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I never saw a paper published in a journal of (pure) math with more than six authors. Is it a rule?
(see this one)

Sebastien Palcoux
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  • In the link you provided, in the Reference list, the #7 article has 7 authors if I count it correctly. (Same authors plus Hagge) – Nobody Feb 24 '21 at 12:53
  • @scaaahu: yes but it is not a journal of pure math. – Sebastien Palcoux Feb 24 '21 at 13:11
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    Who could possibly set or enforce such a rule? – astronat supports the strike Feb 24 '21 at 14:31
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    No. But there is a min number of authors... – Dan Romik Feb 24 '21 at 15:56
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    This blog post may be of interest. I'm not sure what's included in Scopus' Mathematics subject area, but during the 2010-2016 period the highest number of authors was nine, which was a clear outlier. – Anyon Feb 24 '21 at 16:27
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    Not published yet, but we sure hope to publish it soon. It was very hard to collaborate on so many people though... – Denis Nardin Feb 24 '21 at 21:31
  • I remember a paper in pure math (On Invariant Random Subgroups) cowritten by 7 authors who referred to themselves as "7 samurai". – Moishe Kohan Feb 24 '21 at 23:29
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    Let's go one more beyond Denis Nardin's example: the "10-author paper" at https://arxiv.org/abs/1812.09999. – KCd Feb 25 '21 at 00:38
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    Also of interest: https://en.wikipedia.org/wiki/Polymath_Project – Mark Meckes Feb 25 '21 at 10:14
  • 1 - is the spirit of this question actually 'what's the highest number of authors on a maths paper?' ? 2 - what's the highest number of authors on a maths paper? – BCLC Feb 25 '21 at 11:16
  • https://academia.stackexchange.com/questions/16759/is-there-an-inflation-in-the-number-of-authors-per-paper?rq=1 – BCLC Feb 25 '21 at 11:19
  • The MMA monthly Problem Section occasionally has solutions by groups like "Podunk College Problem Solving Team." That could be more than seven. – B. Goddard Feb 25 '21 at 12:24
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    clearly the number of authors could not exceed the total number of people, so there is an upper bound on the number of authors – user833970 Feb 25 '21 at 15:48
  • Yes. 3.1415926, by convention – Magoo Feb 25 '21 at 18:08
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    I ran a quick check in Web of Science: for articles published in journals in the mathematics category for 2020, there were 277 articles with six authors, and 154 with more than six - out of a total of 37,379. 98.8% of them had less than six authors. So not impossible - but also quite plausible you'd not see many on a day-to-day basis. – Andrew is gone Feb 25 '21 at 18:49
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    @DanRomik But is that number 1? Or 0? If I wrote a Markov chain generator or some other kind of AI and trained it on every mathematical paper ever published, and set it to generate a new paper that was plausible enough to be published, am I the author? Or is there no author at all? – Darrel Hoffman Feb 25 '21 at 19:56
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    @DanRomik: Some papers are imaginary and have imaginary authors. So there's no linear order to say "minimum" here. – Ink blot Feb 25 '21 at 20:44
  • @Andrew - nice finding, please consider copy-pasting into the answer box – cag51 Feb 25 '21 at 22:35
  • Why on Earth should this be a rule? – lighthouse keeper Feb 26 '21 at 11:55
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    @cag51 turns out someone did it much more comprehensively two weeks ago! have written that up with my own notes as well. – Andrew is gone Feb 26 '21 at 18:44

2 Answers2

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No: Authorship is governed by the number of contributing mathematicians, rather than some arbitrary limit.

user2768
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    When a math research group grows, so does the likelihood that many questions will be asked within it and sub groups will take them up individually. Six as an "effective" max seems about right, and hard to achieve. Perhaps some of the papers with long author lists also have some other acknowledged people, pointing to the larger group. – Buffy Feb 24 '21 at 13:54
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    @Buffy The number of contributors is certainly limited by the degree to which contributors can effectively collaborate, but there's no rule. Physicists seem to organise in a manner that facilitates a greater degree of collaboration, publishing thirty three page articles that devote a whopping twenty-four pages to list all 5,154 authors and their affiliations (https://doi.org/10.1103/PhysRevLett.114.191803). – user2768 Feb 24 '21 at 14:09
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    Yes, lab sciences in general have a larger number of authors due to the nature of experimentation. And high energy physics in particular. Several physics papers have longer author lists than the actual article. – Buffy Feb 24 '21 at 14:14
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    1 - is the spirit of this question actually 'what's the highest number of authors on a maths paper?' ? 2 - what's the highest number of authors on a maths paper? – BCLC Feb 25 '21 at 11:17
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    @user2768 However, those branches of science use completely different authorship creteria. All authors on the author list of the collaboration automatically become the authors even if they have never seen the manuscript and work on a completely different sub-project. – Vladimir F Героям слава Feb 25 '21 at 11:34
  • @BCLC I can't answer either. – user2768 Feb 26 '21 at 09:41
  • @VladimirF Indeed, comments are off-topic. – user2768 Feb 26 '21 at 09:41
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It turns out that someone put out a bibliometric analysis of publication characteristics in mathematics papers this month, which is very convenient for answering the question!

Richard & Sun (2021). Bibliometric analysis on mathematics, 3 snapshots: 2005, 2010, 2015. arXiv:2102.06831

They found a general increase in the number of authors per paper over time, from 2.1 in 2005 to 2.4 in 2015. (Interestingly, this collaboration was both "internal" and "external" - the number of distinct institutions and distinct countries on a paper also increased steadily). The share of papers with five or more authors was 5.4% in 2015, so presumably slightly higher now. Papers with more authors, or from more places, tended to be more highly cited, which I believe is a common phenomenon across most fields.

They used the Web of Science "research area" classification, which as I understand it will group together a few different Web of Science "categories" (which in turn are inferred from the journal the paper was published in). It will probably thus include more interdisciplinary material than a narrowly defined field of "mathematics" might. They do not break down authorship by category, but it's possible to pull the data and do it yourself.

I ran the numbers for 2020 papers in "mathematics" and in "mathematics, applied", filtered to just "articles". Papers in "mathematics" had an average of 2.24 authors; those in "mathematics, applied" had an average of 2.56. 3.4% of papers in "mathematics" had 5+ authors, versus 5.7% of those in "mathematics, applied".

If we limit it to just those papers published in journals which were only classified as "mathematics" and not as eg "logic / mathematics" or "mathematics / mathematics, applied" (about a third of papers were in journals which were in multiple categories), then we get an average of 2.20 authors, and 3.3% with 5+ authors.

So whole we don't have an explicit classification for "pure mathematics", the non-applied group clearly skews towards a slightly smaller number of authors than applied, and the "just mathematics" group ditto. Papers with five or six authors are not unknown, but they are definitely uncommon - only a few percent of papers. (7 or more authors was around 0.4-0.5%, depending which group you looked at).

Andrew is gone
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