provide a link. As of yet, I'm unconvinced why I should not examine an old preprint in public. $\endgroup$ – SK19 May 11 '18 at 18:27
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    $\begingroup$ @SK19 I suppose there were several posts around this topic, but I was able to find at least these two discussions at the "new" meta.MO that seem relevant: On discussion of published papers at MO and What is our policy on asking about correctness of preprints? (And you can find also some links to the "old" tea there.) $\endgroup$ – Martin Sleziak May 11 '18 at 19:01
  • $\begingroup$ @MartinSleziak thank you. I have now changed the word "policy" in the answer above to "apparent stance." $\endgroup$ – Will Jagy May 11 '18 at 19:07
  • $\begingroup$ @MartinSleziak Thanks, these are good thoughts to be taken into consideration. $\endgroup$ – SK19 May 11 '18 at 19:19
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    $\begingroup$ I've incorporated some of these thoughts into a draft of possible guidelines. I hope I could address your concerns. $\endgroup$ – SK19 May 11 '18 at 20:25
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I think it would be a good idea to create a new tag for this venture, so long as you are really going to create enough content to deserve it's own tag (judgement call though). That way any user can easily find all the questions that have been created for this series.

I'm also curious what the rest of the community thinks of this idea.

Or if you don't think this is a good idea, at least be sure to include a bunch of links in each question to related questions about the paper to link them all together.

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  • $\begingroup$ Do you mean a tag for each series or a tag for all such series? $\endgroup$ – SK19 May 11 '18 at 15:19
  • $\begingroup$ @SK19 Yeah, so long is the series is "big enough," then why not? They should all be linked together somehow, and tagging them as being part of the same series of questions related to a certain paper seems like the cleanest way. $\endgroup$ – Mike Pierce May 11 '18 at 15:22
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    $\begingroup$ @MikePierce The suggestion to create a separate tag for every paper seems rather questionable to me. In the past something similar was discussed for books, and the consensus seems to be that we do not want such tag. For example, here:Is using subtags to identify book source appropriate for this site? and Is the tag [hoffman-kunze] necessary?. $\endgroup$ – Martin Sleziak May 11 '18 at 15:29
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    $\begingroup$ I definitely agree that it is good to clearly identify the source, but I do not think that tags are suitable way to achieve this. I have also left a few further comments in tagging chatroom. $\endgroup$ – Martin Sleziak May 11 '18 at 15:30

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