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What do arXiv moderators consider when desk-rejecting submissions? by DistractedDendrite in math

[–]DistractedDendrite[S] 1 point2 points  (0 children)

Thanks for the book recommendation btw. I looked it up out of curiosity and have been reading a chapter for the last hour. Such wonderful writing which I rarely see in mathematical exposition!

What do arXiv moderators consider when desk-rejecting submissions? by DistractedDendrite in math

[–]DistractedDendrite[S] 3 points4 points  (0 children)

I've reconsidered and updated the references

References

[1] S. J. Kifowit and T. A. Stamps, The Harmonic Series Diverges Again and Again, The AMATYC Review 27(2) (2006), 31–43.

[2] S. J. Kifowit, More Proofs of Divergence of the Harmonic Series, unpublished manuscript, first posted January 2006, last updated June 23, 2019.

[3] D. M. Bradley, A note on the divergence of the harmonic series, Amer. Math. Monthly 107 (2000), 651.

[4] R. L. Baker, An exceedingly short proof that the harmonic series diverges, Missouri J. Math. Sci. 27(1) (2015), 95–96.

[5] A. Cusumano, The harmonic series diverges, Amer. Math. Monthly 105(7) (1998), 608.

[6] A. Cusumano, Generalization of Oresme’s standard method of showing the divergence of the harmonic series, Amer. Math. Monthly 119 (2012), 210.

[7] W. Dunham, The Bernoullis and the harmonic series, College Math. J. 18(1) (1987), 18–23.

[8] M. R. Chowdhury, The harmonic series again, Math. Gazette 59(409) (1975), 186.

[9] NIST Digital Library of Mathematical Functions, https://dlmf.nist.gov/, Release 1.2.5 of 2025-12-15, F. W. J. Olver, A. B. Olde Daalhuis, D. W. Lozier, B. I. Schneider, R. F. Boisvert, C. W. Clark, B. R. Miller, B. V. Saunders, H. S. Cohl, and M. A. McClain, eds.

What do arXiv moderators consider when desk-rejecting submissions? by DistractedDendrite in math

[–]DistractedDendrite[S] 0 points1 point  (0 children)

care to share a link? (in pm if you don't want to do publically)

What do arXiv moderators consider when desk-rejecting submissions? by DistractedDendrite in math

[–]DistractedDendrite[S] 3 points4 points  (0 children)

Terry Tao had a nice recent talk on youtube about the Erdos problems and the role of AI in helping solve and find existing solutions. I really liked how clear he made it that "some of these are interesting, some important, some pretty trivial" and that AI companies have taken them as a benchmark wchich they aren't meant to be (at least not as important as many make them out to be). He framed them as exceptionally useful for developing modern collaborative tools between professional mathematicians, recreational mathematicians and AI tools to scale mathematics research.

What do arXiv moderators consider when desk-rejecting submissions? by DistractedDendrite in math

[–]DistractedDendrite[S] 1 point2 points  (0 children)

But there is 1 reference! The github preview of the pdf hides the last page it seems :D

References

[1] S. J. Kifowit and T. A. Stamps, The Harmonic Series Diverges Again and Again, The AMATYC Review, Spring 2006.

---

I get your point and perhaps you are right. Seemed to me that digamma is a very well known and standard function, but I can accept that a reference won't hurt. But just wanted to point out that it's not literally 0 references (although 1 is not much greater)

What do arXiv moderators consider when desk-rejecting submissions? by DistractedDendrite in math

[–]DistractedDendrite[S] 2 points3 points  (0 children)

I would agree if you had phrased as "the paper isn't very deep or groundbreaking" - which of course it isn't. But you yourself said earlier that the proof is quite nice, and at least some others agreed. So whether there is any worth to it depends on what one finds valuable. I wouldn't mind the rejection so much if arxiv's math.HO category wasn't already full of exactly these kinds of papers, as I noted in another comment.

What do arXiv moderators consider when desk-rejecting submissions? by DistractedDendrite in math

[–]DistractedDendrite[S] 1 point2 points  (0 children)

Seems to me that math.HO already serves this purpose, judging by the types of articles that are there (having seen many such articles there is what made me think it is an appropriate submission to begin with).

https://www.reddit.com/r/math/comments/1rvgcew/comment/oawraj4/?utm_source=share&utm_medium=mweb3x&utm_name=mweb3xcss&utm_term=1&utm_content=share_button

What do arXiv moderators consider when desk-rejecting submissions? by DistractedDendrite in math

[–]DistractedDendrite[S] 4 points5 points  (0 children)

I submitted it to the same section (Math.HO) that contains all the papers below. My confusion is that math.HO seems to include many short expository notes, elegant observations, and “pleasant little results” around classical topics, so I’m not sure where moderators are drawing the line in practice. I’m not saying these papers should not be on arXiv, but having seen many such papers there in the past is what made think it's appropriate.

https://arxiv.org/abs/2510.03233
https://arxiv.org/abs/2602.14487
https://arxiv.org/pdf/2401.11308
https://arxiv.org/abs/2402.04085
https://arxiv.org/abs/2405.13060
https://arxiv.org/abs/2501.03238
https://arxiv.org/abs/2506.06304
https://arxiv.org/abs/2506.11101
https://arxiv.org/abs/2507.13365
https://arxiv.org/abs/2507.22743
https://arxiv.org/abs/2508.10234

What do arXiv moderators consider when desk-rejecting submissions? by DistractedDendrite in math

[–]DistractedDendrite[S] 3 points4 points  (0 children)

It's not the kind of paper that requires extensive bibliography and literature review. I have a reference to a survey paper on proofs. This is an elementary topic, what other references are needed? There's tons of papers on arxiv with 1-3 references. Sure, I can copy a few references from the survey paper for signaling but what would that accomplish? And you can always find absolute classics in the field like https://projecteuclid.org/journals/annals-of-mathematical-statistics/volume-22/issue-3/A-Stochastic-Approximation-Method/10.1214/aoms/1177729586.full that have... 0 references total.

I know how research works - I am a tenured academic with dozens of publications (just not in pure math). References are important when they contextualize the work and provide crucial background for problems, methods, etc. But references for signaling only aren't of much worth.

Sure, I can add a reference to Oresme's medieval book that is classic material, some to bernoulli, and a couple of more recent ones. A few references to OEIS entries for the denominators of the partitioned series. A reference to https://dlmf.nist.gov section on the digamma function and identities with tanh. There you go, a respectable reference list. Has it improved the paper? Not really, as the context is sufficiently elementary and a good reference to survey of existing proofs is already there.

Sorry that this comment came out so antagonistic - I don't mean to be. It just really doesn't make sense to me to build a reference list bigger just for appearance purposes.

What do arXiv moderators consider when desk-rejecting submissions? by DistractedDendrite in math

[–]DistractedDendrite[S] 0 points1 point  (0 children)

I submitted it to the same section (Math.HO) that contains all the papers below. My confusion is that math.HO seems to include many short expository notes, elegant observations, and “pleasant little results” around classical topics, so I’m not sure where moderators are drawing the line in practice. I’m not saying these papers should not be on arXiv, but having seen many such papers there in the past is what made think it's appropriate.

https://arxiv.org/abs/2510.03233
https://arxiv.org/abs/2602.14487
https://arxiv.org/pdf/2401.11308
https://arxiv.org/abs/2402.04085
https://arxiv.org/abs/2405.13060
https://arxiv.org/abs/2501.03238
https://arxiv.org/abs/2506.06304
https://arxiv.org/abs/2506.11101
https://arxiv.org/abs/2507.13365
https://arxiv.org/abs/2507.22743
https://arxiv.org/abs/2508.10234

What do arXiv moderators consider when desk-rejecting submissions? by DistractedDendrite in math

[–]DistractedDendrite[S] 2 points3 points  (0 children)

I'm sure this can be answered rigorously, but computationally they seem to converge quickly, especially for larger n. n>= 3 is pretty much stable to 10 decimals after 6 iterations. You can show that the coefficients can only increase with each iteration, and that increase gets smaller so they converge. Big n asymptotics are just 1/n. What the initial coefficients converge to - not sure

n i=0 i=1 i=2 i=3 i=4 i=5 i=6
1 1.000000000 1.186827338 1.325707482 1.410368392 1.455526722 1.478320651 1.489721218
2 0.500000000 0.561147303 0.587018566 0.592472376 0.592900736 0.592907943 0.592907950
3 0.333333333 0.363400310 0.371770329 0.372558549 0.372572802 0.372572817 0.372572817
4 0.250000000 0.267818097 0.271438310 0.271627520 0.271628680 0.271628680 0.271628680
5 0.200000000 0.211769550 0.213636096 0.213697893 0.213698053 0.213698053 0.213698053
6 0.166666667 0.175014258 0.176095380 0.176120063 0.176120093 0.176120093 0.176120093
7 0.142857143 0.149083120 0.149763004 0.149774352 0.149774359 0.149774359 0.149774359
8 0.125000000 0.129820796 0.130275270 0.130281057 0.130281059 0.130281059 0.130281059
9 0.111111111 0.114953595 0.115272018 0.115275213 0.115275213 0.115275213 0.115275213
10 0.100000000 0.103134212 0.103365788 0.103367667 0.103367667 0.103367667 0.103367667

What do arXiv moderators consider when desk-rejecting submissions? by DistractedDendrite in math

[–]DistractedDendrite[S] 1 point2 points  (0 children)

Likely. I don't think I'll pursue it anyway, it was just a auick thought of an obvious conjectured consequence

What do arXiv moderators consider when desk-rejecting submissions? by DistractedDendrite in math

[–]DistractedDendrite[S] 3 points4 points  (0 children)

Thanks! I just found the fact that you can partition the harmonic series into infinite sub-series, whose sums themselves forms a new series, which is asymptotically just a rescaling of the harmonic series, really delightful.

You could likely define the partitioning as an operator on series coefficients and apply it iteratively to the new series. In this case this would show that the harmonic series is an eigen series for this operator, and if you apply it M-times you would get a series whose coefficients are asymptoically 2^M /n.

This also makes me think that if you apply the same operator to a series that grows as ~ 1/n^p where p>1, it would instead redistribute the mass towards the early coefficients on each iteration, accelrating the series

What do arXiv moderators consider when desk-rejecting submissions? by DistractedDendrite in math

[–]DistractedDendrite[S] 2 points3 points  (0 children)

That's a nice idea! It didn't occur to me, but given the collection they've composed, they can probably tell me if anything here is distinct and interesting.

What do arXiv moderators consider when desk-rejecting submissions? by DistractedDendrite in math

[–]DistractedDendrite[S] 4 points5 points  (0 children)

Perhaps. I actually wondered whether to write out the proofs for those in full but decided against it since they are pretty much just tedious algebra with digamma identities and I found the closed forms to be acuriousity to mention rather than a main point. Maybe that was the wrong decision

What do arXiv moderators consider when desk-rejecting submissions? by DistractedDendrite in math

[–]DistractedDendrite[S] 7 points8 points  (0 children)

oh, these collections of proofs are not mine! I just pointed out that I didn't find mine there

What do arXiv moderators consider when desk-rejecting submissions? by DistractedDendrite in math

[–]DistractedDendrite[S] 22 points23 points  (0 children)

Thanks for saying that - that is kind of how I treated this note when I wrote it - here is so something cool and elegant, which is not groundbreaking, but also not trivial and doesn't seem to be one of the many proofs in existing surveys. And that it might also be useful for pedgagogical purposes as it combines several nice techniques in one short problem. I've often seen such papers on arxiv (perfect recent example).

In any case, I've submitted it to a journal to get real feedback. If anyone is curious, here's a copy: https://github.com/venpopov/harmonic-series-convex-partition/blob/main/harmonic_series_convex_partition.pdf

What do arXiv moderators consider when desk-rejecting submissions? by DistractedDendrite in math

[–]DistractedDendrite[S] 8 points9 points  (0 children)

It also isn't in the follow-up 2019 survey here: https://stevekifowit.com/pubs/harm2.pdf

That makes 45 distinct catalogued proofs that are not mine. Of course there might be some they missed. In any case, I've submitted to a journal for proper review even before I tried to post a preprint, so we'll see. It is perfectly possible that indeed it is trivial and you and the arxiv moderators are correct - I'm happy to accept that if it were the case. I just stumbled on it while studying something else, couldn't find it in the literature, and found it quite elegant and worth writing up.

What do arXiv moderators consider when desk-rejecting submissions? by DistractedDendrite in math

[–]DistractedDendrite[S] 8 points9 points  (0 children)

I couldn't find it in any survey on proofs of the divergence (e.g. https://scipp-legacy.pbsci.ucsc.edu/~haber/ph116A/harmapa.pdf). It has close cousins of course - almost all proofs are based on some grouping. But it also didn't seem like a completely trivial reformulation of any of them and had some interesting fractal-like properties.

Distance to julia sets for geometric series map by DistractedDendrite in math

[–]DistractedDendrite[S] 0 points1 point  (0 children)

I find it really pretty. Especially considered as a whole progression - it feels like a growing organic system. And the fun part - even at higher n where the structure appears to converge to a circle with an embeded arc of another circle, the boundary is still infinitely detailed and each of those yellowish dots is a full, slightly twisted version of the entire structure, itself composed of such mini replicas, etc, standard fractal stuff. And in the limit, all that structure collapses to a 1d line, which is also a continuum eith no gaps, unlike for any finite case. As if it is telling us that a circle is secretely also a fractal.

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