I've mentioned this before on here, but mathematics papers don't use the usual rules for author ordering. By convention, more or less the entire field has agreed that authors shall be listed alphabetically. So, Max Zorn probably got listed last on every single multi-author paper he published, while Odd Aalen[0] has probably been listed first on every paper he's published.
To prove that I'm not just making this up out of my ass, here[1] is a statement from the American Mathematical Society that talks about it. I'll quote the meat of it here:
> In most areas of mathematics, joint research is a sharing of ideas and skills
that cannot be attributed to the individuals separately. The roles of
researchers are seldom differentiated (in the way they are in laboratory
sciences, for example). Determining which person contributed which ideas is
often meaningless because the ideas grow from complex discussions among all
partners. Naming a "senior" researcher may indicate the relative status of the
participants, but its purpose is not to indicate the relative merit of the
contributions. Joint work in mathematics almost always involves a small number
of researchers contributing equally to a research project.
> For this reason, mathematicians traditionally list authors on joint papers in
alphabetical order. An analysis of journal articles with at least one U.S. based
author shows that nearly half were jointly authored. Of these, more than 75%
listed the authors in alphabetical order. In pure mathematics, nearly all joint
papers (over 90%) list authors alphabetically.
Exceptions do exist, as alluded to by the "over 90%" number mentioned in the AMS statement. But, many of those are caused by transliteration artifacts (e.g. Author1 and Author2 are in alphabetical order in the language the paper was originally published in, but the English transliterated versions of their names are not).
This is all true, but it's also reasonably common to make an exception in special circumstances, particularly where one of the authors made the key discovery, and move that author's name to the front.
For example, the recent papers on aperiodic monotiles have Dave Smith as the first author, even though his name doesn't come first alphabetically.
(I can also think of another recent example, which modesty forbids me to detail.)
In the case at hand, we did deliberately intend anon to be the lead author. (I was one of the ‘coauthors’ who helped to write it up.)
Fun fact. Max Zorn was at Indiana University when I was a grad student there in the '80s. He hated to be known for Zorn's Lemma instead of the other work he did. He thought that was just a fairly trivial observation.
Hah. Only on HN does one mention a pseudorandom mathematician, then run into someone who was a student in their department 35-40 years ago lol....
You know how the joke goes, right? “The axiom of choice is obviously true, the well-ordering principle obviously false, and who can tell about Zorn’s lemma?” [0]
I'm honestly not sure I could have resisted the temptation to ask him "What's yellow and equivalent to the axiom of choice?"[1] one day.
Okay, nevermind. I would have resisted, but I'd be chuckling about it off and on the whole time when I was sure he wasn't around, while I was doing my degree.
In all seriousness, though, proving the equivalence of AC, ZL, and WO was probably my first venture into "real" abstract mathematics in undergrad. For essentially the first time, there was no picture I could draw that would have any semblance of accuracy or utility, and yet at the end, the result popped right out just the same.
Unfortunately, I didn't make it to the independence of the Continuum Hypothesis that year, and had to move on to other courses. :/
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[0]: AC, ZL, and WO are also equivalent to the Hausdorf maximal principle: in any poset (P, ≤), every totally ordered subset S is contained in some maximal totally ordered subset T. In some ways, HM is kind of the "dual" of ZL by swapping totally ordered subsets for elements, ⊆ for ≤, and push the whole thing up into the power set realm, I think you just get ZL trivially. Of course, I always found HMP much more intuitive than ZL... basically, AC > HM > ZL > WO in my mind, in descending order of intuitiveness.
I never met Paul Cohen, but he started out in my field, analysis, not logic. When he realized he would not make it to the top he started looking around for easier pickings. He came up with "forcing" that applies ideas from game theory.
When I visited IU in the '90's there was a new stoplight on E 3rd. Max got hit by a car when trundling into his office every day in Swain Hall East and his colleagues somehow convinced the city of Bloomington to put one up.
While misspending my youth playing 5-minute chess at Bear's Place up the street, Raymond Smullyan showed up and asked if he could kibitz. I can write a very short book titled "What is the Answer to that Question?" It would be much shorter than https://www.amazon.com/Million-Zeros-Douglas-Crockford/dp/19.... Bjarne told me the guy had gone crazy. He is right.
I actually picked up a copy of Cohen's book [0] on CH a few weeks ago. It's in my "actually going to read this" pile right now. Looks pretty accessible, even for an ersatz graph theorist/combinatorialist such as myself.
In math, it's primarily because they want credit for the paper to go to the collaboration. This has the secondary effect of eliminating arguments about whose names go where. Is it the same way in those fields?
To prove that I'm not just making this up out of my ass, here[1] is a statement from the American Mathematical Society that talks about it. I'll quote the meat of it here:
> In most areas of mathematics, joint research is a sharing of ideas and skills that cannot be attributed to the individuals separately. The roles of researchers are seldom differentiated (in the way they are in laboratory sciences, for example). Determining which person contributed which ideas is often meaningless because the ideas grow from complex discussions among all partners. Naming a "senior" researcher may indicate the relative status of the participants, but its purpose is not to indicate the relative merit of the contributions. Joint work in mathematics almost always involves a small number of researchers contributing equally to a research project.
> For this reason, mathematicians traditionally list authors on joint papers in alphabetical order. An analysis of journal articles with at least one U.S. based author shows that nearly half were jointly authored. Of these, more than 75% listed the authors in alphabetical order. In pure mathematics, nearly all joint papers (over 90%) list authors alphabetically.
Exceptions do exist, as alluded to by the "over 90%" number mentioned in the AMS statement. But, many of those are caused by transliteration artifacts (e.g. Author1 and Author2 are in alphabetical order in the language the paper was originally published in, but the English transliterated versions of their names are not).
See this Math Overflow post for all the gory details: https://mathoverflow.net/questions/19987/math-paper-authors-...
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[0]: https://en.wikipedia.org/wiki/Odd_Aalen
[1]: http://www.ams.org/profession/leaders/CultureStatement04.pdf