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Using alphabetical ordering for authors' names is a long established tradition in mathematics. In the situations of extremely unequal contributions, is it reasonable to break from this tradition? Has there been any examples? If it is common, what is the threshold for breaking from alphabetical ordering?

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    I don't know how anyone would know how to interpret a non-alphabetical order in math, in any case. Most likely as a failed alphabetization...?
    – paul garrett
    Jun 12, 2020 at 2:01
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    The only recent example that I know of is J. T. Moore, M. Hruˇs´ak and M. Dzamonja, Parametrized ♦-principles. Trans. Amer. Math. Soc. 356 (2004) 2281–2306. My understanding is that the ordering of authors was intended to reflect unequal contributions.
    – Andreas Blass
    Jun 12, 2020 at 2:21
  • Many non-math papers now have author contribution sections. Do math journals have these?
    – Richard Erickson
    Jun 12, 2020 at 16:08
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    Example of a book by Katok and Hasselblatt: cambridge.org/core/books/…
    – John B
    Jun 12, 2020 at 17:53

3 Answers 3

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Edit: this answer is about pure math.

It’s not common. In 25 years of reading math papers I‘ve only ever seen one example of a paper that had a nonalphabetical author ordering. It was an English translation of a Russian paper from the 1970s written by a PhD student and his advisor. I don’t know what the story was behind this unconventional author order, but all I know is that the advisor’s name appears first even though alphabetically he comes second.

In the situations of extremely unequal contributions, is it reasonable to break from this tradition?

No. Since you’re going against the overwhelming norm in math publishing, no one will have a clear sense of what exactly you’re trying to say. Also, consider the fact that it could be that the author order that reflects the actual author contributions might coincide with the alphabetical order (for example in the paper I mentioned, it was competely random that the PhD advisor came second alphabetically and could easily have been the other way around). In that case the signal will be lost entirely.

My conclusion is that the idea of forcing this signaling mechanism on a math publication culture that isn’t adapted to it is illogical, ineffective, and will lead to inconsistent results that are only very weakly correlated with the effect you’re trying to achieve. If I were a journal editor and I received a submission that tries to use this mechanism, I would tell the authors to find a different way to say what they want to say about the author contributions.

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    Out of interest, did you check if the authors in your example were still not in alphabetical order when written in the cyrillic alphabet?
    – mlk
    Jun 12, 2020 at 11:57
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    "to find a different way to say what they want to say about the author contributions." Like a statement of contribution? That also appear to be quite rare.
    – user39093
    Jun 12, 2020 at 13:55
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    @mlk I just checked. The authors were Anatoly Vershik and Sergey Kerov, and you’re right, in Russian the author order is alphabetical.
    – Dan Romik
    Jun 12, 2020 at 21:18
  • @ssquidd I didn’t have a specific way in mind. But yeah, if you want to indicate what the contributions are, then a statement explaining that seems like a logical solution.
    – Dan Romik
    Jun 12, 2020 at 21:19
  • Vershik-Okounkov was the example I knew of this cyrillic alphabetical order issue. Strange coincidence that your example was also Vershik.
    – Noah Snyder
    Aug 31, 2021 at 15:40
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It is not actually true that in mathematics alphabetical order is a long established tradition. This is only true in pure mathematics.

In many parts of applied and computational mathematics, ordering by contribution (or other criteria) is just as widely or more widely used. Only a handful of my my 50+ papers are in alphabetical order.

My take, different from Dan Romik's, is that most professional mathematicians are well aware that there are different conventions in different parts of mathematics, and that they can well put things in perspective. That is certainly true for evaluating colleagues during annual evaluation time or when you apply for positions. If you're in a hard-core pure math area where nobody uses non-alphabetical author order, such a paper may seem odd but I am pretty sure that everyone will still be able to see what the purpose is.

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    This is a question and not snark. Do you find that the practice often generates bad feelings and fights as we see in many of the questions on this site? Or is it not an issue?
    – Buffy
    Jun 12, 2020 at 15:34
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    I advise (and practice) making author order a discussion topic very early on in a collaboration. I have only had one paper (out of more than 50) where there was disagreement, and that spurred me to make the issue a point of discussion early on. In all other cases, we agreed and it continued to seem right.
    – Wolfgang Bangerth
    Jun 12, 2020 at 19:55
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    @Buffy It also helps that I very much try to be generous in letting others be first author, and emphasize this to my collaborators. It's my way of giving back to the generosity I have received early in my own career.
    – Wolfgang Bangerth
    Jun 12, 2020 at 19:57
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In the answers and comments, it's suggested that it's extremely rare in pure math, and there are only one or two such papers. I'd suggest that while it is rare, it's not as rare as Dan Romik's answer and a couple of comment's suggest. I myself have noticed a number of papers where the author list is non-alphabetical (and in fact I'm a co-author on one). My impression is that the two most common reasons for these situations are:

  • there was some confusion about the alphabetical ordering, typically with non-English names (maybe unRomantic names is better?) as in paul garrett's comment and as seems to be the case in Dan Romik's example
  • the contributions to the paper were highly unbalanced among co-authors (e.g., the RSA paper---at least from A's perspective)

That said, just by seeing such a situation, it's probably not clear why the author order is non-alphabetical, and people will wonder why when they notice it. So unless some of the authors feel strongly about it, I wouldn't recommend doing this as a matter of course, and especially not unless all authors agree.

Here are some alternative suggestions for how to handle a situation like this:

  1. Break the project up into two (or more) different papers, using different subsets of authors to better represent author contributions.
  2. Instead of making separate papers, have 1 paper but with appendices with different sets of authors.
  3. Include a comment in the introduction about each author's contributions.
  4. Be generous (or thankful, depending on which party you are), and don't worry about it. (This is the probably the most common solution to this rather frequent situation, and unless the paper is really groundbreaking, sharing credit shouldn't be too much of a burden.)
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