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One year ago, I started working on a subject with one of the professors of our department. The idea was mine, and all of the subsequent steps including modellings, simulations, generation of figures, writing the paper and even responding to the reviewers were done by myself completely, and the professor just reviewed the paper and reminded some typos and minor mistakes of this kind, and also added a short paragraph (completely unnecessary in my opinion) to the Introduction section.

But at the end he wrote his name as the first author and submitted the paper. He told me that being second author for him means getting no credit from the department.

Anyway, I'm going to apply for grad school, and he told me he will compensate in the recommendation he will write for me.

As this is my only published paper as an undergrad, and being first author means everything for me in my application, is there any way for me to prove to the admission committees (or the professors; whoever will review my application) that I was the main contributor of the paper?

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    Don't underestimate the importance of the letters of recommendation when you apply to graduate school. They are just as important as your vita - and for things like research, they are perhaps more important. You will also describe your own work in your research statement. In comparison to those things, the author ordering on a publication is not going to be very significant. – Oswald Veblen Nov 20 '14 at 13:09
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    @Kurt That depends entirely on the field. In my field, theoretical computer science, one-author papers are not uncommon but two to four authors (almost always ordered alphabetically) is very much the norm. You certainly wouldn't hold it against somebody that they had "only" worked in collaboration with others. – David Richerby Nov 20 '14 at 15:22
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    @Kurt Honestly speaking, I doubt whether your statement is true in any field, and I am curious what field you have in mind. Single-author papers by undergrads are very uncommon, unless they appear at undergraduate research venues (and then they are usually not full papers). So I'd think a paper authored by an undergraduate and a professor (no graduate student collaborator), that appears as a regular scholarly publication in a reputable journal or conference, would get any committee's attention. – Sasho Nikolov Nov 20 '14 at 19:25
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    "He told me that being second author for him means getting no credit from the department." I am stunned to see how common this kind of argument is! Authorship and order of authors are not decided according to needs or benefits of the people involved, but according to their contribution and merit. Unfortunately, your best move right now is plausibly to let it be, and move on (while putting that professor in your personal black-list for the future). – Benoît Kloeckner Nov 20 '14 at 21:44
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    Let's not forget that what the professor did was unprofessional and (imho) unethical. Think twice (or thrice) about if you want to work with them in the future. – Raphael Nov 20 '14 at 22:18
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As this is my only published paper as an undergrad, and being first author means everything for me in my application, is there anyway for me to prove to the admission committees (or the professors; whoever will review my application) that I was the main contributor of the paper?

Short answer: no. Aside from the professor writing in his letter that he did indeed not do the work and just put his name front to brush up his CV, I see no way how you can prove that you were indeed the "actual" first author. And, given that this would essentially mean that the professor confesses unethical behavior, I see very little chance of this happening.

Anyway, I am not so sure whether being first author means "everything" for you. Undergrads are often not the first authors of publications (for many reasons, not just the unethical reason that you were denied first authorship). Further, if I see a paper with a senior author and an undergrad, I am not assuming that the professor did most of the hard work and undergrad just advised - independently of how the authors are ordered. I would assume your average admission committee to be similarly realistic.

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    This. It's implied; most will assume you did most of the work and know that having the professor as first author is really a (bad) formality at some places. I also agree that being first author doesn't mean everything; even being a co-author on a paper as an undergrad is a feat that fewer-than-average students accomplish! – Tommy Nov 21 '14 at 3:41
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Your question breaks down into distinct subquestions and assumptions, we need to call out each of them separately, especially because you have the importance wrong:

  1. How important is being first named author [as long as you're second, obviously], in your field. You claimed "being first author means everything for me in my application"
  2. Is fighting this fight worth it? Is it strategically worth picking this one or letting it go? 2b) Also: is it important going forward to preserve your relationship with professor (especially if it sounds like you'll stay in the same dept?)
  3. How do you actually prove you originated the work/ideas? (This is pretty self-evident and is the least important question)

Answers from experience (almost all of us know people who've been in this situation):

  1. You seem to be making a huge wrong assumption here, seems like you extrapolated the application's artificial format to believe in general you will not get any credit unless you're first-named. Generally everyone knows the deal with academia and tenure-track, it's an imperfect little world, people will understand he is under pressure from his own tenure-track metrics. Yes it's somewhat bad ethics, but this is utterly different to omitting your name entirely, stealing your idea for a startup or patent, esp. when rejecting the associated thesis, stealing your funding and redirecting it to other purposes etc. Outside in the real world noone gives a **** if you were first named author; at interviews or in applications you will be given adequate chance to demonstrate whether you were/were not the prime mover; in fact people may respect the team-member vibe if you diplomatically say "we" and "our idea" while making it blatantly obvious you did the work and wrote the professor's promotion ticket.

  2. To quote Def Leppard's fine song, "Let It Go..." You have to answer this question: on a scale of 1-10, how was prof's behavior overall, and factor in "he told me he will compensate in my recommendation". Sounds like an 8/10 to me. Believe me, there are scumbags out there, and it ain't him.

  3. Pretty self-evident, and irrelevant. Notebooks, notes, SCM checkins, emails, drafts. If in future you get a really clever idea [while in academia], send a dated email to yourself (/burn a CD and certified-mail it yourself, unopened). Read also about the concept Reduction to practice in US patent law, for the future when you're working for a company.

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If you kept a stack of drafts, produce them. While not definite proof, it would be very hard to overcome even if the professor were to try. Likely, he won't and you win by default.

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    Seems like a perfect way to start one's career. – Cthulhu Nov 20 '14 at 19:53
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    Even if this is probably a fight you can't (or don't want to) win -- *sigh* -- note that versioning repository timestamps or similar may work as proof, as long as you don't control the server (and hence the timestamps/commit messages are believable). – Raphael Nov 20 '14 at 22:21

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