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If a paper is written by multiple authors, say in mathematics, where it is clear who did what, is there a way to find the specific contribution of an author?

For example, say a person name Paul Erdős solved a problem based on a lemma proved by another person, say, Atle Selberg, and in a parallel universe, they agreed to write the paper together, how do I, as a reader know, who did what?

If there is no way (whatever little I read, I could not determine), isn't it a big issue? Is there a way to solve this issue?

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    If/when people are collaborating in mathematics, if they're super-worried about who gets what credit, there is a problem already... And, no, it's not an issue. Jul 15 at 19:32
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    Some people are better typists and compositors than others, but that doesn't really count as a mathematical contribution. Also, it should be noted that many mathematicians subscribe to the "Hardy-Littlewood rules", which amounts to saying that they'll specifically NOT try to say who did what. Just that they were collaborating long-term. And, indeed, with long-term collaborations in mathematics, it's hard to see all the causalities... And maybe not time well spent... Jul 15 at 19:37
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    These days, nearly all mathematicians typeset their own papers, with TeX or LaTeX. Whether or not a journal re-types something is irrelevant. I had mistakenly thought that you might have thought that the person who literally types the thing up (so there will be a draft) gets more credit. In any case, usually a good draft exists only fairly late, and involves lots of compromises and omissions, so much of the wrangle is not about who does/did what. Jul 15 at 19:43
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    Also, the written-out paper is very often a narrative of some chain events... as opposed to being the chain of events itself. So the actual work involved the events, and then there was the auxiliary work of writing the narrative about the events. Jul 15 at 19:51
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In general it is very difficult to sort out mathematical collaborations. The issue is that it is insight driven, not time in the saddle or effort or much of anything else, though effort can lead to insight.

But when two mathematicians talk to one another a sort of synergy can develop and a single, simple, comment can lead to a breakthrough, either in what is true or in how to demonstrate it. There can be a mutual ping-pong effect in which each comment leads to the next, and deep insight in both.

Sometimes authorship is due to someone you meet for coffee who answers a simple question with a simple answer that brings the insight.

Very infrequently such a coffee discussion might be described by one party or the other. Sometimes one party makes an hypothesis and another party proves it. Then it can be clear, but in many collaborations it is more synergistic and emergent. Organic, perhaps.

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  • You brought a complete new problem, what if my insight/hypothesis is not acknowledged, isn't it an injustice?
    – Michael
    Jul 15 at 19:37
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    It can be, but then you are probably collaborating with the wrong person. Note that mathematicians usually use alphabetical author listings to avoid issues. But if you are not an author when you should be it is a serious problem.
    – Buffy
    Jul 15 at 19:39
  • Well the point of my query is to point out, if you allow me my highness, that it is an easy problem to resolve, just by writing who did what on the paper, it occasionally happens on the book, we see the name of the author who wrote the lemma/proposition, why don't do that more explicitly on the paper?
    – Michael
    Jul 15 at 19:44
  • If I understand correctly, it is because books are an accumulation of knowledge over the ages and names are attached to many things due to contributions mades. Some names are attached when the one named didn't really contribute directly to the ideas. There is a classic example of this but I can't remember the details. Maybe Banach Spaces. A paper is usually devoted to a single (possible expansive) idea that is fixed in time.
    – Buffy
    Jul 15 at 19:59
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    @Michael I think the point that Buffy and paul garrett are making is that it doesn't really make sense to divide a typical collaboration in mathematics by "who did what". If you mean "who first wrote a step down on paper" that may have very little to do with who provided the actual insight that led to that step. It doesn't address all the other possible steps that were ruled out in one way or another by a different person. It may not make sense to credit someone who had the most proximate connection to some step because that occludes all the previous work and discussion.
    – Bryan Krause
    Jul 15 at 19:59
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I don't think either @Buffy or I are being obstructionists here... but only saying that fine-grained attribution is not usually possible... nor interesting to the parties involved!

As in an earlier comment of mine: I think that, in fact, many substantial mathematics papers are not "the thing itself", but are narratives of something, some chain of events, some discussions among the authors, etc. So "the paper" can often be somewhat artificial in format and voice. In particular, with some exceptions, the lemmas and theorems are just a way of formatting and organizing that narrative. That formatting and organization need not much reflect the authors' conceptions... but things have to be written out, and there are strong traditional rules about how things should be written out.

And, again, it seems that many mathematicians are somewhat allergic to the idea of discrimination among authors. Hence, alphabetical order of authors, and definitely no tradition of having the introduction tell who did what. With some exceptions, of course.

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The contribution of an author is often described in a letter of recommendation that supports an application of that author to a position. Of course, such letters are not made public, and they are seen by few people.

If you are not one of these people, why would you worry about specific contributions? Don't recommendation letters solve the issue for all or most practical purposes?

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People contribute to papers in many different ways that are not always easy to identify when the paper is actually written (neither by outsiders nor by the authors themselves), and as a consequence most people resist the idea of being to specific and explicit in providing a statement that breaks the contributions apart. For those journals that require them, you will find that these statements of who contributed what are often very short and not actually particularly specific. People use them as an affirmation that everyone who is an author is justifiably so, rather than a precise instrument.

Underlying your question is the assertion that being able to find out who did what in a paper would actually be useful. But I don't think that's actually true, at least from the perspective of the authors of a paper. In the end, everyone among the authors is better off if individual contributions remain murky, because that allows the authors to claim that they substantially contributed to the paper, and for letter writers to claim that one of the other authors contributed substantially -- and nobody can call them on the slight inaccuracy.

One might argue that it would be useful for others to see who did what in detail on a paper, for example hiring or evaluation committees. But then how do you compare someone who had the idea but did not put it into software and did not apply it to a data set; to the person who did these tasks; to the person who has a comprehensive overview of the literature and is a good writer and so did most of the writing and putting in context? It's hard to know how one would balance these contributions, and so I will claim that there is little to gain from knowing who did what exactly.

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