Every now and then, one sees in mathematical papers appendices, authored by person(s) different from the authors of the main body of the paper.

  1. What is the rationale behind such appendices? In most of the cases I have seen, it can be a bona fide short separate paper (granted, tight closely to the main paper in question, but many papers are tight closely to each other).

  2. What is the complete list of authors of a paper with an appendix? I belong to the school of thought claiming that references should be given according to the first letters of authors names. Each time, when citing a paper with appendix, I am agonizing over whether the authors of the appendix should be included or not in this abbreviation. More seriously, if a person is a (co)author of such an appendix (but not of the main body of the paper), how it is reflected in his list of publications?

  3. My impression is that the number of such appendices has been increased drastically in the recent years. Is it true? If yes, what may be reason(s) for that?

Edit May 27, 2011: DamienC made an interesting (and looking plausible to me) suggestion that the purported recent increase of separately-authored appendices is a way to cope with no longer fully adequate convention of authors ordering. If so, it would be interesting to compare with how the things evolved, say, in life sciences, from the situation where coauthors were not acceptable - a situation, as far as I understand, common to all scientific papers at the beginning of XX century - till today ugly state of affairs with convoluted and self-contradictory rules who goes first, who goes last, how the authors should be clustered, etc. This may suggest that in mathematics things evolve in a different direction, which, though not perfect, is sort of reassuring.

2nd edit May 27, 28 2011. My question is not about appendices in general, including differences in various subjects and subcultures (for example, in statistics it is common to defer all proofs to appendices) -- this is an entirely different topic. My question is about the sutuation when the set of the authors of an appenix is different from the set of the authors of the main paper -- and, bibliographic (and bibliometric, and social, if you wish) difficulties (or at least what I see as bibliographic, etc. difficulties) arising from such situations. Sorry if that was not clear enough from the first place.

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    $\begingroup$ I guess this should be Community Wiki $\endgroup$ – DamienC May 27 '11 at 8:31
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    $\begingroup$ @DamienC: I do not want to turn it to "Communiti Wiki", as I do not mind to earn a couple of extra points here. But if you or anybody else with appropriate authorities will do that, I will not whine either. $\endgroup$ – Pasha Zusmanovich May 27 '11 at 9:43
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    $\begingroup$ Damien's points was that "earn" $\neq$ "receive". $\endgroup$ – Alex B. May 27 '11 at 10:44
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    $\begingroup$ One possible answer to (1) . I've sometimes been the author of an appendix when I didn't understand the techniques of the paper well enough to feel comfortable in claiming to be a co-author. $\endgroup$ – paul Monsky May 27 '11 at 11:31
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    $\begingroup$ @Alex Bartel: Thank you for the elucidation of Damien's point. Please read my relevant comment as "I do not mind to receive a couple of extra points here". $\endgroup$ – Pasha Zusmanovich May 27 '11 at 12:22

I surmise that the speed of communication now exceed the speed of publication (or even the speed of the typesetting/proofreading cycle). So, you prove something, send the rough draft to people who, in your opinion, may be interested, start preparing it for publication, and in the middle somebody answers one of the questions in your paper. The best thing is if his answer makes your paper obsolete. Then you throw it to the garbage and waste no more time on the boring writing routine. But more often than not the answer is given to some not so important question that doesn't really change much but still adds an interesting twist. To publish it separately would be ridiculous. To ignore it would be strange. So what to do? Well, it becomes an "appendix". Now, the gentleman's way is to offer the full co-authorship. Also the gentleman's way is to reject it. Now we are stuck with either an extended thanks, or a separate "appendix authorship", and here goes. I believe we'll get even weirder things like "This paper supercedes the work of X who improved the result of Y, which was a generalization of theorem by Z proved in responce to my question (all 4 private communication)" if the speed goes up a bit more. I personally am in favor of pushing the gas pedal to the floor and shaking the current ideas of priority and authorship off entirely but I know that my mathematical opinions are very non-orthodox...

  • $\begingroup$ Thank goodness for the braking system called "peer review". Gerhard "Typing As Fast As Able" Paseman, 2011.05.27 $\endgroup$ – Gerhard Paseman May 28 '11 at 0:26

I guess that the answer to 3 is the following. The tradition in math is to write the names of authors by alphabetical order. But then the number of collaborations has been increasing, and the contribution of different authors is not always well-balanced. Such appendices are, in my opinion, a way to keep the tradition and adapt it to the new situation (more and more collaborations, with sometimes contributions being somehow significantly different).

About question 1 let me consider an example. It is a paper by Galyna Dobrovolska, John Kim and Xiaoguang Ma, where the authors study the lower central series of an associative algebra, regarded as a Lie algebra. At some point they need a general result, which was proven by Feigin and Shoikhet in the particular case of a free algebra. I guess that Pavel Etingof told them that he knew how to prove this result, but probably did not want to write an independant paper about it. On the other hand it might be that this contribution is not as significant as the work of the main authors. So he wrote an appendix to the paper.

Now about question 2, if we still consider the same example, here is how I would quote the paper (according to mathscinet):

[DKM] G. Dobrovolska, J. Kim, X. Ma, On the lower central series of an associative algebra (with an appendix by Pavel Etingof), J. Algebra 320 (2008), no. 1, 213–237.

Concerning list of publication, if you write an appendix to a paper it probably means that you don't need/want to increase the number of your publications. But anyway, for the list of publication you can write something like this

Appendix to the paper On the lower central series of an associative algebra by G. Dobrovolska, J. Kim and X. Ma (J. Algebra 320 (2008), no. 1, 213–237).

  • $\begingroup$ Your answer to question 3 is very interesting and looks plausible to me. I would like to elaborate on it further, but this does not fit the comment space, will do that in the main body of the question. As for the MathSciNet citation example, it is awful: why on earth the name of the author of the appendix goes to the title? I think this reflects the fact that MathSciNet is not ready (yet) to this (relatively) new "appendix" phenomenon. $\endgroup$ – Pasha Zusmanovich May 27 '11 at 9:59
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    $\begingroup$ That is the actual title of the paper so it's not the fault of MathSciNet! $\endgroup$ – ulrich May 27 '11 at 11:41

I can't resist mentioning the following paper of mine: Random diophantine equations, B. Poonen and J. F. Voloch, pp. 175–184 in: Arithmetic of higher-dimensional algebraic varieties, B. Poonen and Yu. Tschinkel (eds.), Progress in Math. 226 (2004), Birkhäuser.

It has two appendices, one by Colliot-Thélène and the other by Katz. The first appendix, by Colliot-Thélène, proves a result we quote, which he had proved many years before but never published. This proof required a variant of "weak Lefschetz" for which there was no reference. Katz supplied a proof that ended up being the second appendix which, strictly speaking, is an appendix to the first appendix!

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    $\begingroup$ +1 for appendix recursion! $\endgroup$ – Charles May 28 '11 at 2:16


The main point of this addition is to give some answer to the 3. point in the question.

First, just to repeat what others have already said on 2.: If P writes a paper or a book and A and appendix to it, then the author is just P; the fact that A wrote an appendix is sometimes contained in the title, or it can we added ('with an appendix...'); in the bib-tex data of MathSciNet this information is strored as a 'note'. Looking through MathSciNet one can also find appendices (written by other authors) that are an item in there own right. (Search for 'appendix' in the Title to find example of this; though not everything returned is an example for this). Sometimes, but by no means always, they appear with a certain delay (and also contain some corrections); yet in other cases this is not so and this differences might (but I am not completely sure), be merely a technicality how the journal handles this. In general, I think a good solution is to simply follow the way in which MathSciNet handles this.

Now for question 3. "My impression is that the number of such appendices has been increased drastically in the recent years. Is it true?"

My answer to this is: No.

Remark: of course the absolute number increased quite a bit, but so did the number of papers in general (as well as the fraction of co-authored papers). I thus think the relative frequency is key, and while there seems to be some increase to call it drastic seems more than too much.

Here is what I did: I searched MathSciNet for 'with an appendix by' in the field 'anywhere' and limited the search to 'journals' [to avoid appendices to books]

This is certainly not a perfect method and does not catch all appendices by other authors and might also yield some false positives, but to get a rough idea it seems good enough, in particular if the goal is to get an idea of the development.

So here are the numbers (hits for the search / approx. total number of items in millions)

  1. All: 509 / 2.2
  2. 2000 and earlier: 264 / 1.4
  3. 1990 and earlier: 116 / 1
  4. 1980 and earlier: 42 / 0.6
  5. 1970 and earlier: 12 / 0.3

Thus, I would say there is some increase but by no means a dramatic one; and the existing increase should be easily explainable by the general increase of papers written in collabortation.

As an add-on some older papers with appendix (all in pure math):

Mazur, B. Rational isogenies of prime degree (with an appendix by D. Goldfeld). Invent. Math. 44 (1978), no. 2, 129–162

Lang, Serge The group of automorphisms of the modular function field. With an appendix by P. Deligne. Invent. Math. 14 (1971), 253–254.

Pólya, G.; Schiffer, M. Convexity of functionals by transplantation. With an appendix by Heinz Helfenstein. J. Analyse Math. 3, (1954). 245–346.

So, as said, I think this phenomenon has quite some tradition.

First answer:

You do not mention it explcitly, but there are also appendices to papers by the same authors. Thus, author-credit can certainly not be the only rationale.

Two other reasons for an appendix:

  1. The content of the appendix are 'just technical arguments' and the authors do not want to clutter the main article with them.

  2. The appendix contains some investiagtions tagential to the actual article but suggested by it.

In particular, 1. is I believe quite common in (some) more applied parts of maths, in particular TCS.

And, point 2. can reasonably be done by a person not the author, and even after the article is essentially complete. Thus, one reason for an appendix can be that one receives significant comments on a preprint, yet possibly on a tagential point. Something like, some technical lemma when considered right is of idependent interest or alike.

One thing that is also worth pointing out I believe is that the general idea that if A has an appendix to papers of B and C, then B and C did not let A 'in' as a main author, is certainly a misconception (as a general reason, in particular cases it might be like this). There are papers where the author of the appendix is by a significant margin the most well-established of the authors, and the idea that the main-authors did not want him/her as a co-author seems strange.

Regarding frequency, I do not really know whether the increase of appendices is higher then the general increase of co-authored papers, it might be due to more rapid communication.

As a final remark: an appendix authored by somebody else is not a very recent (mis-)developpment prompted by the fact that people now care or have to care more about author-credit. By contrast, I think it is a good tradition and a consequence of the fact that paper-count is not (or at least was not) considered overly important in maths.

  • $\begingroup$ Your addition of May 28 is very interesting, I appreciate it. $\endgroup$ – Pasha Zusmanovich Jun 3 '11 at 20:57

I completely agree with the previous answer. It is not true (as stated in the OP) that most appendices could be bona fide separate papers. Typically, when separate from the main paper they would be very hard to sell (they have no introduction, etc...). In most of the cases I am aware of, appendices are: 1) lemmas proved by someone who was not part of the main effort behind the paper, and which turn out to be important for some part of the paper (this is the typical example that would be rejected if separate from the paper: "it's just a lemma"). 2) new approaches or alternative proofs which came up after a first version of the paper was circulated. After all, it's not that easy to publish papers entitled "A new proof of...", especially if the result you re-prove is not a time-honoured one.

  • $\begingroup$ The order the answers are presented in change. What was "the previous answer" that you refer to? $\endgroup$ – Joel Reyes Noche Jul 20 '11 at 9:05
  • $\begingroup$ @ Joel Reyes Noche: If I remember correctly, I was referring to Gordon-Royle's answer. $\endgroup$ – Alain Valette Jul 25 '11 at 1:54

In a paper that I am currently writing, we have an individually-authored appendix, although the author of the appendix is also a co-author on the paper.

In this situation, the appendix is a relatively long and technical proof of a fact that is used peripherally in the paper. The proof is not sufficiently important to the main thrust of the paper to be incorporated into the body of the paper, and the major results of the paper do not rely on it. However it provides an explanation for some of the phenomena we describe (and prove) in the paper. Although this self-contained fact is not proved in the literature, it is probably not enough to make a separate paper without the context and motivation provided by the rest of the paper. As it is solely my coauthor's work it makes sense to include it separately with only his name attached.

I imagine that the same applies to an appendix with a separate author not among the main authors - a piece of work that is self-contained, of sufficient scale and scope that it warrants separate authorship, and yet whose significance is greatly enhanced by the motivation, context and results of the main paper.


I do not care much for this question. This is too long for a comment, so here are my reasons.

  1. What is the rationale behind such appendices? The single, most accurate answer is that it depends on the paper/authors. For that matter, what is the rationale for appendices in general?
  2. What is the complete list of authors of a paper with an appendix? Do your homework here. There is a standard way to cite those papers, which is Authors X, Y, Paper Title, Journal, with an appendix by Z. It works.
  3. My impression is that the number of such appendices has been increased drastically in the recent years. Is it true? If yes, what may be reason(s) for that? The first question is factual and can easily be checked using a database. Answering the second question will be purely speculative and I don't see any value in attempting to answer it.
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    $\begingroup$ 2. The top answer gives an example different from what you claim is a "standard way". 3. I don't see how that can be checked "easily" using a "database". Oh, I don't like your tone. $\endgroup$ – Pasha Zusmanovich May 27 '11 at 14:04
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    $\begingroup$ +1 from me for the answer. And Pasha Zusmanovich, I don't like your tone. First, 'there is another way' does not really contradict the assertion 'there is a standard way'; the point is that being an author of the appendix doesn't make you an author of the paper, and this should be reflected in the bib-entry. And this issue is not so unique to appendices; you face related issues when quoting a book having an editor whose chapeters were written by different authors. $\endgroup$ – user9072 May 27 '11 at 18:35
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    $\begingroup$ Pasha Zusmanovich, you can have a look at my answer to see a way how Thierry Zell's suggestion can be carried out at least to some extent in a really simple way within minutes. $\endgroup$ – user9072 May 28 '11 at 11:38
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    $\begingroup$ @Pasha: you did not address the issue of the inherently speculative nature of your last question, which is by far the most questionable part of the whole post as far as I am concerned. Different people have different reasons to write appendices, and I don't really care to know them. In many instances, you could make a good guess as to what the reason was anyway. $\endgroup$ – Thierry Zell May 28 '11 at 15:42

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