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Is it plagiarism if someone else came up with something before you did?
Say you come up with an idea, but X already has written about it before, even though you don't know about this.
Is it plagiarism to then publish the idea, even if during publishing you still are not aware that X came up with this idea first?
That is, can you accidentally commit plagiarism in this way?

You can (and should) prevent this from happening by doing a proper literature search before working on your ideas!

Plagiarism requires dishonesty or negligence. If you were completely honest and weren't negligent, you did not commit plagiarism. Period.

@JayFromA: Supposing the similar idea is published in a different field, and is described in unfamiliar terms so that your literature search doesn't happen to hit on it?  Lesser instances of this happen to me all the time, when I do a Google search for something using what seem to be to be natural search terms, yet someone else can do a search on what they think are relevant terms and get back a bunch of different results.

@JayFromA How do you do a "proper" literature search ? And how do you prevent using slightly different wording and not finding any results ? I mean you could search through every paper ever written, but even then noone knows what people are currently working on that isn't published yet, but that would take an unreasonably enough time.

@DavidSchwartz How can negligence ever constitute plagiarism?

@DavidRicherby I can imagine lots of ways. For example, say you find something you wrote on a piece of paper. You don't remember whether it was original or you copied it from someone else. You negligently fail to check and publish it as original work when actually you copied it from someone else. Here's another: You think of something you think is original. You negligently fail to do basic literature searching to see if someone else already published it and publish it as original work. Someone else already published it in a place you would have found had you not been negligent.

@DavidSchwartz The "piece of paper" mechanism seems a bit far-fetched to me but OK. However, independent recreation followed by a failure to do an adequate literature search is not plagiarism: it might be hard to convince people that you didn't plagiarize but plagiarism is fundamentally an act of deception, not of negligence.

@DavidRicherby the piece of paper is far-fetched, but something I've seen students do is paste text into a notes file when learning a topic, then paste again into their final work without caring where the original came from (it's pretty obvious when the source is wikipedia and the writing is much better than the rest of their work)

@DavidRicherby I agree that plagiarism is fundamentally an act of deception, but it doesn't follow that negligence can't be an act of deception. For example, if the standard in a field is to conduct a diligent search to determine if your claims are original before publishing them, then being negligent in that search is deceptive because the act of publishing implies you were diligent. It's the same as a car dealer selling a car while being negligent in ensuring it's safe to drive -- that's deceptive because selling the car implies it's safe.

Like integration, you mean?

@DavidRicherby I have witnessed acts of academic negligence where the person justified their negligence by claiming that they did not want to "stain" their own thought process with the knowledge of other people's work on the topic. I don't think there's a particular term for this act of negligence, so I am happy to refer to it as "plagiarism".

@LeeMosher I'm sorry, but something not having a name isn't any sort of a reason to call it plagiarism. I mean, I don't think there's any particular term for the act of writing a paper without drinking any coffee, so let's call that "plagiarism", too!

@LeeMosher Lev Landau (as the story goes) was famously disinclined to read anybody else's work, and found it more straightforward to re-deduce all of mathematical physics from first principles, when required. His papers do indeed have rather thin bibliographies (and are regarded as valuable for the clarity of their thought). I don't think anyone thinks this was plagiarism on his part, but equally don't think folk can get away with this unless they're quite as good as Landau (which is approximately zero people).

No, but, ... (as other comments and answers have said... ). .............

Personally, I would say yes, it is, but if you had not known, then you're right, it had only been an accident. It's trying to prove that it had only been an accident that makes this tricky. In the meantime, I would go with others' comments that say it is our responsibility to do a literature search beforehand if not to protect ourselves, than at least to check that we're not saying something that's already been said (similar to read others' answers here on SE prior to posting new ones).

It isn't plagiarism if you didn't copy it. It is prior art.

@DavidSchwartz : and how do you prove you didn't know about it?

@vsz Exactly. One of the reasons negligence is almost always considered equivalent to dishonesty is because they are so difficult to distinguish and there's really no reason to treat them differently for precisely the reason I explained, negligence is often inherently dishonest.

Related: How common is it to reinvent the wheel in acaemia?

If you publish an idea that turns out to have been previously known, but you were unaware of the prior work before you published it, then it's not plagiarism.  Depending on the circumstances, it could be considered poor scholarship, or even negligence if you really should have found the reference.  However, it's not a form of academic dishonesty if you truly didn't know.
If you come up with an idea on your own, learn that it was previously known, and subsequently publish it as original work without disclosing the prior source, then it's definitely academic dishonesty.  I wouldn't use the word "plagiarism" if you came up with the idea independently, but it's still misconduct to act like you're unaware of the idea's history.
The trickiest case is if you may have been aware of the idea in the past, but forgotten about it.  That's a horrible mess, since the rest of the world has no way of knowing whether you genuinely forgot or are being dishonest.  (You really don't want to have to argue that you aren't a thief, but rather massively screwed up.)  This is the only case in which I think accidental plagiarism is really plausible.
This is not at all common, but it can happen more easily than you might hope, so it's best to be careful to keep track of what you've heard about.  The worrisome scenario is the following: you hear Smith give a talk, but you don't really understand it or care very much, so you basically forget about it.  Some years later, you are faced with a similar problem and come up with more or less the same idea to solve it.  You don't realize how similar it is to Smith's talk, but you may have been influenced by subconscious memories, so you haven't really discovered it independently.  When you publish your idea, Smith writes to you to say "How dare you use my idea without giving me any credit!  I know you were at my talk, since we chatted afterwards, and your colleague X confirms that he remembers you there as well.  Did you really think you could get away with this?"

If this happens to you, how can you prove that "you truly didn't know"? Of course you could hope people give you the benefit of the doubt but doesn´t it all go back to bad literature search if the idea was already published?

Yeah, you generally can't prove it.  If you're lucky, you'll have a good reputation for honesty and the way you express the idea will be different enough that people will believe you.  If you're not lucky, you may never escape the suspicion of plagiarism.  (But that doesn't mean you were actually guilty of plagiarism, just that you couldn't prove you weren't.)

As for bad literature searches, if the idea was easy to find in the literature, then the best you can hope for is looking sloppy or lazy, which isn't a good outcome.  On the other hand, sometimes it's not so easy.  (Maybe it was published somewhere very obscure, or it came up in a completely different research community where a reasonable person might not have done much looking.)  In that case, you have more of an excuse for not knowing it, even though you have to acknowledge it once you know.

There’s actually a name for unconscious influence by something you don’t knowingly remember.  I’d link to it but I can’t remember what it is.

@JDługosz Cryptomnesia

@Miles, I'm not entirely sure that JDlugosz didn't remember what it was.  :D

@anonymous mathematician, this is really the answer I was looking for, thank you. I have one important followup qurstion: If you are in a situation where you've published something that is similar to some other idea that is easy to find, but out of lazyness you didn't find it: would in that case the principle of "innocent until proven guilty" apply, or would it be presumed that you've been dishonest? In other words: if there is no "smoking gun evidence" that you've been in contact with that earlier work, would there still be the presumption of dishonesty and punishment by your university?

Interesting (maybe) non-academic example of this: Mick Jagger and Keith Richards unintentionally plagiarised kd lang's "Constant Craving". Of course they could never prove it was unintentional, but once the similarity was pointed out they gave her a writing credit on "Anybody Seen My Baby?". Given how well-known her song was, this would probably have been considered negligent in academia...

"Depending on the circumstances, it could be considered poor scholarship"-- agreed. In my field, this would be extremely embarrassing and reputation-diminishing, as it would indicate that one did not read one's own field. However, I imagine graduate students are more likely to fall into this than postdocs and faculty, in which case your supervisor should be able to prevent this from happening (if only by asking, "Did you read x/y/z?"). Side note: this actually happened to me the other day, where I thought I had an 'original' idea and then discovered a whole monograph about it. XD

@SteveJessop Great, now I have "Constant Craving" stuck in my head... ;)

If you completely 100% wrote a paper based on your own findings and then find another paper with similar findings before you go to publish (but maybe mildly focusing on a different aspect), then what obligation would you have to cite the other author? Citation and referencing refers to giving credit to a work that you read as inspiration for yours or to provide credibility. I mean no offense, but citing things simply for being similar makes absolutely no sense whatsoever.

@TheGreatDuck:  If nothing else, you should cite the earlier work and point out why your work differs from it so that the referee is less likely to say "there's nothing new & interesting in this paper, don't publish it."

@MichaelSeifert alright, but let's say you are self-publishing. It isn't plagiarism if you never used it as a reference. Plagiarism is just referring to another work without providing a proper citation.If you've never read the other work,then yes it is good to refer to it in hindsight for reasons of comparison, but there shouldn't be an issue of plagiarism when neither work refers to the other.I could write a paper on trying to solve a difficult math equation on my own for leisure.That doesn't mean I ripped off some other paper about the same equation assuming it's easy enough to stumble upon.

@AnonymousMathematician "If you come up with an idea on your own, learn that it was previously known, and subsequently publish it as original work without disclosing the prior source, then it's definitely academic dishonesty. I wouldn't use the word "plagiarism" if you came up with the idea independently, but it's still misconduct to act like you're unaware of the idea's history." But is it academic misconduct as in plagiarism type misconducts or is it misconduct in the sense that it just indicates incompetent research? I'd argue that either is bad, but one just indicates poor writing ability.

I happened (two or three times)  to ask twice the same question on SE. I had forgotten I had the problem and that there was (or not) a solution to it.  This was thankfully found via the automatic search propositions (the question was very specific and did not show up in a search) and would have been otherwise closed as duplicate -- but the real world does not have this notion (unfortunately)

I would think that if other similar research was published between the time one wrote one's paper and the time it was published, the best action would be to write an addendum recognizing the additional research and identifying which parts are similar to one's own, and which parts of one's own research have independent value.

There is such a thing as independent discovery. In the 17th century, Newton and Leibnitz apparently discovered calculus a year or two apart, but without either knowing about the work of the other. Nowadays, information travels at "warp" speed and "a year or two" would be an unacceptable time lag. Even so, it's possible that two people would publish similar findings, drawn from common sources, days or even hours apart. (And on SE sites, it gets even more intense; sometimes people "publish" similar answers minutes or even seconds apart, neither knowing of the other.) Under such circumstances, concurrent publication is usually excused, but it also behooves one to do a literature search to see if the idea has, in fact been published previously.

What about badly worded or named discoveries? What if a work is so unknown or not accesible to most/your search? I guess even then the time lag would be acceptable or not?

@HopefullyHelpful: If a work is "unknown and not accessible," to the point where you and others honestly didn't know, and reasonably didn't know of it, then you deserve credit for popularizing the work. Then it would be up to the other person to clarify his position, using his previous work as a "hook." I remember reading that the credit for the invention of television hinged on the testimony of the inventor's high school science teacher, who testified to the clarity and completeness of a formulation  that predated a rival's earlier publication.

Perhaps the best historical example of this was Darwin and Wallace independently coming up with the theory of evolution.

"Newton and Leibnitz apparently discovered calculus a year or two apart". It was more than a year apart. I think there is some evidence that Newton discovered the basics of the calculus while still a student.

As a more recent example, credit for the discovery of the human immunodeficiency virus (HIV) as the cause of AIDS was in dispute for quite some time, as it was independently discovered by two teams working separately. A French team at the Pasteur Institute announced the discovery of a virus they called LAV in 1983. In 1984, a US National Cancer Insitute team published their discovery, HLTV-III. How can both teams have discovered a virus responsible for AIDS? Because LAV and HLTV-III were ultimately found to be the same virus.

Building on David's comment:
If you inadvertently reinvent the wheel, without contributing anything additional and meaningful, your paper is unlikely to get published anyway.  So let's start with the assumption that you inadvertently reinvented the wheel, did not credit the original inventor, and then added something meaningful.  It is likely the review process would trigger a correction in this situation.
I think it would be helpful to review what plagiarism tends to look like.  I have seen the following, as a copy editor:

Neglect to give credit for a creative assertion
Lift text from someone else's work, without putting quotes around it
Same as 1 or 2, but from your own previously published work

Other types of sloppiness I've seen:

Cite the wrong author(s) for a creative assertion or quote
Make a significant mistake in the citation
Cite the wrong work (but at least getting the researcher right)

As addition to the other answers: I think it is possible to distinguish if you are academically dishonest or that you really invented the wheel again.
If you reinvented the wheel, you will have worked with the new method a longer time to verify that it really works and you will therefore know its merits and its disadvantages. Moreover the path how you invented will be almost always different from the original author, so it will give you very specific insights which you intuitively grasp, but it does not give you the insights if you followed another path.
So a short interview (preferably with the original author if he/she is not malignant) would settle with high probability if you really invented the method yourself.
The Newton-Leibniz controversy is a good example: Newton used the "fluxion" approach, always dividing out the resulting equation and neglecting the remaining part while Leibniz see them as "differential", a ratio of infinitesimal changes, so he could cancel out e.g. (dy/dx) * dx = dy. Both used the same method to finally get the derivative at one point, but their interpretation varied. Both methods were attacked for their lack of rigour, but Leibniz approach was formally more elegant and easier to handle, so his integral notation prevailed.

There is a famous example for this question. Some people re-discovered calculus in the following paper:
“A Mathematical Model for the Determination of Total Area Under Glucose Tolerance and Other Metabolic Curves”, Mary M. Tai, Diabetes Care, 1994, 17, 152–154.
You can laugh, but no, they did not commit plagiarism.
More details.

Some assumptions here are that you are intellectually honest, you use a reputable publisher, and the prior work in question was done some time before yours. If your due diligence (and your publishers) didn't discover it in mainstream publishing in your field, it couldn't be considered plagiarism. While this answers your question, it still leaves open the likelihood of conflict over credit. Even without political considerations, history is replete with antagonism that carries for generations. While we as a society consider publishing important work of any kind to serve mankind, you can see how vital it can be to the author.

Real plagiarism involves deliberately copying someone else's work. I saw this when editing a paper for a PhD candidate who was worried about his English. Parts of the paper were badly constructed, but other parts were letter perfect. So I used Google to check for some of the unique phrases in the well-written section. Bingo! Wikipedia!
I did not tell him what I found. Instead I fixed the most glaring of his errors in English, gave him a note that Wikipedia was not an acceptable source, and hoped that his advisor and his examination committee would discover his malfeasance. They needed to hang him by his thumbs.
Generally if you find that you have inadvertently used someone else's idea without attribution it is good if you can later publish something that corrects the situation. It's better to do it that way than to have someone else point you out as a possible thief.

This is basically a definition of plagiarism, which the existing answers already cover, plus an anecdote that has nothing to do with the question.


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Asked editor for review prolongation to do further experiments, can't meet deadline. What do?
My paper received a good review, but we've been implicitly asked (interpretation of my supervisor, not mine) to do two experiments to verify a method I use. We then asked the editor for some time to perform these experiments, which the editor accepted. Then two things happened:

The experiments were messed up due to some unfortunate technical error and now I can't meet the deadline.
After some deep digging in preliminary experiments and literature, I found data that could replace these experiments just good enough in my opinion.

The question is now: Should I ask for more time to retry the experiments, or should I just send the literature/preliminary data to the reviewers? Which choice would be wiser?

You should ask both your supervisor and the editor which is the best way to proceed. Your supervisor might find it acceptable to reuse existing data; the editor might give you time to redo the experiments.

Which choice would be wiser? This is completely a judgement call that depends on your specific paper. Nobody here can answer it for you.

Based on the reviews and the willingness of the editor to provide an extension, your paper clearly is worth it for the journal. You should definitely contact the editor, briefly explain the problems (don't focus on excuses but on what remains to be done) you have had to meet the deadline and ask what can be done. It will be advantageous to provide a solid plan for the remaining work so that this is clear from the beginning to the editor. So assess the remaining work, make up a realistic plan for what is required and provide this to the editor. If all this requires the assistance of your advisor then plan it together. In the end, it will be up to the editor to provide an extension and a clear plan is necessary.
In my own experience as editor, I much more appreciate realistic plans than optimistic ones that fail. In your case it seems as a case of force majeur and such things happen. I am, however, always suspicious of long excusing accompanying letters since I really do not care about the reasons but need to focus on the timing of revisions for planning issues and the like.

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What is the etiquette for CCing faculty in eMails?
I'm working in an international collaboration (Germany and Netherlands). It happens quite often that I'm asking technical questions to fellow postdocs by email, just sending the email to this single person. When I receive the reply, I almost always see that the head of the group has been put in CC.
I'm wondering why this is done. Is this some kind of etiquette I'm not aware of? I imagine that as a group leader you get flooded with emails, so why would you request more?

I like to know when people ask about my group's research.

Yes, that sort of etiquette (CC'ing the PI of each involved partner in a collaboration, even for exchanges at lower level) exist in some groups. It is particularly true of recent collaborations, either because they have been established recently or because the research is still in its infancy. In both case, I suppose it is nice to help PI's stay on top of how things are progressing, both on the science and on the interpersonal relationships (like, is everyone acting professionally).
It's not universal, but it is common. It depends a lot on the nature of the relations between the PI's and their groups. I tend to ask students/post-docs to keep me in CC of the first few emails to our collaborator after they arrive/we start the project, then after sometime I tell them to drop me when it's evident things are going well.
In your situation, the safest course of action is to keep people on the CC list. You didn't CC them, but someone did, so don't drop them unless they ask for it. Also, ask your own boss how he likes to do things.

“I imagine that as a group leader you get flooded with emails, so why would you request more?” — Whatever you do, you will be flooded with emails. You don't read them all, but you may skim those for tone/content, keeping an eye on things.

It is a fairly normal practice to cc: your boss on correspondence that is outside the organization, especially if he or she has a vested interest in the response. As you note, though, it does require some judiciousness to keep from overpopulating your boss's inbox. I'd say it is more rare in the case of technical back-and-forth, but I have seen it before.
I have also seen the "cc the boss" mentality from people who want the boss to know they're keeping busy -- I wouldn't suggest this kind of toady behavior, but it does exist.
The bottom line is that you shouldn't be concerned to see others do this on their correspondence, and you could certainly ask the head of your group if he or she wants to be cc'd on correspondence from you.

I haven't heard the excuse to let your boss know your busy, but I do know people who often do it as more a lack of authority or CYA.

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How do you thematically include accidental findings ("serendipity") in a dissertation or paper?
I'm asking for approaches to include interesting, but not perfectly fitting results in a dissertation or a paper.
During my PhD project I have made an accidental discovery, which is what I believe you call serendipity. The finding is related to the overall topic of my dissertation and certainly interesting, but it interrupts the "leitmotif" of my argumentation, as this discovery is really just the result of a stupid mistake. So my question here is: How do you eloquently include stupid mistakes (aka accidental findings) in a dissertation or a paper without sounding stupid or breaking the flow of arguments apart? Is there even a generalizing answer to this question?

If it's good research, publish it.  If it's not good research, don't.

It's worth publishing, but it needs more work, but is certainly worth a section in a dissertation at the current state.

When I was in grad school, a labmate of mine worked for five years to get no results on his main project (bioreactors), but ended up making a significant advancement in the field of electrochemistry. He published this work and ended up following this line of research for a few years. Moral of the story: definitely write it up as a section, and if it's important, publish.

I have no idea why you put stupid mistakes = accidental findings. Could you explain it?

@PiotrMigdal, I made a stupid mistake during an experiment which led to this finding. Hence, it was an accidental finding. :-)

Have you heard the saying that great discoveries aren't marked by a cry of "Eureka", but by "oh. that's interesting. I wasn't expecting that" (credit probably Feynman, but I forget who)

@EnergyNumbers Sure, and I'm completely aware of the situation, but yet I have to implement it in the dissertation somehow. ;)

@EnergyNumbers it's Asimov, I've added it to my answer :)

Does it matter how you discovered your results? Will you also write "These results were obtained while thinking in the shower. These were obtained bashing my head against the desk. These were obtained by divine inspiration."

If the finding is significant enough,how about writing a separate research paper?

“The most exciting phrase to hear in science, the one that heralds new discoveries, is not 'Eureka!' but rather, 'hmm... that's funny...” (Isaac Asimov, thanks to EnergyNumbers for reminding me of it)

If you're worried that it will distract the flow of your thesis, why not put it in a “special” part of your thesis (e.g., an appendix) and refer to that from the main text, at the point that would be most logical.

[Following the description of your experiment.] In the next few sections, I describe the results obtained from operating the Pocket Helium Flux Positron Annihilator on a variety of samples: metals (section II.B), graphene (section II.C) and heavy water (section II.D). You will also find in Appendix A a description of the observations made following an accidental operation of PHFPA without a helium flux [you may not want to be specific and say: some moron forgot to replace the bottle] which allowed to check what happens when electroneutrality is violated on the µm scale.

An appendix is a good place, or maybe a small section as the end of the relevant chapter.

I used an appendix for a similar ancillary finding during my research as well. By having it there I supported my discussion/evaluation, reinforced my methods and rigor, and it also helped to support the premise of 'a valuable contribution to [my] area of science'.  Your mileage may vary, but I found it useful. (Full disclosure, I'm still working on it but so far, so good :)

"you may not want to be specific and say: some moron forgot to replace the bottle" - perhaps a "secret appendix" is in order for such things. If nothing else I can see it being a useful way to relieve thesis-induced stress. :-P

You can always thank the moron in your acknowledgements for an unspecified but significant contribution or so ;)

Also, as this answer and others suggest, there is no grand law of research that suggests you must present your work in the order that it happened. Usually we choose to imply a more logical structure to the work.

Thesis is a good place to place things not yet developed enough to make a full paper.
If it is at least tangentially related to you thesis topic, just add a relevant (sub)section (e.g. in further discussion, or near to the place where it is the most related).
BTW: Many groundbreaking discoveries were accidental. So I don't see a reason to value them less than ones planned in advance.
Again, if "accidental" means than some values were set such as a mistake - again, mentioning such is related to motivation/story, not the value of results.

The traditional ways people introducing important or interesting peripheral information without breaking the flow or core thrust of a manuscript is with footnotes/endnotes or with an  appendix as F'X has suggested.
If it's a short aside, consider making it a long footnote. If it's longer, put in in an appendix and reference it either in the footnote or in the text. Long — even paper-length — appendixes are not abnormal in dissertations.

In the social sciences, there is traditionally a section in the concluding chapter that discusses limitations of the present study and scope for future research.
You can include your 'discovery' in this section. In this way, you are presenting your 'discovery' and suggesting some ways in which it can be researched - two-in-one, I suppose!
The other section in which you can include your 'discovery' is where you highlight what contribution your research is making to the body of knowledge in your field. This is traditionally another section in the concluding chapter of a social science dissertation. You can 'wrap' your 'discovery' as an accidental but important contribution to knowledge.
In my case, I talked to a number of people in my field as part of my stakeholder consultation. I soon discovered that they were telling me far more than what was needed for my topic. I summarised this information in my concluding chapter and said that it represented an important contribution to knowledge because it would lost if not captured in writing (the stakeholders were mostly from the older generation).
So, there are many ways to include it in your dissertation.


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The chances of postdoc position higher in PhD country
Are the chances of getting a postdoc position or full academic position higher in the country you are going to study your PhD in? What if you are not a citizen? Is it important to take into account postdoc stage and career path possibilities when you decide the country you want to study PhD?

See: http://academia.stackexchange.com/questions/9133/why-should-or-should-not-a-university-have-a-policy-of-not-hiring-its-own-phds/

The question @posdef linked is definitely something you should read. While I'm not sure if the chances are higher or not (so, I'm not making it an answer), it might be better (to your academic career) to try and get a postdoc position in a different country than the one where you got your PhD.

In my surroundings (Germany, Switzerland), normally it's not a problem to get the first postdoc after you get a PhD in the same country.
However, a PhD in some country that is (sometimes wrongly) believed to have an inferior level of scientific merit may actually block the further scientific degree carrier abroad: impossible to start PhD studies a second time ("already has PhD"), and impossible to get a postdoctoral position as well ("bad PhD").
As a result, it is important to weigh the situation and think where and how to earn the PhD degree. I know people who have dropped basically complete PhD works right before defence just to be able to restart in another country.


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"This is very interesting as a project" What is the next step to obtain PhD position?
I am submitting to several schools for PhD position in CS. I am following the advices about how to contact professors.
One professor I sent to suggesting some idea about her previous research and asking that I want to indicate my desire to work under her supervision. She replied "This is very interesting as a project. Please apply for the next deadline". It is very encouraging response. However, the admission decision is at the department level. So I will have to apply and there are several other requirements which I am not completely sure if I entirely meet.
I feel like I must focus on this positive side in order to increase my chances, but I do not know how. Should I keep in touch with the professor although she can do nothing now until the decision is made? Should I send more details about the suggested idea in order to show how motivated I am (I am not sure if she's part of the admission committee). What is the second step to increase my chances to get admission?
Do you think sending more emails to the professor is annoying or does show my enthusiasm? Any thing I can do to support more application at this time?
Update for who may concern
The application has not been accepted.

I am not sure I understand the question. What is the second step? Apply to the PhD. What else?

@scaaahu What is the next step to increase my chances to get the admission. Thanks for helping out clarifying my question

The second step is to submit a strong application: Good grades from a good department, a compelling statement of purpose (which reiterates your interest in your target advisor), and strong letters of recommendation that address your research potential in personal, specific, technical, and credible detail. And then write the professor to tell her you've applied and reiterate your interest.
As long as you're building a strong application, you should send it to several other schools as well (minus your interest in that particular advisor, of course).
There is absolutely nothing you can do to guarantee admission to  your first-choice program, so you need to cultivate other options as well.

last advice, do you think mention that "I had contacted the professor and she had sent positive opinion" in the statement of purpose is a good idea or it might be perceived as "showing off"?

@hawk: If you keep the PI informed of your application status, she'll let the evaluators know of her interest in your project directly, which is far more meaningful to them than your claim.


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Canada vs. Australia for the academic career
Two days ago I was in discussion with a colleague of mine about the possible PhD studies destinations. We both agreed that the chances of getting post-Doc job or any full position are higher in the country we finish PhD (Maybe you have different opinion). However, we ended up discussion two potential (native English-speakers) countries, namely, Canada and Australia. We both had a vague idea about post PhD stage (academia or industry), so we had not much to share. My question is which country is generally better in terms of the following (computer science field):

Research sector prospects (is there any studies indicate which country has stronger research profile in computer science - my gut feeling is Canada at least from  the world universities ranking in computer science)
Academic career path (What are the possible career paths for PhD graduates? (tenure track, postdoc, lab researchers ... etc.).
Finance benefits (taking into account the living cost in both countries, which of the countries, the academic career stand stronger comparing to the industrial jobs in terms of financial benefits)

Any advice to improve the question is most welcomed.

This seems far too broad.

@NateEldredge It is disappointing that I am almost sure that who voted to put this question on hold have not read the entire post down to the last line.

I'm voting to leave closed for now, and I've read it all. I'd suggest narrowing down what you mean by your bullet points, or asking about one or two of them at a time in separate questions. Your third bullet, "Job chances..." is almost specific enough, but even that seems hard to answer, as there are an awful lot of personal factors involved, and separate sectors of computer science to consider on the job market even within academic or industrial and not both.

The reviewers and voters are acting as they're supposed to. The problem is that this a very broad, opinion-based question. "Better" is just too unspecific a criterion to allow for a reasonable answer.

@aeismail Thank you, I tried to narrow down my questions. I hope it is easier to answer now

I don't think I follow your parenthetical in the first (edited) bullet: Is your gut feeling that Canada has no world class CS, or that it does, where Australia does not?

@MatthewG. I said that my gut feeling is Canada has stronger profile in CS research. My analysis is based on the universities ranking where Canada has much more universities in the top ranking universities in the world comparing to Australia. That does not mean Australia has some strong Universities. On top of that, this is only one metric, I posted the question seeking approval, disagreement and more factors

@Hawk Oh! Ok, I totally mis-parsed your sentence, leading to an ambiguity. Mea culpa.

Just a quick comment though, about 20% of the institutions in Canada would require you to have a working knowledge of French to become a professor (University of Montreal, University Sherbrooke, University Laval, etc.). This is something to take into account, especially since a strong portion of CS research (at least related to deep learning and machine learning) takes place in Montreal.

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text:
Programming Interview for PhD Admission in Computer Science
A prospective supervisor is interested in me, and has asked me for programming interview. As I have been told, his research group does a lot of system programming, and he is seeking a good programmer.
I have no industry experience in programming, though I have programmed for assignments, projects, and a Master's thesis. I know that, as a computer scientist, it is essential to have good programming skills. I tried to search for some tips about programming interviews for prospective PhDs, but could not find anything.
Does it differ from industrial interview? Did anyone have similar experience? Any references or tips?

This is the first time I've heard of this. By "academic" do you imply that you have never programmed before but have only discussed topics, or do you mean that you have only programmed the petty assignments that come with a Bachelor's program?

@JonathanLandrum I have programmed my assignments, projects and master thesis implementation. I even taught programming in lab as a tutor. But all this is incomparable to industrial programmers who spend 8 hours daily dedicated for programming.

In that case you should be fine. I don't know what country you will be attending school in, but in the US where I am from, it is not uncommon for PhD students to only have a Bachelor's level of programming ability. But even in Europe, with a Master's degree, you are on par with everyone else.

I think you have much too high an opinion of "industrial programmers who spend 8 hours daily dedicated for programming". Some of these people are excellent programmers, and some of them are not.

Thanks for sharing, but it would be better if you formulate your edit as an answer, so that it can be upvoted (and also accepted by you).

@xLeitix Thank you for your suggestion. I have posted it as an answer

I had the interview yesterday. I would like to share the experience as it might be useful for anybody who might go through similar kind of interviews in the future.
The interview was via Skype with an outsourced software engineer (not the prospective supervisor), and we used shared .doc file to solve two programming problems about strings. By the way, most of programming interviews I had (mostly industrial and this academic one) pretty much involve strings manipulation and sometimes data structure.
The interview lasted for an hour whereby I was given 20 minutes to solve each problem and 10 minutes to discuss. The general impression was positive. The concept was always known, yet I needed some practicing to make my code works.
I was given the choice to choose the programming language I like to write in.
I would say, bachelor level of programming is enough. You will just need to revise and practice a little bit your information. You might need to focus on the logic you follow more than the small details that differ from language to another.


text:
Why don't I want to learn anything?
I'm an undergraduate student, rising senior. I've been immersed in academia now since freshmen year, and I'd like to pursue a PhD in Computer Science in the future. I'm posting here because I just feel hopeless right now.
I've had research experiences at top schools, like MIT, and now, at a top research company (where I've been for a couple of months).
I know to the readers these sound impressive, but with every experience, I feel like I let my mentors and advisors down. I feel like they all had really high expectations for me -- and I just disappointed them.
With every opportunity -- and in every scenario, whether it was in school or some other aspect of my life -- I noticed a common pattern in myself :
 I just didn't want to learn.
I did very well in high school. I do very well in college. But I just don't have the motivation to learn ... anything. I want good grades. I want to build the projects I have in mind. I want to finish my research project and get that publication. But I don't want to put the work in. Everything I achieved through academics was done under some combination of procrastination, stress, fatigue, and luck. I never really cared about what I was learning. I often did things just the day before, or late. I only learned just enough to do the assignment or get the grade I want. I always thought -- I can learn it the way I'm supposed to later. I just wanted the results. I wanted to look good on paper. I didn't want to feel ashamed in front of my mentors and co-workers, so I always did just enough to look like I was doing something.
These couple of months that I've gotten the opportunity to work as a research intern at a top research company (I didn't even get an interview to get there, I think I just got lucky), I've felt like shit. I knew nothing about NLP when I got here, and now it's the focus of my project. I've been working with neural nets for 2 years now, but I still don't fully understand the basics. I just feel like I should know this by now. And with every meeting, I feel like I'm doing the bare minimum -- just enough to look like I was doing something.
I feel too slow. Whenever I have to learn about a new topic or read a new paper, I get overwhelmed. I think I will never understand it enough to be able to contribute anything meaningful. And when I see how knowledgeable, motivated, and quick people are about their work, I get discouraged. I feel like time is quickly passing me by, and I am crumbling under every passing day.
Now I'm contemplating whether I will even have potential for an academic career in computation, or an academic career in anything, or a career at all. I know I love solving problems. I know I am creative and have good ideas when I really understand something. But that's what I'm worried about. What if I never attain that level of understanding?
I just don't know -- is this normal and must I just learn to deal with it? Am I experiencing this just because I'm at a different level than my co-workers here, who are PhD's and research scientists? Have academics gone through this phase where they feel like they just can't do it?
Or is there some underlying issue? What have been people's experiences?

Have you considered depression or burn-out as a reason? Or maybe Academia is just not a good career choice to you? We act like as it would be shameful or dull, but It is not: Academia is a strange career choice, don’t fit all the people, even if they are smart.

Do not listen to the Impostor Syndrome.

Imposter syndrome is getting a lot of attention these days, but I also recommend you research the connection between task difficulty and motivation. That seems to be one of the important keys to understand behavior such as procrastination. Generally tasks too hard are not very motivating because of little progress (reward) and tasks too easy are not very motivating because you get bored. Which btw. is why games are so successful in generating motivation. And the research line of work has lots of tasks, both too hard and too easy. So learning to deal with this is very important.

Of course if you go to "top" schools expectations and pressure will be highest, maybe you can find places that will leave more space and time to be yourself.

Possibly related, and wonderful to read anyway: https://academia.stackexchange.com/questions/2219/how-should-i-deal-with-discouragement-as-a-graduate-student

I just wanted the results. Sounds like you're just efficient and goal-oriented. Some people thrive on going down rabbit holes; and some on going from A to B as efficiently as possible. Perhaps you're the engineer/problem solver type more than the explorer/philosopher type. Both can make good scientists.

@JeffE  The thing with impostor syndrome is that, sometimes, it's actually correct.  Plenty of people are smart enough to understand and recognize their own limitations.  Throwing impostor syndrome around all the time can lead to people second guessing, incorrectly, what might be a very correct assesment of their situation.  Sometimes the right answer is that OP is actually on the wrong career track and that they might be altogether happier and more successful doing something else.  I don't think that distinction is easily made from an armchair on the other side of the world.

You describe me exactly through undergrad and grad school. In my experience, I felt like I was faking it until I was able to think of small projects on my own. To develop them myself, and I had to go back and learn things I had "faked" with more rigor to defend my work to others; this finally motivated me to learn. Quickly, I realized that most people are doing this too, and their daunting expertise is only in the tools they've needed to complete specific tasks in their careers. You'll eventually find your motivation, but for complex fields this takes a lot of time.

@J... Being on the wrong track (This is not what I should be doing) and impostor syndrome (I’m a faker; all my successes have been trivial or due to luck) aren’t incompatible. But you have to get rid of the latter to see the former clearly.

This sounds like a classic case of burn-out. You've been working hard, maybe too hard, and it isn't fun anymore. I think a lot of academics do that at some point and you need to find a way past it to be successful.
Some of the solutions can be fairly simple and others not. Getting advice from a counsellor or therapist may be needed. Probably useful in any case.
Some people can just find a non-academic activity to spend time and effort on. I usually recommend something physical, but that will also engage your brain in a different way. My own go-to activity is Tai Chi, a mind-body fusion. In the past, I also used bicycling and skiing to get away from the academy.
Such things can even be beneficial in solving academic problems, such as mathematics. When you get stuck on a problem, often letting it go for a bit will let your subconscious mind work on the problem and get you past the block. This too is a common experience.
On a larger scale, a year away, doing things that aren't so academic or that use your mind in a different way can be helpful. Students who had the means, often spent a year "bumming around Europe" after graduation. A museum tour of the great cities.
But if you just keep pressing and increasing the pressure, you probably won't improve.
You might also want to look at some other answers here that discuss Imposter Syndrome (search for the phrase here to get some idea of what it is and how to deal with it.) I'm not reading clear signs in your question that you are "suffering" from that, but take a look.

+1 for this: "Getting advice from a counsellor or therapist ... Probably useful in any case." There is such a thing as preventative care in mental health!

-1 As nothing in the post described someone who was working too hard in the past. I mean, still could be burn out, but burn out tends to happen to people who describe that they used to be motivated.

Welcome to the high ability/high achievers club, or ‘HAHA’. We’re happy to have you!
But in seriousness you make two errors. The first is thinking you are letting your advisors down, which while you don’t specify, is often a reaction to advisors constant commentary on what to change. Advisors don’t push inept students. They critique and challenge the good ones.
Second, you believe your lack of motivation is a personality flaw, when it is actually a characteristic of most successful academics.  Once you find the topic that flames your fire you’ll be relentless. Topics outside of your interest just isnt worth your time, right?  Join the club.
Lastly, you are falling prey to imposter syndrome - you’re too slow/not smart enough/not productive, etc. 75% of us feel that way but lie about it. The other 25% of people work 23 hour days and sacrifice the rest of their life.
Unfortunately, you likely won’t believe all of what I’ve just said...I didn’t until much later. But your feelings are the rule, not the exception.

All this impostor syndrome talk, but people forget there are a lot of real impostors too. I'm not judging op, I simply don't know enough about them, but this answer doesn't seem to suggest any course of action other than “suck it up“, which wouldn't have needed all that bragging speculation.

There are a lot of good answers, but one topic I want to also address this:

And when I see how knowledgeable, motivated, and quick people are about their work, I get discouraged.

One aspect of it is the fact that in (young) academia, there is 1 thing people are terrified of, which is to be considered "not smart". Peers around me showcased their intellect in any single way possible. Every discussion was one to be won, mainly by technicalities. Nobody admitted not fully understanding a talk (however complex it might have been). Not (yet) knowing about an important topic was taboo.
Don't get bedazzled by your colleagues' displays of intellect. A lot of it is an act, and even when it isn't, it doesn't mean you're inferior. Even in academia, not everyone has a 150+ IQ, or needs it for that matter.

I agree, a lot of apparent dazzling displays have a background story anyway. That they previous experience of a particular thing that you don't, then automatically you're on the backfoot. This happens to everyone it is just day to day stuff.

I want to build the projects I have in mind.  ...  I just wanted the results.

Wanting practical results on projects that are interesting to you is a great place to start when looking for lost motivation.  Find a simple project you are interested in, that is not too large or abstract, and have a play with it.  Learn only what you need to learn to get it working, on an as-needed basis, and see if you enjoy this.  If that works out, think about extending your project to make it bigger, and learn more as needed to expand on it, until it is how you want it to be.  You might find that this gives you an interest in the underlying abstract subject material, since it is now connected to a practical problem of interest to you.
Most of my own training is in statistics and economics, and like you, I muddled through classes with decent grades and often minimal effort.  I have always found that learning something I'm forced to learn is laborious, but learning something I need to understand to do a project I am interested in is a lot more fun.  For example, a few years ago I was playing Guess-Who with my (then) two-year-old daughter, and I wondered what the optimal subgame-perfect strategy in the game would be.  That led me to muck around with the problem for a couple of weeks, and teach myself a whole bunch of game theory, and a bit of discrete math to boot.  I had done classes on game theory before, but I was never really motivated to learn it properly until I needed to apply it to a problem of my own.
From your description of your education and career, it sounds to me like you are not motivated to learn because the learning has little to no connection to any project outcome that you are actually interested in.  Working in a field as esoteric as neural nets, where the end product is removed from the underlying theory by many levels of abstraction, is likely to exacerbate this feeling.  Since you are in computer science, you will have different interests to me.  But regardless, forget about what they want you to do at work, and think about some of the fun projects you'd like to build on your own.  Maybe you have an idea for a small computing project you could try in your spare time.  Start by making something small and don't worry if it has any broader significance or value to others; treat it as a toy problem, solely for your own recreation.  Most likely you won't know how to do every aspect of the project ab initio, so that will necessitate learning the bits you don't know how to do yet.  If the project is fun and motivating, then you will probably find that learning those bits will not be a chore.  You might even find that the project gives you a renewed interest in a more general field.
If you have not already done so, make sure to read the "plate story" about the physicist Richard Feynman (see his excellent book, "Surely you're Joking Mr Feynman!").
Feynman talks of having suffered career burnout, where he was not accomplishing anything.  He decided to avoid trying anything important, and just work on toy problems that were interesting to him (e.g., figuring out the physics of why a plate wobbles when you throw it up in the air).  As he puts it, "So I got this new attitude. Now that I am burned out and I'll never accomplish anything, I've got this nice position at the university teaching classes which I rather enjoy, and just like I read the Arabian Nights for pleasure, I'm going to play with physics, whenever I want to, without worrying about any importance whatsoever."

Yes, exactly: one should not self-censor on some grounds of mythical "importance"... but, rather, follow one's curiosity, without censoring. Yes, for start-up-company-oriented engineers, as opposed to academic scholars, this may not make sense. But I think it is the real crux-of-the-matter for academics. Don't self-censor. Be curious, and indulge that curiosity. Don't think about "funding" or "marketable products" and so on... unless, of course, that is really your goal... :)

Yes, in theory it could be burnout or impostor syndrome and what not and it's not bad to ask yourself whether those things could fit. Were you in the past more motivated and did everything become too much to handle? Did you get any negative feedback from third parties or is it just you who thinks you aren't doing well enough?
Anyway, an option that's not brought up in other answers and sounds like it could fit with what you are experiencing: Is it possible you were too smart to need to learn in the past, and now that you need to learn you realize you don't really know how to motivate yourself to do so?
It's something I have seen a lot of people struggle with (including myself) and some of the more extreme cases literally end up with young people hitting a complete stone wall they aren't able to get past. This is a quite well known problem gifted people have and tends to show during the end of high school or early during their university career (although I know of people who only hit this wall during or after their PhD), but only in recent years has there been a bit more attention to this problem.
Anyway, if you think that this might be the case for you: You will have to ask yourself what you want in life. Either you can use that intelligence to allow yourself to be lazy for the rest of your life - at a not too hard and not too easy job - and focus your energy on different pursuits. Or you can go down the path of trying to learn how to study. The latter will be a long process where you will need to find small stuff that motivate you and start binding that into the things you wish to achieve. Some of the other answers touch upon how to achieve this, but the approach will be slightly different if you don't take it as "regaining past motivation", but rather as a way to teach yourself how to study.

is this normal and must I just learn to deal with it?

Yes, this is perfectly normal. You also need very much to learn to deal with it, or unhappy times will be coming your way.
You need to reframe this until you get it into a non-self-destructive perspective. For example: you say you are "only" interested in the results of your work, not in doing it "right". You are feeling bad about this. But... convince yourself that the rest of the world is also primarily interested in results; few care about how you arrived there. There are very many archetypes of how to get work done, and all of them are as valid as the next one.
Then, you are afraid that you don't really understand things that you work with. Let me assure you, you are by far not alone. I'm working in an IT company as a team lead with a lot of contact to colleagues, customers and management of all levels, and the amount of people that really understand what's going on is, on all levels, much smaller than one would expect. Things get along just fine, anyways.
What you really need to worry about is to get into a "flowy" state concerning your life. If that means that you find a few hobbies that really interest you, or get into Meditation, or go hiking a lot, or straighten up personal issues that you didn't mention, is obviously up to you (and you may need to get a bit creative there). Too much work, too little play leads easily to your current state. Also, if you really don't understand what you are doing, and this leads to internal stress all the time, you indeed may want to look into shifting your work around so it maps better.
My experience is that people automatically and effortlessly learn those topics that really interest them; and vice versa, if someone has to do something that does not interest them, they usually never really get it. So see if what you are doing is really what interests you - if you find that you don't actually care about the topic, then accept that and hunt for another. How you do that you should find out yourself - either look on the side, or make a hard cut, you should know yourself best in that regard.
Good luck!

You mentioned that you wanted the end product, the goal, but were less interested in the steps to achieve it.
This reminded me of the end of my academic pursuit of the "Next" degree. I wanted the letters after my name and it was the next step in school, which I had enjoyed up to that point. But after moving around the variety of math and computer science subjects I figured out (took a while) that the only thing I was truly interested in was the final achievement. I was not actually interested in the courses/subjects needed to get there. The path should be your passion or at least parts of it.
Side note; I know now that a skill I developed in school was "Finding the Path". This means given a goal getting all the steps in place to achieve it. I rush to do this when I hear of any result/goal/degree; make the path and get going. Then I look around and see that this is not really a goal I woke up this morning looking for.
Answers here are quite correct in that students, gifted and otherwise, will hit the wall at some point and often have a crisis when they do.
Your counselors are there to pull you along and not let you get discouraged. They already believe that you have decided on the path. If you have doubts then you must let them know or else they will not be able to give you the best advice.
I'm familiar with the Imposter idea and do not, myself, see it applying in your case.

The problem isn't you, it's the system. Globalism (one-world fascist government) leaks far down to all aspects of society designed to retard progress and reward corruption, dishonesty and stealth. Schools and colleges are particularly targeted since it is easier to dominate people whose lives have been made pointlessly convoluted; in your case you're likely being "required" to learn tons of unrelated stuff that you will never use, which also creates debt that you'll be enslaved to for decades unless you got very lucky. I'm not saying all colleges are "colleges" in name only though the less on-topic your classes are the more red flags should be flying in the wind...besides those red flags.
I left a for-profit "college" in the 2000s after I realized it was a pointless waste of time and money. I had learned nothing useful and had accrued lots of pointless debt. So, in combination with not encountering people willing to carry their own weight I spent ten years working on creating my business. Granted, mine is exceptionally ambitious, though you could learn if you knew that your efforts had purpose and build something that would help people to the extent that they would be willing to pay you. You will need to learn about the secret political corruption going on in the world - if you do not know the politics that are involved then you do not know what is involved. Disregard the tools calling "conspiracy theory", that's one of their dead terms that only effects those who can't think for themselves. You are smart to get through everything thus far and you can and will learn tons though it will be much healthier when you break away and find your real purpose. Mine? Making money while genuinely helping people far beyond what anyone else on the planet can in my line of work

The first thing I would recommend is asking yourself the question: "what are you trying to achieve?" Is it I want good marks/prestige or is it I want to do X? If its the first one then that might help to explain your lack of motivation, in a sense you are lacking any real goal. If it's the second one then try to remember and focus on why X excited you and try to make sure the research you do is somehow related to that. From what you wrote I suspect the answer is "I want to do X", though you may be using "I want good marks/prestige" as a proxy and therefore are starting to burn out.
Given that you did very well at high school and undergrad work so far, one possibility is that you aren't use to doing difficult things, which could be as bad as you don't really know how to learn. If you tended to just absorb things in high school then you may have missed out on learning how to learn, if that's the case (and even if it isn't) you could take a look at the online course "Learning how to learn" or the book its based on "Make it stick".
At a research level this will be much worst, most research material is written by people at least a few years into their PhDs, and each paper is on a small topic. Therefore just having a goal "I want to understand Neural networks" is too broad a goal and too undirected. You may have an ultimate goal "I want to understand why and how neural networks work" (which I believe is a research goal, i.e. nobody could answer that, though I don't know the field), but the subgoal you are working towards may be "I want to understand when I should use a convoluted Neural net" (though that may be too broad as well at the moment), or even just "What did the authors do in paper Y".
As you learn more and more reading and understanding papers becomes easier. In part because you can skip to whatever part of the paper has useful details and in part because you know where this fits into the field of research. Once this happens you can start returning to setting yourself broader goals (but if you move into a different field you tend to start again at just trying to understand a paper).
Finally with respect to your supervisors, I agree with the others with looking into the imposter syndrome (and the Dunning–Kruger effect). I think often a supervisor will try to push students if they are excited in their work or if they see potential in the student (in order to try to help them be their best).

Note that the question seems mainly related to psychology. So StackExchange Academia might not contain the most qualified people. I will provide my opinion which did help me, I hope it can help you (and others who stumble across this question) as well.
As a computer science student who felt 'down' pretty much all the time I have done some reading. Generally I think reading some self-help material would be beneficial for many academics. Note that self-help books do not describe formal logic. Please read material of multiple authors and don't take it too literally.
What helped me in these self-help materials was to define a clearer goal for myself based on a better life-goal. Life-goals like 'high grades' or 'get rich' are considered not good. Self-help books helped me in understanding why these goals will let one down in the long run and how one could pick them better. For me the goals also helped me in taking some difficult decisions which I now think were the right ones since I feel happier.
Edit: Easy accessible starters material can be found on YouTube. In my opinion Tom Bileu and Mark Divine are good.

Everybody here is giving you an essay. I don't have my motivational essay handy, but here's a list:

You Can Do It. Say it 1000 times a day. Repeat until you die.
Motivation is a lie. Embrace the cold hard truth of Discipline. Do the thing anyway.
Learning is like a hammer.
Hammer nails one at a time.
Make a list of other nails that you want/need to hammer.
Throw it away, make a newer smaller list of things you will actually practice on daily.
Hammering for the sake of hammering is masturbation. Hammer new stuff anyway.
When you have a hammer, everything is a nail. Always be on the look out for a bigger, better hammer. Get better at spotting nails.
An end goal where you are fully self-actualized, surrounded by loved ones, academic accolades, personal and professional success is vanity. Talk to friends, get the academic merit badges, and try your best anyway.
Unplug, unwind, tune in, and drop out. But don't run away. Run towards something.
Childhood dreams lead to adult aspirations. When the dream dies, all that's left is to adapt. Grab a little piece of sanity, some concrete thing to stand on, and you hold on to that thing with both hands. There is no magic bullet, no secret sauce, and no quick easy path to anywhere from where you are right now. Just hammer the bloody nail.

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text:
Do I point to mistakes in a paper if I cannot contact the authors?
I am about to submit a manuscript in which I point to some methodological errors that I found in some literature. The error may significantly change part of the results and conclusions if those papers.
I thought I should first contact the authors of those papers to discuss the issue with them. Especially, to check if they actually made that mistake or if their methods were not detailed enough.
However, most of the authors that I tried to contact did not answer back (I checked their actual email address) or did not remember the details of their analysis.
What should I do? Am I "allowed" to point to some papers that I repute wrong only on the base of the details given in their method section?

Have you tried asking the ones that answered, but did not remember to contact the other authors which they think should be the ones that do remember?

Of course you can publish it if you think someone is wrong. This is the entire point of science. Always do so in a nice way though: it is very well possible that everything appeared to be correct with the knowledge at the time the paper was published. Or that it is you who misinterpreted the methods (possibly because the paper was a little vague), as you suggest in your question.
Even if it was really a mistake: everybody makes mistakes from time to time and that is nothing to be ashamed about. You did the right thing by contacting the authors first. Not only is it the correct thing to do, but I have also seen this lead to new collaborations that resulted in multiple papers.
If both the paper and the errors were important, it is your responsibility as a scientist to correct the errors. But if the errors are minor, the result is "unimportant", or you are not 100% sure that there actually is a mistake, you could also decide to simply ignore the paper. There are plenty of bad and/or unimportant papers out there and frankly, they do not deserve the attention even if it is to correct mistakes.

Good points. You might want to point out in your cover letter to the editor that you unsuccessfully tried to contact the original authors, that will make a good impression. And be polite, because the editor will quite probably invite the original authors as reviewers, or even suggest that they write a comment on your paper. Even if they didn't answer your email, they might be more active if they are contacted by a journal editor.

Did you try contacting the publisher of erroneous paper, not the authors?  Having a conversation with them might result in better success in reaching the authors.

In reference to "Especially, to check if they actually made that mistake or if their methods were not detailed enough." and "did not remember the details of their analysis."
Be very careful when you write your manuscript, and do not assume that authors made this mistake. It is perfectly fine to say something like, "There are two ways to do this procedure, and it isn't obvious in the literature which is the right way. In fact, many authors do not specify whether they do A or B. We show that only B is correct." It is also fine to say, "If the authors did A, it would bias their analysis by [...]" - and to point out whether or not there are signs of this effect.
This is both polite (by providing the benefit of the doubt) and also allows you to make a more conservative, but confident claim. This also helps you! If you write your paper assuming other people did their analysis wrong, a referee could say, "No, we didn't do A, we did B, everyone who isn't an idiot knows to do B" - and that doesn't bode well. But if you say, "Given the methods commonly described, it's impossible to tell if these results are accurate," this is both true and much more difficult to dispute!


text:
How can I deal with low-key plagiarism?
I am relatively new to academic publishing. However, there is an uncomfortable situation which I have already encountered multiple times by now (about five). It is what I would call "low-key plagiarism". I will explain what I mean by this (completely made-up) term in the following.
I don't have many papers and citations yet, so I tend to check out papers that cite me to see how my work is being used and if the new result is relevant to my own work. In the mentioned occasions, I found that the authors used my work extensively or built directly on it. The way the citation was phrased, however, implied that my result was only tangentially relevant or somewhat helpful. Sometimes the relevance is also disguised by citing further irrelevant literature.
The goal of the authors in both cases seems clear: to mislead a reviewer or readers into thinking the result is more significant or innovative. Of course, an ideal reviewer should spot this. However, in highly specialized fields and if the formulation is sufficiently vague, this is very difficult and does not happen practically.
I am not sure if this should really be called plagiarism. It is the kind of borderline case where, most likely, nobody will bring up the argument publicly. If someone does, the authors will most likely say "but we cited you here and there". No matter if plagiarism or not, it is certainly misleading to reference in this way.
When I find a citation like this, it feels very uncomfortable to me. Especially for interdisciplinary research, people might start citing the newer result and forget the older one completely if the citation chain cannot be tracked properly. This is the exact same effect as completely leaving out the citation (i.e., plagiarism) would have.
How can I deal with this kind of misleading citation practice? Should one just get over it? Should one contact the authors to express disappointment without asking for consequences? Should one fully escalate and demand a correction or bring the editor's attention to it? Should one do it even if the chance of success is low and the chance of hurting one's own reputation by being perceived as petty is high?
Concrete example
As suggested by Dan Romnik, I've tried to come up with a fictionalized example for what the misleading paper might be saying. The example contains three tricks which I have encountered on separate occasions. 1. List citations to hide relevance. 2. Shifting the citation to a supplement and omitting the citation in the main text summary of the method. 3. Attaching the citation to a meaningless side sentence instead of to the main result.
Here is the example: Let the main text contain no reference to the paper, except for a bit in the introduction citing it as previous literature as part of a list citation. Instead, it is stated in the methods that

We derive our main result using some abstract formulation of the method for brevity.

The method summary thus misses the citation, which is shifted to a supplement.
In the supplementary material, it is stated that

Introductory discussion to notation. Eq. (1) coming straight out of my paper. We derive our main result based on this equation by solving some integrals for a special case. This includes a completely standard step, which was also investigated in [1]. Our result is then obtained this way: concrete formulation of the method which was abbreviated in the main text and which is a special case of my method.

where [1] is my paper. Therefore, even if the reader looks in the supplementary material, they will not know that the central Eq. (1) is straight from my paper. The citation is there, but attached to a completely meaningless side-sentence. Of course, a careful reader could go and compare the two papers, but without that, it is not clear how the result was used.
Even if the example is not great, maybe this gives an idea of what kind of tricks I mean. One of those can be accidental; in sum, they are likely intentional and designed to mislead. They certainly do mislead, but are they plagiarism?

Most papers are some tweak of a prior paper. One goal is to publish in a different journal so it's viewed as slightly more new.

To clarify: Your concern is that the sentence in which the citation of your work isn't appreciative enough?

@AzorAhai-him- Not really. My concern is that I believe the sentences in which my work is cited are systematically misleading the reader. I guess not being appreciative is another effect though.

Interesting question, upvoted and I think this can lead to a really good discussion. However: can you give at least one concrete example that illustrates the problem you are describing? This stuff about “assume that the citations are clearly misleading” isn’t very helpful because what I expect would happen (because I’ve seen it happen many times here) is that each answer will still make slightly different assumptions about what the problem is that you are describing, leading to confusion and pointless disagreements. So an actual example with (suitably redacted) details could really help.

Misleading them into what? Entire years-long projects are often reduced to single-sentence citations when people build on them. That's just how science is. What is someone supposed to do when they "[use] your work extensively"? Write a paragraph extolling it? I agree with Dan, please include an example.

@DanRomik Thanks for the upvote and the input. I will do that! Actually I had one in my initial draft for the question, but thought it might break anonymity. I will try to give a fictionalized version of the example. Hopefully that will also address Azor's concern.

In your example, is "Eq. (1)" something one would only ever find in your paper? Or would one find that equation (or perhaps a simple algebraic equivalent) elsewhere?

@BryanKrause "Eq. (1)" was introduced by my paper in this context and even the conventions are the taken over in the citing paper. I can't be certain if my paper is the first mention of the equation in the general literature, but I checked that it appears in no other of the cited papers.

Thanks, I think it’s a pretty convincing example and posted an answer with my thoughts.

Hmm ... fyi your examples don't contain a list citation

@AzorAhai-him- true, but I’ll pass on coming up with that fictitious introduction ;)

Don't worry; the given example will not fool anyone. If a paper gives an equation out of the blue without explaining where it came from, that's a huge red flag. "Here is an equation we pulled out of our asses, ... and by coincidence, later in our paragraph, here is a reference to someone's paper[1]. If you happen to look into [1], try not to see the equation."

You will also find that someone will cite you for not real reason. I think that you assume too much relevance for your work (I do the same, this is not a criticism). Enjoy that your work is cited, at least.

This is a sad obvious consequence of publish or perish. If those authors did not have the urgency of getting something published, they ma spend 2 years more in pushing the science to do much more with your work than just a tiny increment.  They need to hide how tiny it is because its important that they have a publication

Some good points being made and good answers, as always, by Dan Romik and Buffy. I'd just like to add, I'm sorry this has happened to you. It sounds grossly unfair. Thank you for your contributions towards science!

I happen to have just read my university's plagiarism guidelines for students (see https://ethz.ch/students/en/studies/performance-assessments/plagiarism.html), and your example seems to fit their last bullet point exactly. So at this (somewhat prestigious) institution, I presume there would be strict consequences in such cases.

There have been a lot of useful comments, which I have upvoted. Thanks to all for that! I won't respond to them since they seem to stand alone just fine, but wanted to say that some of them may qualify as answers.

Being harsh, doesn't that detailed exposition come down to "The citation gave my work less respect than it deserved"?
Since as you said, this is "low-key" why not first take it up with the offenders and if that gives no useful result, with their institution, their publisher or both?

I agree with your assessment that this is misleading behavior on the part of the authors. I have run into this kind of behavior myself, including from authors who were famous researchers (and who were famous because they actually did very good work and not because they were good at misleading people about doing good work). It seems like it’s just human nature for some people to feel a need (probably driven by insecurity and lack of self-worth) to play up their own greatness and belittle others’ achievements.
As for what to do, I’d say just keep publishing good work and don’t worry about it. It’s not worth the time and energy it would take to fight such petty misconduct, especially when there is no hard evidence for a dishonest motive. Moreover, the advantage that these authors derive from such underhanded behavior probably does not outweigh the disadvantage of other people looking down on them and not wanting to work with them (I’m willing to bet you’re not the only one who noticed this), so their behavior is self-defeating and self-punishing. And your own contributions are documented in the scientific literature, so in case a dispute ever arises over something important, the truth will will be easy to establish and will come out.

+1. I like this answer a lot, because it has a very positive and constructive mindset. The input I got from people around me was more harsh, either in the direction of "just leave it, you're being oversensitive" or even along the lines of "we'll do the same to them in our next paper then". I'll reserve the accept tick for a bit to motivate others to contribute.

"it’s just human nature"  It's the nature of the science funding system.

@AnonymousPhysicist sure, some of it is competition-driven. But the famous researchers I mentioned did not have any funding problems. So I stand by what I said that it’s human nature.

Regarding the human nature, with good people there is also a reasonable chance that they came up with the ideas independently and only found the prior work at the last moment. This makes it much more tempting to just add a single, barely sufficient citation somewhere in the introduction, instead of replacing large parts of the paper with a comment that X did it first. Though this seems not to be the case in the question, where even the notation was copied.

It isn't plagiarism to suggest that your work is less relevant than you think it is. It is only plagiarism if they use it in any way without a citation and then give the impression that the ideas in the work are their own and not yours.
But, if they are clear about whose ideas are whose, then you should let it go - as plagiarism anyway.
Saying misleading things, or misinterpreting your work to others is also malfeasance, of course. People need to be honest about their own work and the work of others.
And if they say that you did X and they did Y when, in fact, you previously published Y then that is back to plagiarism again. But "almost Y" rather than "Y" likely doesn't count.
I'll also note that if the citation is there, then a reader can settle in their own mind how much of an advance the newer paper makes over your original contribution. It is when citation is absent that the thread of scientific knowledge is broken.

Thanks for your answer and +1! I think this is very useful already in getting the terms straight. Would you mind also having a look at my edited question including examples of some of the tricks I was alluding to? I believe that this fulfills "the thread of scientific knowledge is broken", but a concrete statement on such a case would be useful.

I agree with the other answers, in that you should probably let it go.  But I think it would also be helpful to point out a broader lesson that I learned through similar experiences: take your frustrations as opportunities to get better.
Like you — and most researchers — in my early years I was particularly anxious for the recognition that I felt my hard work deserved.  Naturally, I would get annoyed when I saw other people getting recognition for work that was based off of mine, but didn't give me any credit.  I actually had two really egregious examples of this during grad school, and they ate away at me.  It upset me, which just made life less enjoyable; it embittered me, which led me to close off from possibly productive collaborations and friendships; and it distracted me from my own work.  These were all bad for my career and for life outside of my career.
I realized that this was heading in a bad direction, and resolved that every time I start to get annoyed with colleagues I should take a step back and think about what I could have done better to avoid this situation in the first place.  This helps because I stop thinking about those annoying colleagues for a moment, and therefore become more objective in seeing the situation for what it is.  More often than not, it actually helps me see things from their perspective, which gives me much greater peace of mind and helps me be more effective going forward.  This is true for everything from teaching and mentoring, to how I give talks and write papers, all the way to office politics.
So let's apply this to the concrete example above.  The basic fact here is that your work didn't have the impact you wanted it to.  This is undeniable.  This may be due to intentional malfeasance or negligence on the part of those other authors, but that won't get you anywhere.  You also need to consider other possibilities.  Maybe your paper didn't actually say what you thought it said;  you might just understand parts of their paper because of all the background work and thinking you've done on the topic, but didn't actually include that in your paper.  Maybe your paper wasn't as clear as you thought it was.  Was Eq. (1) so novel that it was the main point of your paper, or was it just the starting point for both you and them?  Was it clear to them that their result was actually a "special case" of yours?  Was yours couched in esoteric general formalism that they found hard to apply to their case?  Should you have talked specifically about that special case in your paper?  Was the result given context that was explained clearly and prominently in the abstract and/or introduction?  Did you discuss your work with people other than you supervisor and/or collaborators before publishing so that you could work out how to explain things better?  Did you use the referee reports during publication to actually improve the paper, rather than just respond to comments to placate the reviewers.  Did you go to conferences and interact with people after publishing to make your paper known?  Could you have possibly done a better job on any of these points?  The answer to that last question is always yes, so focus on that.
To summarize: stop thinking about them, and start thinking about yourself.

A few notes:
This process shouldn't get you down on yourself, or exacerbate any impostor syndrome.  You're in the position you're in because you are good, but every one of us can get better.
Also, don't be afraid to be an academic rainmaker — someone whose work provides inspiration and a starting point for others.  That's exactly the position you want to be in.  You won't always get the credit you deserve, but eventually it will build up.
I still get annoyed at colleagues all the time.  In fact I'm currently writing a paper that shouldn't need to exist.  Don't people know that a simple boost is just a special case of a general BMS transformation?!  They should have just understood my first paper, and not written all those papers that misapplied it so badly and got everything wrong ARRGGG!!!  ...  Ah, but I guess I was striving for generality like a mathematician, without thinking about the astronomers who actually need to use it for relatively simple cases.  Readers misunderstood my paper, but maybe it's not all their fault.  My point is: You get to feel your feelings, but use your brain to try to understand and redirect those feelings.

Excellent answer. I particularly like the point about engaging with reviewers. If a reviewer misinterprets something that I wrote then it means I was not clear in my explanation, not that the reviewer is an idiot (thought the latter might also be true)

A bit of a heads up to Mike. Saying you "agree with the other answers" is a bit dangerous, since others might later appear that you don't agree with. Also note that the ordering of answers isn't fixed. It is a bit safer for yourself to specify which answers you agree with. Even "earlier answers" can be a bit ambiguous with editing. I sometimes edit posts when it is obvious at the moment, but can't guess here. Not a criticism, just something to think about.

Let it go, you won't be able to get a published paper changed in retrospect.
But if you review papers, keep this in mind and ask the authors to give proper credit to cited work. This would be the right point to change misleading texts when changes are likely.

useful comment, not really an answer. OP proposes multiple ways to deter people citing them specifically (not just whomever they get to review) from this behavior in the future, the only justification here ("won't be able to retro-change") does not concern that.

Nice, you have another citation to show! Great. :-)
Is that plagiarism? No. They built on what you published and referenced your work.
Is it fair? Depends. I can imagine it's a mixture of

Perhaps they read your paper a while ago when they started out with that research and mentally incorporated it into their idea of a general canon of prior art, and made it mentally their own. We all do that when we learn. They would then indeed — inadvertently — misrepresent the importance your paper has for their work.
They really think (as Allure said already) that the "stepping stone" they built on which they took from your paper is pretty standard.
It is also possible that your work is indeed one of several works about the same theme complex, and that you don't know as many of the other, similar works as they do. You would then consider your paper more unique than it seems to them. The differences to other papers may seem larger to you as the author than to uninvolved third parties. (This does not diminish your achievement; often certain things are "in the air" and worked upon independently by more than one group or person, often with similar results.)

In general, I'd be happy that somebody could use what I wrote. Since they work in a related area: Do they do interesting stuff? Would it be worthwhile to get to know each other? Keep an eye out for them at the next congress, once we can travel again!

Based on your example it sounds possible that the authors actually do consider the "completely standard step" to be completely standard. In other words, they could've done the step without your paper to guide them. As an elementary example, say you need to compute the derivative of a complicated function. You could work your way through it, or you could cite the paper that did the calculation for you. If you opt for the latter, giving it heavy credit might not be warranted.
If the above does not apply to your case, then blame the culture of asking for sexy results. Everyone (and I mean everyone, including non-academics like journalists or the government) want sexy results. We want Big News that generate excitement, citations, and funding. It's why theories such as MOND, which tries to do away with dark matter, attracts so much press time even though they're on the fringe of astrophysics; it's why null results are hard to publish.
Given that, writing a paper with "these guys did awesome work, we extended it in XYZ"  is like saying "these guys did awesome work, you should've published their paper [and not mine]". If you've ever received a rejection not because your paper was wrong, but because it's not novel enough, you'll know what it's like. It also means that when you submit to a new journal, you'll need to make your paper sound more exciting ...
Ultimately this culture won't be changeable by one person, and it's not clear how one would change it even if one could do so (e.g. Nature wouldn't be Nature if it started accepting all technically correct papers regardless of novelty). You'll probably have to learn to live with it. On the bright side, your contribution is marked in the academic record, and you will be able to point out what you accomplished if it's ever necessary.

So OP should “blame the culture of asking for sexy results” for people making a conscious decision to behave dishonestly, instead of blaming those specific people? What about all the other researchers who operate in the same culture but don’t make such decisions? Perhaps we should acknowledge that culture or no culture, people are still responsible for the decisions they make as individuals? I might accept that the culture was a contributing factor, but the way you present it seems very one-sided.


text:
How should I credit the advisor's help in my thesis?
I am graduating soon and in the last minute my advisor found an issue in one major theorem in my thesis. In an hour, my advisor sent me a write up with a fix. The result is a little bit different than what I have, but it does the job.
I was not expecting him to fix this issue. We were supposed to meet and discuss this issue. Instead, my advisor just sent an email with this fix. Since this is the major result in my thesis and my advisor's contribution is more significant than mine, what is the appropriate way to acknowledge this in my thesis?

If it is actually the major result in your thesis, I highly doubt that an adjustment to your theorem or proof that your advisor could throw together in an hour or even in a day is actually more significant than what you did. And I also doubt that your advisor was staring at this for an extended period of time before revealing what they were working on at the last moment. It's much more likely that the issue is more or less trivial and the main ideas of what you worked on are correct. Especially since your advisor didn't express a change of heart about you graduating.

@Ian, there are a lot of other factors. My advisor came back after staying in ICU for 2 years and we have to wrap up things quickly. I did much more than my thesis, but we don't have time to put everything together since I need another year or so to finish off everything. I am trying to put together what I have and graduate before time runs out. The issue is a bit more complicated. Moreover, this last minute change nullifies a lot of work I did since we were assuming that I proved a stronger result. This change makes significant parts of my work is unrelated and we don't have time for changes.

Clearly your advisor thinks well of you and thinks you are ready to move to the next level professionally. You both missed the issue at an earlier stage. Had he found it then he might well have pointed you to a fix rather than providing it.
He is probably as pleased as you are that a fix was possible.
So thank him for support and guidance (perhaps "particularly on Theorem X") and move on. Remember this incident when you advise your own students.

I know this type of comment is prohibited on this site, and if it gets removed, so be it, but wow. What a great answer.

I like the last line of your answer (and the rest of it as well).

Thank you, I will do this.

+1, but I wouldn't mention the concrete theorem. Helping, finding errors, filling the odd gap is what advisors do.

@MartinArgerami Normally nor would I. Here the OP refers specifically to on important theorem, so the special mention might be appropriate.

Just write a short paragraph at the end thanking your advisor for all their help during the writing of the thesis. If you ever turn it to a research paper, they’ll be a coauthor obviously.

Yes, if I am fortunate to complete and publish this work, he will be the coauthor. Thank you for your suggestion.

When I wrote my Master's thesis, I had several parts where other group members and my advisor contributed parts, even if those were only helpful discussions that lead to further insight. Apart from mentioning this in the usual acknowledgements at the end of my thesis, I also added references to "private communications" with the respective contributor wherever possible or added a short entry in the references section that described the exact contributions from said person.

Thank you thats helpful.

With other group members this might be a good idea. For the advisor, I would expect major contributions to a mather's or PhD thesis.

You credit your advisor's help at the front pages of your dissertation, where he or she is listed as your advisor. In a regular advising relationship, the contributions of the advisor are diffuse, at multiple levels, and impossible to quantify or pinpoint meaningfully. No need to make special mention of the very special circumstances that you relate, it will already be understood that your advisor has had a significant impact on your work.
So the advising relationship is sufficient formal recognition; the rest you can reserve for the acknowledgements section, and for your in person conversations. (For comparison, it would be a rather different situation if someone other than your advisor had contributed a fix to a problem of the magnitude that you describe.)

This is your thesis advisor's job, even though this might be a borderline case. He does represent your findings with his own name, after all.
What I would suggest is to thank him in the preamble, and make a footnote in that specific place the contribution took place in the text.