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tl;dr: Skip the first two paragraphs.

I'm a student working in theoretical computer science. I recently did some research where I came up with most of the ideas, but would regularly receive feedback from a professor. (I am not receiving money from said professor.) After I was finished, the professor suddenly decided to get heavily involved in the project, rewriting the entire paper (aside from pseudocode). This was offensive, but no deal breaker as he was not trying to claim first-authorship and some of his contributions (e.g. background research) were a huge improvement. Then I read his proof. It was incredibly non-rigorous and, after spending 10-20 hours parsing it, I realized that it was totally invalid and that he definitely does not know if the algorithm is correct or not.

Also, there was a glaring error in the first draft of my proof that was repeated in his rewritten version. This is the second time that I have caught an error in a proof that I have written and both he and the 3rd author has checked and told me is correct. This is totally my fault but, at this point, I have lost faith in my ability to rigorously prove something of this complexity with total certainty, and lost confidence in the two professors involved to check it. I would not be confident our work is correct without writing up a rigorous proof and getting the opinion of a mathematician.

When I told the professor that his proof was way off, he was furious and refused to be a second author on the paper unless he is the sole writer. Is this reasonable? He wants to publish work that I'm not sure is correct, and has a proof that I consider embarrassing because 1) if someone skims it, it's obvious that it's not rigorous, and 2) if somebody does take the time to fully understand it, he is exposing that he does not know if the algorithm is correct or not.

One comment I have received is that I should do whatever he says and that, as a student, I don't bear responsibility for the paper's correctness. Another is that if it is wrong, the responsibility is on the review process to catch it. However, I suspect that the conference we're submitting to will not rigorously check the proof and the argument in the proof does sound intelligent and plausible at first glance.

Is it true that I do not bear significant responsibility for the correctness of my work?

What should I do?

Also, the other professor involved (third author) suggested I just ask him if I can publish as a single author. He made it sound like no big deal, but I got the sense that this is a very bad way to go; after all, the second author spent many hours advising me on this project, did most of the background research and wrote the introduction and much of the less technical parts of the paper.

Some context (put in spoilers in case you want to think about this post with less bias first):

I am an undergraduate senior working with a professor at a lesser-known US research university. I have secured my own funding for a PhD and I have objective evidence that I am one of the top students at my present university. I have reviewed one paper for a conference; however, I have no prior research experience and this professor has many years of experience as a researcher and a reviewer. I am applying to top Master's programs (and have been accepted to some), with a view to probably going on to PhD. This professor wrote me letters of recommendation. He also controls the grade for this research. So I did not take defying him lightly.

All comments, no matter how frank, are appreciated.

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    If you are unsure about the correctness of the proof or how to fix it, maybe you could ask about it in the appropriate math/cs stackexchange. Mar 8 at 7:52
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    "I would not be confident our work is correct without writing up a rigorous proof and getting the opinion of a mathematician." This is what you should do. It might not even be necessary to get a mathematician's opinion. When you write up the rigorous proof, or when you share it with the professor, everything might become clear and you might both agree about what is correct.
    – toby544
    Mar 8 at 10:28
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    Just a side comment on "if it is wrong, the responsibility is on the review process to catch it". Don't ever rely on peer review to fix your own sloppiness. Peer review is rather the final line of defence, not the main guarantee of a paper's correctness. You as the author should be convinced the paper is good before submitting it to peer review; reviewers have orders of magnitude less time than authors to look for flaws so they're pretty much guaranteed to miss most errors.
    – TooTea
    Mar 8 at 12:04
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    "Is it true that I do not bear significant responsibility for the correctness of my work?" No. "What should I do?" Start to act like you bear significant responsibility for the correctness of your work, the rest will follow.
    – EarlGrey
    Mar 8 at 14:10
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    The professor is wrong on both counts. You are right to be skeptical whether the review process will catch any mistakes. If he missed actual mistakes (not just typos or slightly misstated equations and such) in your proof which he claimed to check for correctness, then you are right to be skeptical of his claim that the proof is correct. If this is a possible scenario for you, I'd consider stalling until you no longer need his letter of recommendation / grade. At the end of the day it seems like you are entitled to submit the paper as a solo author, though perhaps omitting his contributions. Mar 8 at 18:36

5 Answers 5

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We don't have enough information (nor can you provide it) to know whether the algorithm is correct or not or, if correct, whether the proof of correctness is correct.

Wrong proofs and faulty algorithms occur naturally when exploring new areas. Some have been published - but not by honest people who knew at the time that was the case.

You should not be an author of a paper that you know is wrong.

You should not be an author of a paper containing a result that you suspect is wrong unless the result is potentially interesting even if it is wrong. Then it might be OK to publish it with sufficient expressions of doubt.

This rather blunt answer does not address the personal issues between you and the other contributors, nor the possible effects on your future academic career.

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    The statement could be formulated a conjecture, with the proof idea suggested, rather than asserting a formal proof. This is a bit wobbly, but at least it is not claiming rigorous correctness, and might still be a valuable publication if the method is promising. Mar 8 at 1:48
  • "You should not be an author of a paper containing a result that you suspect is wrong unless the result is potentially interesting even if it is wrong." That's a bit of strange advice. One does not just write down a proof and add a caveat that the proof might be wrong. Mar 8 at 16:44
  • @CaptainEmacs Thank you. In this case, the result would not be interesting enough for publication unless it is proven.
    – Fricis
    Mar 8 at 20:12
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    +1 thank you. I see one definite error, but after that is corrected, I only have generalized uncertainty, and I do not believe the professor's proof is rigorous. If there is another error in our work, the current proof would not be rigorous enough to reveal that.
    – Fricis
    Mar 8 at 20:19
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Academic papers have a long life. If you go on to get a PhD and want to have an academic career, the last thing you want is a paper on your publication list that you are not only embarrassed about, but actually know is flat-out wrong. This will literally haunt you forever. Even if the error is not detected for a while, you will see this paper every time you look at your publication list (and you will be looking at it a lot, every time you update it, or convert it from LaTeX/PDF to HTML, or reformat it for a grant application, etc). You will think about it every time you mention how many publications you have when preparing a cover letter or updating your CV. And you will live with the knowledge that you knowingly published something incorrect. It will be a most unpleasant feeling, which will be made worse if you actually achieve a good level of success publishing correct and even good research. You will probably feel like a fraud, and come back to this site in a few years' time with a post saying you cannot live with this error from your past and asking what you can do to fix it. (I have seen such posts here, maybe you can find them if you spend some time playing with the site's search feature.)

Of course, there is always the possibility that the error is detected. So you'll need to worry about the paper some day being retracted, possibly after other authors have published papers that make use of your incorrect result. It will be a mess to deal with, and will hurt your reputation. Even if the risk of that actually happening is low and in the most likely scenario the fallout may end up being minimal, just having to worry about it happening over an indefinite amount of time sounds extremely unpleasant.

I am very sorry about the unfortunate set of circumstances that make you feel it's difficult or impossible to resist this lunacy. It's a tough situation for sure, since all the practical, short-term incentives are pushing you to do something that in the long term will be very damaging to you mentally and possibly to your reputation. But the bottom line is, publishing a nonsense proof is a Really Bad Idea.

What should I do?

No one can tell you that, you must decide for yourself. But do think about the bigger picture and the things I mentioned above. Good luck!

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I think there are many good points in the other answers and comments that I will not repeat here; instead, I want to highlight one aspect of something you can do that I think has not been fully explored in the other answers, which is to improve how you identify and communicate your concerns about the proof.

In particular, if the proof is truly objectively and overtly wrong, then you should be able to provide a concrete counterexample to aspects of the argument in the proof that are invalid. Such counterexamples should make it unassailably obvious to your professor and coauthors that the proof is invalid. Note that I am not suggesting you should find a counterexample to your overall conjecture; rather, just to the individual logical inferences in the proof's internals that are suspect. Moreover, the simpler and more direct of such a counterexample you can Construct targeting more specific internal steps of the proof's arguments, the better, in terms of it's ability to communicate the errors you observe with the proof.

What if you can't find such counterexamples, or otherwise can't construct a "formal proof" for the proof's incorrectness? Then, frankly, you don't actually know that the proof is wrong. It is possible that you are just unsure of the proof's correctness (which is very different from being sure that the proof is wrong). While you absolutely are responsible for the validity of work that you are an author on, as others have said, it is acceptable to rely on other, more knowledgeable authors for aspects of the work that you are less certain of. E.g., if you don't fully understand aspects of the proof, but the professor asserts that it is correct, it is still reasonable to remain an author od that paper and submit it.

The underlying message of my answer here is that I suspect some of the difficulties you're experiencing here (especially those difficulties that you can control) boil down to how you have communicated your concerns to your professor. When pointing out things that others have done wrong, you want to appear as humble as possible and make it as clear and concise as possible what said others have done wrong, that way the easiest and (in some ways) only option for the person you're talking to do is to acknowledge and respond to the objective errors (and to feel safe from judgment in doing so). It doesn't sound to me like you you did this from your description. E.g., "when I told the professor that their proof was way off" seems like a very different way of communicating your concerns.

Another strategy you can take is one of asking questions -- e.g., rather than saying "your proof is wrong because step 3 is invalid with this counterexample" which carries with it undertones of judgment and can lead to conflict, you can say "This proof is really interesting! Can you help me understand step 3? I'm not following the logic here--how does this work given that in counterexample it seems like it would behave differently?" which is much more conciliatory and invites your professor to identify their own error and use it as a teaching moment which can enhance their own status and standing.

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  • "Then, frankly, you don't actually know that the proof is wrong. It is possible that you are just unsure of the proof's correctness (which is very different from being sure that the proof is wrong)." But the OP never said they were sure the proof is wrong. What they said is that the proof is not written at a sufficient level of clarity/rigor to be able to tell whether it works. This is a major problem regardless of whether or not there exist counter-examples to any of the steps in the proof. Mar 14 at 16:45
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What will most likely to happen? You will lose your faith in the academia. Your paper will be published, a chance that reviewers catching the error is low. In a typical TCS venue, reviewers need to review a dozen of papers within a month. If your professors couldn't catch the nonsense, it is quite likely that these reviewers couldn't catch that too. After publication, almost no one will notice that error unless your paper got famous or written by famous people.

I've seen quite a number of nonsenses in TCS, theoretical ML papers but never raised a question, simply because there are so many and no one cares about them.

This field (math-heavy-CS) is broken by design. Conferences are not the right way to publish technically delicate works. Heavily mathematical works typically require at least an year to review rigorously. Frankly, everyone in this field knows that but they choose not to fix it because you can publish more papers per year in this conference system.

If you want a rigorous review process, I guess math journals are better place to put your work in. Or become a real mathematician not a theoretical -ist.

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tl;dr

Is it true that I do not bear significant responsibility for the correctness of my work?

No, it is not true.

What should I do?

Start to act like you bear significant responsibility for the correctness of your work, the rest will follow.

(it may even be that you give up on doing stuff because you realize you cannot take responsiblity of the possible outcome...)


We see only your side of the story. And there are some unclear things in the description and temporal order of the "facts" you present.

As a frame change, I suggest you to read the situation this way:

First, the "good" aspect: you working for them without them paying you ... they sensed you could do good stuff, otherwise it's just a burden! A professor may or may not have money to support research, but they have a fixed amount of time. A professor get money to do research but the funds they get goes to both them and their hired researchers. Professors always get a slice of their students money, directly or indirectly (at the very minimum they can put in their CV they supervised a grant winner). In your case, they used their time with you without paying you, it means they did not get any slice of the money cake, and they solely invested their time on you, expecting to have some return on their investment.

Unfortunately for them, you provided research that looked good but it had flawed proofs. It happens, you are only a student, their bad, they could not figure out your proof was wrong (and consequently they cannot produce a correct proof).

Now let's start with the "bad" aspects:

This is the second time that I have caught an error in a proof that I have written and both he and the 3rd author has checked and told me is correct.

So you prepared two times a written manuscript and you submitted it to your co-authors, only to tell them afterwards "sorry, the proof is wrong".

I will be frank, sorry being abrasive: you are a PhD student, you think you are one of the best in your cohort, but you are still learning and you still do sh%t as every other human. One thing you have to learn during your PhD is that you carry responsibility for your errors. Your co-authors are not simply (and not only) reviewing your work. And the co-authors are peers. If you prepared the proof and the proof is wrong, the fault lies on your shoulders because you published some wrong stuff, your peers may or may not find it out, if the proof is wrong you carry down them with you. If the only reason for them to be in the paper is because they are only reviewing your work ... well, then they are reviewers, not co-authors.

Should they have spot your error? yes, but not at the paper writing stage: did you not present them the proof in advance? did you thoroughly check your proof before writing it?

Be glad for their contributions, not for missing your errors.

Should you tell your co-authors their proof is wrong? absolutely. How should you tell them this? this is a matter of interpersonal relations. If a peer of mine does something wrong, does tell me about it at a late stage and then I have to rush to put a patch on it, and afterwards said peer tells me "you are way off" I would be at the minimum disappointed, thinking "well, then you provide me a decent and correct proof firsthand, if you are so smart". To say in the most neutral terms possible, at this point you put yourself in a narrow corner: there is an issue with the paper, you pointed out strongly there is an issue but you did not provide a solution. Note for the future: if you have a strong opinion about an issue, you should have also a quick solution to the issue. It's very easy to say "this is crap", it is very hard to replace crap with "something meaningful". As you showed with your first iterations of the proofs, it is even easier to produce crap, just with different flavours.

Your professor is probably not strong on the theoretical proof side, they may even have started working with you because that was your potential strong point in your CV/profile (we do not know), so they are let down a bit by your inability to come up with a correct proof (I mean, if you were writing a paper with them it means they had full trust in you).

Afterwards, with the pressure of publish-or-perish or whatever time constrain/availability they had, your professor put together some kind of proof to make up for your wrong proof.

To conclude:

I have lost faith in my ability to rigorously prove something of this complexity with total certainty, and lost confidence in the two professors involved to check it.

Science is not about providing answers, science is about building the path to provide the answers. Build the correct path and you may (may) get the correct answers. Having doubts about oneself ability to tackle complex issue is the best spark you can have to actually find a way to tackle the complex issues.

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    I think you missed reading the spoiler. The OP is an undergraduate, not a PhD student. And if they asked their co-authors to read and correct the proof and neither of them found the error, this doesn't speak very highly for their capabilities. Of course we, at all career stages, are responsible for our own errors, but if an undergrad asks two profs to check their proof, and the profs fail to find an error the undergrad later finds themselves, that is to the undergrad's credit and reflects very badly on the professors.
    – terdon
    Mar 8 at 12:42
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    "I am an undergraduate senior working with a professor at a lesser-known US research university. I have secured my own funding for a PhD [...] I have no prior research experience [...] I am applying to top Master's programs (and have been accepted to some), with a view to probably going on to PhD." (emphasis mine).
    – terdon
    Mar 8 at 13:11
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    OK. This makes no sense to me, you are categorizing an undergraduate who hasn't even graduated from their first degree yet, one who has simply "secured" funding (apparently; this seems odd and is contradicted by the other statements, so I think it might just be a "sure kid, I can fund you, talk to me when you graduate"), who then says they are probably going to continue on to PhD, presumably after the Masters to which they are currently applying, as a "PhD student".
    – terdon
    Mar 8 at 13:27
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    I agree with @terdon in that it does not make sense to me to describe this person as a PhD student. However, I also agree with some of what EarlGrey is saying in that even an undergraduate researcher has responsibility for their own work if they'd like to be considered seriously, and clearly that is OP's intent: they want to publish this work, they see themselves as a top student, they feel in some cases that they know better than people senior to them. So, if OP wants that, they need to be prepared for the responsibility that comes with it and understand what the expectations are.
    – Bryan Krause
    Mar 8 at 14:35
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    @Fricis It's clear that many people get ahead in academia by various levels of fraud and misrepresentation. In general, I think they pay too little a cost for those misdeeds. So, strategically, should you join them? I can only tell you what I would do, not what you should. At the same time, I don't really know the full situation here; I've heard your telling of it. Maybe it's not actually as bad as it seems, maybe you're misunderstanding something. I don't and can't know.
    – Bryan Krause
    Mar 8 at 20:16

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