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    • CommentRowNumber1.
    • CommentAuthorRichard Williamson
    • CommentTimeFeb 1st 2018
    • (edited Feb 1st 2018)

    Not of any direct relevance to the nLab, but I thought one or two of you might be interested in this note. It will appear on the arXiv on Friday (European time).

    • CommentRowNumber2.
    • CommentAuthorRichard Williamson
    • CommentTimeFeb 12th 2018
    • (edited Feb 12th 2018)

    A few of you are I think interested in sociological issues in mathematics. If so, you may be interested in my comments here.

    • CommentRowNumber3.
    • CommentAuthorUrs
    • CommentTimeFeb 12th 2018
    • (edited Feb 12th 2018)

    Hi Richard,

    with all likeliness, given their resources and the scale of the task, the arXiv moderators do not spend a single serious thought on the actual content of a submission, but just look for notorious keywords. They are not like referees nor even like editors, more like a human spam filter.

    If tomorrow a real proof of the Riemann hypothesis appears, be it as watertight as it may, it will probably not have the slightest effect on the alarm bells that its submission will trigger with the arXiv moderators.

    For serious contributions to such topics one will just have to wait for some actual referees of some actual journal to make their way through it.

    There are many faults with the maths community, but the standard problems with running large websites that allow user input I would not blame on them.

  1. Hi Urs, thank you very much for your thoughts! I basically agree with you, and mostly expected that the note would not be accepted in math.NT. What I find unacceptable is that they did not allow removal rather than placing in math.GM.

    • CommentRowNumber5.
    • CommentAuthorDavidRoberts
    • CommentTimeFeb 12th 2018

    Well, you can remove it now, of course, leaving a note in the comment section. Not sure it would look very good to the casual bystander…

    • CommentRowNumber6.
    • CommentAuthorUrs
    • CommentTimeFeb 12th 2018

    I can certainly understand that this is extremely frustrating.

    I have heard some weird stories about arXiv moderators taking weird steps, and never reacting to any requests. In an extreme case I heard of somebody who they blocked for good from the arXiv the moment that he submitted his PhD thesis, for reasons which they will take with them into their grave, maybe as a kind reminder to never ever take anything for granted in life.

    Myself having once tried my hand on moderating a public forum (not this quiet one here), I can see where such failures of the system can come from, even if everyone is operating on good intentions. The real mystery is that the arXiv persists as an essentially free public place, despite these pitfalls.

    Anyway. I gather from the nature of your note that, if correct, a few months of delay in it becoming officially public will be vanishing time span compared to the eternal life that it will lead afterwards as part of mathematics.

    • CommentRowNumber7.
    • CommentAuthorRichard Williamson
    • CommentTimeFeb 12th 2018
    • (edited Feb 12th 2018)

    Re #5: exactly, that is the problem with manually withdrawing it.

    Re #6: thanks very much again for your thoughts, I appreciate it. I do agree that the job of the moderators is difficult. On the other hand, they do have a very weighty responsibility with regard to the dissemination of mathematical ideas, and thus I think it is reasonable that they consider the consequences of their decisions.

    Your words about the note are kindly meant, and I appreciate them a lot, but it rather depends on how forbidding the conjecture that I formulate is. If it turns out to be equally as hard as the Goldbach conjecture itself, not much may be gained. I am more optimistic, but what I would really hope for, as I write in the note, is for someone who is an expert on sieve theory to take a look at it and see if it might conceivably be approached in that way; it looks possible to me, but I know almost nothing about such techniques.

    I am attempting to interest some experts in the conjecture. This has almost entirely fallen on deaf ears so far (i.e. I receive no response whenever I contact someone), but one has very kindly shown at least sufficient interest to be checking the proofs. I am waiting to hear back further from him.

    • CommentRowNumber8.
    • CommentAuthorDavidRoberts
    • CommentTimeFeb 12th 2018

    I would have thought that number theorists would enjoy a conjecture even harder than a known open conjecture (cf the generalised Elliott-Halberstam conjecture being used to get the prime gaps bound down to 6, whereas the plain EH conjecture only got it to 12) :-)

  2. Interesting point, David, I hadn’t thought of that!

    One thing I can say is that it seems unlikely to me that there is any easy argument to show that the conjecture in my note follows from the Goldbach conjecture. We are using so little that the two conjectures might well ultimately be equivalent (e.g. if it were possible to prove the conjecture I formulate using only elementary techniques together with, say, Bertrand’s postulate, then we would know that it follows from the Goldbach conjecture), but a proof of such an equivalence is likely to itself be very interesting.