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I was asked to be a referee of a PhD thesis. The thesis is completely based on several papers published in journals. All the papers have, besides the PhD student, other authors (different authors for different papers). Also, the field of study is Mathematics, so the order of authors is Alphabetical, and there is no information about the contribution of each author.

Given this situation, how should I evaluate the thesis? Is there any general advice on how to proceed in such a situation?

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    The thesis is based on several papers, I'd say you can evaluate the thesis on its own merit, the author is presumably claiming they produced the work it contains. Any work that appears only in journals is not the author's contribution. For clarity, email the PhD candidate, their supervisor, or their institute.
    – user2768
    Commented Jun 15, 2020 at 8:02
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    There should be some guidelines by the department for which you review the PhD thesis. Many actually require an explicit contribution statement from the PhD candidate (signed by all collaborators). If you were not presented with any such guidelines, it s a legitimate question to ask them. Commented Jun 15, 2020 at 8:02
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    So is it a kind of "stapled thesis" consisting of the papers, or is it a reformulated coherent thesis which main results coincide with those of the published papers? Commented Jun 15, 2020 at 11:37
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    @J.FabianMeier, it's roughly a stapled thesis.
    – the L
    Commented Jun 15, 2020 at 13:33
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    I've been a referee for exactly one "stapler" thesis, but its introduction included a description of the candidate's contribution to each of the joint papers. My report included a summary of that information as part of my overall assessment that the candidate had demonstrated the ability to carry out independent research. So I agree with @lighthousekeeper that, if such information is not available to you, then you could reasonably ask for it. Commented Jun 15, 2020 at 15:29

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Let me start with a story. At Harvard, before a PhD student is allowed to schedule their oral dissertation defense, which (as is the case in many places) is usually a formality, the advisor is required to explain the significance of the dissertation work at a faculty meeting, and the faculty have to agree that the work is significant enough for a dissertation for the defense to go forward. The possibly apocryphal story goes that, after a contentious faculty meeting at which a dissertation was grudgingly approved, the advisor, a well-known mathematician who has had many students, remarked, "Well, this isn't the worst dissertation I've written."

The point is that, while we claim that a dissertation is the work of the student, in most cases, this claim is really partially true polite fiction. Certainly the student is expected to understand all of it, and to have contributed significantly to it, but, in any sort of collaborative theoretical work, it doesn't even make sense to precisely separate out which ideas came from whom. I've heard mathematicians claim that they correctly decided which idea to pursue to solve a problem based on the quality of the silences during a conversation with their collaborators, and I believe this claim. When ideas are developed with such subtle yet vital contributions, it makes sense to just give each co-author 100% credit for the ideas.

Unless you have a policy that theses should not be based on collaborative work - and, frankly, this policy is unenforceable due to the common but not universal custom for advisors to decline co-authorship with students on papers where they would otherwise be a co-author - you really have no choice but to take at face value the claim that the thesis represents the student's work. At the least, you can expect the student actually wrote the text of the thesis and understands its contents, and if there is an oral defense you can test whether this is true. Beyond this, you will have to trust the student and the advisor that some acceptable portion of the ideas in the work actually came from the student. Someone contemplating hiring the student will get more information in the recommendation letters from the advisors and the other collaborators.

It's generally understood that an advisor usually ends up spending more time advising a student on solving their dissertation problem than it would have taken the advisor to solve the problem themselves. You might want to read between the lines of the following statement about the culture of PhD advising from the American Mathematical Society: http://www.ams.org/about-us/governance/committees/Statement_DirectingPhDTheses.pdf

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    I am not sure if it matters, but actually, non of the four papers is coauthored by the advisor of the student.
    – the L
    Commented Jun 15, 2020 at 10:17
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    And note that collaborative mathematical work is often synergistic and that is a good thing.
    – Buffy
    Commented Jun 15, 2020 at 14:17
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    I'd add that the purpose of a PhD thesis is to train the student to be an independent researcher. Even in the case of a "single-author thesis", it's not clear just from the written thesis how far this aim has been met, depending on how much help they received from their advisor. And even someone who is capable of independent research may need help finding new problems and additional mentoring at the postdoc level.
    – Kimball
    Commented Jun 15, 2020 at 14:36
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    @Kimball and beyond!
    – Matt
    Commented Jun 15, 2020 at 22:19
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You don't say which country you are in, but if this were the UK, I'd evaluate the work in thesis on its merits, and then interrogate the student on which parts of the work they consider to be their contributions in the viva. If you are convienced in the viva that the student had made a significant personal contribution, I would work with them, through the corrections process to add a statement/statements to the thesis to make clear what the students contribution to the work was.

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French perspective here. My understanding is that the contents of the PhD manuscript handed by the candidate should mostly consist of their own work, or things of which they are a main contributor: they should definitely understand it, probably have written it (or wrote a version of it), etc. If the candidate is an author on a paper to which they only contributed in a minor way, they can mention the paper in the PhD but probably not include the material in the manuscript. And by extension: if the candidate hasn't been a major contributor to any paper to which they are listed an author, then the manuscript should be pretty lightweight indeed. :)

Concretely, if you have doubts I'd advise getting in touch with the thesis advisor to clarify expectations, i.e., ask them to briefly describe the personal contribution of the student to the works they have co-authored, clarify if the contents of the thesis is indeed the candidate's specific contribution, etc. If phrased politely, I think this is a pretty sensible request.

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    I doubt that if such regulations were in place, that such a thesis even would be contemplated or attempted and the question would be moot.
    – Buffy
    Commented Jun 15, 2020 at 19:11
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    @Buffy: this is an informal "expectation" I've heard, not a formal regulation.
    – a3nm
    Commented Jun 15, 2020 at 19:13
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From your comments I understand that the coauthors are not advisors and that the work itself is more or less a verbatim copy of the papers.

In this case, I would indeed ask back which parts of the papers are the results of the PhD student.

Alexander Woo is certainly right that in many cases, the work of a student and his/her advisor cannot be separated (although there are advisors which do not discuss ideas with students), but if the student collaborated with other people, there should be a statement about what (roughly) belongs to whom.

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    Your last sentence is not the view of pure mathematicians.
    – Buffy
    Commented Jun 15, 2020 at 15:08
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    Let me be more precise, then. If you and I have a series of conversations in which we, over time, close in on some important mathematical concepts and it results in a paper, then it is, in essence, to split up who did what unless you want to include the tapes of the conversations. I have a wild thought. It triggers something in you. You bounce it back. I take it around a corner. We both say wow. 42 iterations later we have a theorem. Now what? Mathematics isn't a mosaic, but a unified whole. Not always, in any case.
    – Buffy
    Commented Jun 15, 2020 at 17:37
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    Absolutely. It is actually how professionals work in the internet age and tried to prior to that. Being an "independent" researcher doesn't mean toiling in isolation. It means using best professional practice to advance the art.
    – Buffy
    Commented Jun 15, 2020 at 17:59
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    @JFabianMeier: If formal rules cause trouble in this case, those rules are bad. The way Buffy describes it, fruitful research has happened by the candidate which is exactly the goal of a phd programm.
    – user111388
    Commented Jun 15, 2020 at 19:56
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    @J.FabianMeier - I think we have a difference in national cultures here. In the US, when there are stupid formal rules, we usually look the other way and either pretend they don't exist or comply with them in some meaningless formal way. Commented Jun 15, 2020 at 22:57
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I do not see the problem.

The fact that the work was already been published is irrelevant as long as the student is an author. The order of names may not be representative of the actual contribution due to publication tactics, although it is very good practice for the student to be first author. I assume that the thesis is not a monograph but a collection of papers (e.g. "Essays on Aztec Riding"), so there is no structural problem. The most important point is whether there is enough of a novelty to justify awarding a PhD. Unless the student has collated published work of others in the thesis papers to such a large extent that there is no own theoretical or applied contribution in the papers and the thesis as a whole (in essence a literature review, a press article or a generic opinion publication), I do not see a point for concern.

Of course, if collation and a patch-up of papers published by others is what has happened, there is a huge problem.

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    The order of authors in mathematics is usually alphabetic. This does not reflect "publication tactics", it's just the norm in the field. Thus, "it is very good practice for the student to be first author" only makes sense if the student's name is "Aardvark". (Pity Zermelo.) The key aspect is not whether there is enough novelty in the papers, but whether the student's contribution was sufficient. In an extreme case, the papers may be extremely important, but the student's role may have been very minor. Commented Jun 16, 2020 at 7:54
  • @StephanKolassa If you have contribution but no novelty you do not have a PhD of any merit. Also, what you say does not explain why the mathematicians I know and have worked are concerned about authorship order in their papers, both for their students and their own work.
    – user117109
    Commented Jun 16, 2020 at 8:48
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All the papers have, besides the PhD student, other authors (different authors for different papers)

This student can work with different set of co-authors, and be productive. This shows that (s)he is already an independent researcher. Moreover, they are also independent from their advisor:

I am not sure if it matters, but actually, non of the four papers is coauthored by the advisor of the student.

If the papers are good, then they are good, what else do you want to check? Is there a mediocre student who manages to publish good papers with different set of authors? if there is, it is also a fantastic skill that I want to learn :)

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    The main point of a PhD thesis is not to show that the candidate can work independently with others, but to show that the PhD student is capable of setting up, leading and completing their own scientific project (potentially with contributions from others). In fields where first authorship is a thing, a candidate wouldn't get away with having only middle-author papers. Commented Jun 16, 2020 at 6:23

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