It seems in writing math papers collaborators put their names in the alphabetical order of their last name. Is this a universal accepted norm? I could not find a place putting this down formally.
This tendency of mathematicians is so well-known and universal that it has been taken as an axiom. See Andrew Appel's seminal work establishing whether different computer science conferences are mathematics or science.
I had always heard that there was a famous counterexample to alphabetization, the Zucker–Cox Theorem (where they flipped the order for obvious reasons), but apparently the non-alphabetization in this case was apocryphal.
But indeed, non-alphabetization is very rare.
As far as "a place putting this down formally," see the AMS's 2004 "Information Statement on Joint Research and its Publication" at http://www.ams.org/profession/leaders/culture/CultureStatement04.pdf.
The AMS has several of these "culture statements," intended to "highlight the ways in which the traditions in mathematics differ from those in other disciplines." I.e. to convince the skeptical dean that you really deserve that promotion.
In general, I think that alphabetical order is very common. However, sometimes this should be alphabetical order in other language, and in english translation this order becomes different. For example, take several papers by Vershik and Kerov - the Russian alphabetical order is VK, but in english this is not alphabetical.
My understanding (as someone who hasn't been in this business very long) is that when pure mathematicians co-author a paper, they form a kind of partnership as equal partners, and all credit for everything in the paper goes to the partnership rather than individuals, regardless of what actually happened behind the scenes. As for why:
It is seen to be unfair to say one person's work is more important than another's when each depends on the other's results and insights in a critical way.
Giving academic credit for anything other than a novel intellectual contribution to the content of a paper, for instance for securing funding or having a higher professional status (eg a professor vs a doctoral student) is anathema to most pure mathematicians, in a way that it wouldn't be for other scientists.
The culture of humility is particularly strong in pure mathematics. If a mathematician insists on being 'lead author' on a paper, that's bad for his/her reputation among mathematicians, which cancels out the extra credit that would otherwise accrue to a lead author.
This question often arises also in the promotion issues, since faculty in other sciences (esp. biological and medical sciences) and humanities have a very different approach to listing the co-authors. I am not totally sure, but I think mathematics is more of an exception than the rule in this respect for whatever cultural reasons. This "ordering" problem is especially difficult in CS and applied math departments, I think, which have both people who order according to the research contribution, and people who use alphabetical order.
In any event, in the last few stages of the promotion approval, when the candidacy goes to the faculty senate, president/chancellor, board, etc. there is often the need to explain this. To clarify this issue, the chairs/deans often write guidelines where they explain the conventional alphabetical order, which sometimes become a part of the faculty rules. My quick search returned these faculty rules: at UGA and UMN. So in the event you need to make a promotion case at your institution, you can use these as a "supporting evidence".
P.S. National Academy of Sciences also voiced these concerns here (search for "alphabetical").
It is always interesting when I meet professors in other sciences, particularly biology, to see their reaction when the issue of author names on papers comes up. The last time this happened, I was speaking to a cancer researcher at Harvard medical school. When I told him that author names in math are universally in alphabetical order his eyes got really, really big. He was amazed because he couldn't imagine how you could figure out by such conventions who did what amount of the work and he then explained to me some intricate rules by which researchers in biology determine the placement of author names. I told him that one plus of this alphabetical convention in math is that we don't need to deal with all the games they play in biology about who goes where at the start of the paper.
One practice which supports our practice of listing authors alphabetically is our practice of setting a fairly high bar for what counts as sufficient contribution to merit coauthorship.
I am only exaggerating slightly when I say that in some disciplines people become coauthors merely for sitting in on meetings where the paper was discussed.
Certainly, in the more expensive experimental sciences the scientist whose grant paid for the costs of the experiments is always an author, even if he or she made no intellectual contribution to the work.
This convention is not universal in mathematics, and it's annoying to some of us.
See this corrigendum from Inventiones Mathematicae.
"On page 79, line 24 from the bottom and on page 110, lines 21, 13, 7 and 5 from the bottom, replace "first" by "second".
Editor's note. In the original manuscript the order of the authors was I. Rivin first, C. D. Hodgson second. This was changed in order to conform with the usual custon, adhered to by Inventiones mathematicae, to have the authors of a paper listed in alphabetical order. We regret to have had this modification made without informing the authors and to have overlooked the fact that it entailed the changes stated above."
In the sciences, it is common to use a convention such as that the first author is the principal investigator for the research while the last author is the leader of the research group. That was not the convention used for a paper published 20 years ago today, W. H. Knox, R. S. Knox, J. F. Hoose, R. N. Zare. "Observation of the 0-fs pulse" Optics and Photonics News, April 1990.
It seems to me to be common that if one author (call her author A) contributes significantly less then the others, but still enough to warrant more than an acknowledgement, the paper will be attributed to the other authors (in the normal alphabetical order) with an appendix by author A. This seems to me to be a reasonable way of doing things, since first of all the normal alphabetical order is kept and secondly author A gets credit for her work.
My limited experience agrees with Ryan Williams's answer. As an undergraduate, I wrote a paper with my advisor (last name Mills) and she insisted that my name appear first (my last name is Shelly) so that readers would know that I did most of the work. She was actually being quite generous, and I think really she just wanted the publication to benefit me as much as possible. As she said, if people saw my name second they would assume that I helped out with some trivial aspects of the paper.
Ever number theory paper I have ever read has listed the authors in alphabetical order, with one exception:
Heath-Brown, D. R.; Goldston, D. A., A note on the differences between consecutive primes, Math. Ann. 266, 317–320 (1984). ZBL0514.10031. PDF (Wayback Machine)
I guess this was due to an editorial error. Dan Goldston once jokingly told me (paraphrase):
"The rules of mathematics do not apply to Heath-Brown."
Placing the authors out-of-order in a mathematics paper makes a strong statement -- that one author has contributed significantly more than another. There are problems with the alphabetical system, and there are also problems with the ordered-by-contribution system, e.g. when authors contribute comparable amounts to a paper, who comes first?
To be fair, the proportion of papers that have authors out-of-order should be contrasted with the likelihood of a random permutation of those authors' names being out-of-order. So, we should disregard papers with a single author. If there's two authors, then there's a 0.5 probability that "alphabetical order" = "ordered by contribution". Then we need to keep in mind that there's fewer papers with 3 or more authors.
There are examples (not just famous ones) around in the mathematics journals if you look for them (I'm guessing often people wouldn't even notice that they're out of alphabetical order). My former supervisor has two:
S. Taylor, I. M. Wanless and N. L. Boland, Distance domination and amplifier placement problems, Australas. J. Combin. 34 (2006) 117-136.
I. M. Wanless and E. C. Ihrig, Symmetries that Latin squares inherit from 1-factorizations, J. Combin. Des., 13 (2005) 157-172.
I was once told that defying the almost ubiquitous alphabetising convention may create difficulties in referencing the paper later on. It is thus in all the authors´ best interests to stick to this convention.
Incidentally a similar discussion was recently had on the Secret Blogging Seminar:
(the discussion began on slightly different matters, but by around comment 20 discussion turns to precisely this question).
In Medicine and in Surgery, the convention is similar to that of the Physical Sciences with the most significant contributor being first or last, or with the owner of the lab equipment or funding getting senior author position as the last author.
However, there is a curve ball in Medical and Surgical Journals in that the first three authors are the ones who gain the most credit. The reason for this is that back in the pre-WWW-historic era, when I wrote papers that went into Surgical journals and when I went through medical school and surgical residency, the medical journal articles were all indexed in the Index Medicus.
The Index Medicus was a hard-copy index prepared at the end of each year and found in every medical library with three sets of listings sorted by Medical E-something Subject Headings (MeSH), title of the journal article, and the last name of the first three authors. This paper index was how people found journal articles of interest and how the authors gained "publication cred." I ended up as third author on many papers giving me a lot of cred even above some grad students and post-docs who helped with experiments but had not supervised or designed (or originally proposed some of, i.e. conception and design, as I had) the experiments in these papers as I had.
Because of the problem with "author inflation" (people being added to author lists as a courtesy or to accomodate seniority), journals in medical fields such as JAMA (Journal of the American Medical Association) now require authors to submit signed Authorship Responsibility Forms (Wayback Machine) which outline specifically what constitutes valid criteria for being listed as an author on a paper:
Obtaining funding is listed as one of the possible criteria, as are administrative, technical, or material support. Some of these criteria surprised me as being rather flimsy in some contexts.
In medicine, I have seen two standards used. In one style, the first author is the one who has contributed the most to the paper (or the senior most author), with the rest in order of the degree of their contribution. In the other style, the first author is the "second in command", often the graduate student or medical student or surgical resident who was written the bulk of the paper, with the leader of the lab or the senior-most researcher listed as the last author.
I have seen this explained in both ways to students: that the first spot is the most prestigious according to some researchers and that the last spot is the most prestigious according to some researchers. There seems to be a dividing point between biologists and chemists as to the ordering of prestige. In either case, for a paper with $n$ authors, the ordering of the listed author number $1$ to the author number $n-1$ is in decreasing degree of contribution.
Alphabetical order is used for the sub-levels of contributors: i.e. multiple surgical residents who have contributed equally in performing the clinical science or multiple medical or graduate students who have performed essentially equivalent roles in the laboratory are included in the middle in alphabetical order.
Don't know if the question is appropriate for math-overflow, but I will try to quickly answer it anyway.
The rule is not totally universal, but it has become very common. It is certainly the norm in theoretical computer science (my area). It is common enough that when the author order is not alphabetical, it looks strange. One assumes that the first authors must have done almost all the work (and the others probably insisted on being listed behind them).
See authors written in reverse alphabetical order on Atlas of finite groups page.