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I'm working on a paper which involves the application of a particular equation to sets of experimental materials science data. I devised the idea for the equation and collected/collated the data. With my PI, I then drafted an initial form for the equation. Once I applied it to the data, though, I caught an error. My PI was really reticent to change it and I had a hard time convincing him it was necessary. Neither my PI nor any of my coworkers have a strong math background, so I turned to a personal friend who was a math major in college to help me show that a better equation exists.

My friend helped me to identify the correct functional form and, critically, drew up a mathematical proof showing that the resulting equation gives a particular value if and only if our assumptions are true. This basically shows that the equation is not just right but also meaningful for interpreting the data, and that's a huge deal for the paper.

I feel like this warrants co-authorship, but... my friend is currently unemployed and last worked as a middle school teacher. I checked their work (I was a math minor and am confident it's right) but it is their original contribution, not mine. My friend also hopes the publication of this paper could help them land a "more serious job". I just don't know how to note their affiliation for a journal and have no clue how I'm going to sell this to my PI.

How should I properly attribute authorship for an unemployed non-academic? I also welcome ideas of how to convince my PI that this authorship is necessary, but that's much more subjective and I'm not asking for an answer. I have told him that I had a "math major friend" assist in the development of the new equation. He seems ok with the new form because the proof exists, but he didn't read the proof when offered. I'm worried he'll reject the paper if he decides my friend's credentials are insufficient when we go to submit, but I'm not going to lie and say the proof was my work.

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    There are two questions here, one about how to attribute authorship for your friend, and one for selling it to your PI, which is potentially domain-specific. Please ask one question per quesiton.
    – Azor Ahai -him-
    Commented Nov 25 at 22:28
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    That said, I'm not really sure why he'd "reject" the paper. PIs don't "reject" papers, and credentials are not part of the peer-review process.
    – Azor Ahai -him-
    Commented Nov 25 at 22:28
  • @AzorAhai-him- Edited to clarify what I'm really asking, ty. As for rejecting the paper: in my group the PI has final say on whether to publish any paper in the group. That practice is pretty much ubiquitous in my field. I'm not 100% sure what would happen if I tried to publish without consent, but it would not look good for future PIs in my field and there might be some issues with attribution of funding (award went to PI, not institution).
    – user213999
    Commented Nov 25 at 23:10
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    This is how I ended up as a last author while being an uni dropout - with no affilation and no degree prefix. The PI was not happy, but my friend was not happy with them either. If you think this is the right thing to do, it is unusual, but possible.
    – fraxinus
    Commented Nov 26 at 11:05

7 Answers 7

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One doesn't need to be an "academic" or even employed to be an author. If the person has made significant intellectual contributions to a paper then they are rightfully an author. Your friend can be listed as an "independent researcher" or, perhaps even, an "independent mathematician". "Unaffiliated" might even be acceptable to a journal.

Your PI probably has to agree to this, and I hope they do, as it is probably the ethical path. But fighting with a supervisor isn't a viable path and you might need to settle for a "significant contribution" statement in an acknowledgements paragraph or section.

But, it seems to me that authorship is warranted, since it makes the result feasible. "Huge deal" is almost always authorship. In math related things, even very short conversations can lead to authorship if they provide key insights.

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    I like the idea of "independent researcher" - that's what my friend is and likely will remain by the time the paper is published. Good phrasing.
    – user213999
    Commented Nov 25 at 22:43
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    It is also fairly common. Being retired, I'm currently "unaffiliated" and would be listed as such on any publication.
    – Buffy
    Commented Nov 25 at 22:44
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    I like "unaffiliated" better than "independent researcher". Somehow, the latter has the whiff of "crackpotism", I feel, that the former does not.
    – Captain Emacs
    Commented Nov 26 at 1:41
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    "'Huge deal' is almost always authorship." - And if they wrote an actual proof, I can't imagine it not being worth a coauthorship.
    – Ray
    Commented Nov 26 at 17:24
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    Academia has never opposed unaffiliated researchers or independent researchers for being unaffiliated or independent; what it opposes is their frequent rejection of a rule that goes back to grade school: "Show your work."
    – EvilSnack
    Commented Nov 27 at 3:09
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Congratulations to your friend, they have made a great coauthorship-worthy contribution to an academic paper. And congratulations to you for having such friends and for having a better paper now.

An important thing you need to keep in mind as you enter the discussion with your PI is that there is nothing to “sell” here. Academia simply does not frown on unaffiliated researchers in the way you imagine it does. If your friend would have deserved coauthorship if they had been a “proper” academic who had made the same contribution, then they deserve coauthorship in the current situation.

Your PI may not like the idea of adding a coauthor, for a variety of reasons (all of them unethical) that people have for making such objections. I wish you luck with this discussion, but I think it’s extremely unlikely that a lack of affiliation would be a serious issue. I see no particular reason for you to even mention the affiliation issue yourself unless the PI brings it up - it’s simply immaterial to the discussion. However, if it does come up, be honest and don’t use euphemistic or defensive language to disguise the true situation.

Finally, a small note of caution. You wrote:

My friend also hopes the publication of this paper could help them land a "more serious job".

This seems unlikely to be true. Not that many people outside of academia care about scientific publication, and one coauthorship in a paper (which will probably take quite a while to get published) isn’t going to make a huge difference to anyone. Even in an academic context, a single coauthored publication doesn’t carry much weight these days.

Well, anything helps of course, but your friend may want to temper their expectations on this particular issue. Regardless, they still deserve the coauthorship.

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    I don't quite agree that academics generally hold no bias against independent researchers. Right or wrong, people will be more skeptical of work coming from someone who doesn't have formal qualifications or a support network of peers to discuss their ideas. See this question which describes work from independent researchers as "99% wrong" without so much as blinking an eye: academia.stackexchange.com/questions/211904/…
    – Nuclear Hoagie
    Commented Nov 26 at 14:32
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    @NuclearHoagie I disagree. The discussion you link to is in the context of amateur scientists claiming to have solved “big problems”. In that case, the “99% wrong” estimate is surely correct (and may be an underestimate). To fairly predict, based on a real understanding of how the world works, that someone’s work is very likely wrong, is not “bias”. OTOH, to unfairly assume that an ordinary scientific contribution is wrong because an amateur came up with it - that would be an example of bias. I stand by my claim that that type of bias is very uncommon in academia.
    – Dan Romik
    Commented Nov 26 at 16:00
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    I don't think it's common to simply assume that any work by an amateur is wrong, but I'd say it's less likely to be taken at "face value" than work done by a prominent academic who works closely with other credentialed individuals. It's not too different from why peer-reviewed work is generally more highly regarded than work that isn't - it indicates that someone other than the author thought it was correct. Affiliation suggests the researcher has an accessible network of knowledgeable peers.
    – Nuclear Hoagie
    Commented Nov 26 at 17:09
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    @NuclearHoagie A paper by a single unaffiliated researcher is a red flag, and I will dread reviewing that paper (but I'll still do it fairly, even if I know how it's likely to end). But a single unaffiliated researcher on an author list with a bunch of people from a university? No worries, since if it was a crackpot paper, one of those people would have called them on it before it went out for review.
    – Ray
    Commented Nov 26 at 17:33
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    @DanRomik I thank you for your note of caution and I agree completely. From the beginning I tried to make clear to my friend that a paper =/= a job. They just feel like having last taught middle school math makes potential employers less confident in their skills beyond, say, prealgebra, and that the paper could be useful "evidence". I suppose it goes back to the discussion of academics and independent researchers, and I hope everyone involved just takes the math on its merits.
    – user213999
    Commented Nov 26 at 22:45
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This kind of thing is not uncommon. In this paper of mine, a good friend is even first author. He is simply listed by his name and the city he lives in. He works for a company in Germany, but worked on the paper in his spare time and so no affiliation is given. The example shows that whether or not any author is actually employed, or where they are employed, is not important. What is important is that they contributed significantly to the paper, in which case they should be co-authors.

As for how to break that to your PI: In an ideal world, they would always have known about your friend. If someone contributes to a paper, all current authors should know. It's not clear to me how your friend contributed to the paper, but it's for sure awkward that they contributed a whole method and a proof and you never mentioned that to your co-authors. If I had been one of them, I would be upset with that, given that you made it look like it was your contribution rather than someone else's. In any case, this would be a good time to come clean on this with your co-authors and explain why you think it is ethically the right thing to make your friend a co-author given their contributions. This would also be a good time to be honest and forthcoming with what precisely they contributed, rather than beat around the bush.

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From what you say, your friend should be an author. List them as an author. You don't need to tell your PI that your friend is unemployed. If an affiliation is asked for, just list them as "unaffiliated".

I am not sure why you think your PI will reject this. Are you concerned that they will not have confidence in the proof given the source? Show them that you have checked it yourself and invited them to do the same. Are you concerned that they won't want to share credit with a non-academic? This suggests that you have a rather poor opinion of your PI.

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    Actually, lack of honesty with your PI isn't a good path. What happens when they learn and think they were misled.
    – Buffy
    Commented Nov 25 at 22:37
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    @Buffy I agree -- the OP should be honest with their PI. Listing the friend as "unaffiliated" is honest, and tells everyone concerned that the friend is not an academic. Sharing that the friend is unemployed is no more relevant than sharing what the friend has for breakfast or what health conditions they have.
    – Significance
    Commented Nov 25 at 22:41
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    @Significance I appreciate your thoughts as an "unaffiliated" observer :) I agree that honesty is the best policy esp. with a PI. My concern is more that he was reluctant to accept that his initial math was wrong. I think he believes that he and I have at least the same amount of math knowledge here and he did not spot the error. Yet he knows my abilities, hopefully trusts my honesty, and can see the data indicating the error. With my friend's proof, I'm relying on the data to make him trust what he has already been reluctant to accept, and I want to make sure he knows the proof is valid.
    – user213999
    Commented Nov 25 at 22:57
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John Citizen, Independent Researcher.

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Perhaps, it is best to show all your working and to be honest regarding all contributions big and small. Reluctance in doing so, may only show why your friend is reluctant to accept the proof is valid.

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In some cases, it is possible to call your co-author a visiting researcher or visiting scholar at your institution. This will require, at minimum, approval by your PI. There may or may not be any formal process at your institution beyond that.

We often do this when scientist and engineers at major companies contribute outside of their employment, often students who graduated. The company is fine with the employee's help, but doesn't want their name associated with something they aren't involved in, and often requires a lengthy approval or review process on their end.

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    Actually it might require agreement from the institution not just the PI.
    – Buffy
    Commented Nov 27 at 23:32

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