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My coworkers are pursuing a generalization of one of my (recent) results. Is it wrong of me to frown a little on this? I would prefer it if they had an original idea of their own, or that if that they had to generalize a result, it would either be one of their own or one of someone they do not know.

The way I see it, a paper has a certain lifespan in terms of being read and cited. Once it has been generalized, that lifespan is in most cases over. If someone wanted to understand a theorem, they would probably look for the most general version. Of course, this does not always apply, for example if the work represents a milestone of some kind. One consequence of obsolescence is the stream of citations to my paper is short circuited. This will, in a sense, benefit them at my expense. Of course, I realize that my paper will eventually (hopefully) be generalized and become obsolete (i.e. no longer state-of-the-art). I just rather prefer that it wasn't my coworkers who are working towards that goal (they even started while I was still drafting my paper).

Please note: I do not mean for this to be read as a rant or a complaint. I do understand how science works by expanding on previous knowledge. I just want to know how others feel about the prospect of their research becoming obsolete, and how to approach that from the perspective of someone in the beginning (and at the same time, possibly the end) of their academic career. I imagine that for a professor such a thing would not be a big deal, for a number of different reasons.

While I sympathize with you, I find it hard to answer your question.

On the one hand, as phrased you are asking whether an emotional response is valid. Well, it is not really for anyone other than you to determine the validity of your emotional responses, and in all of my experience, "That is not a valid emotional response" is rarely a useful piece of advice. On the other hand, your question is pitched in a certain level of generality, but understanding why you feel the way you do seems to require knowing more particulars of your situation than you have disclosed.

But let me say what I can and what might be helpful:

The way I see it, a paper has a certain lifespan in terms of being read and cited. Once it has been generalized, that lifespan is in most cases over. If someone wanted to understand a theorem, they would probably look for the most general version. Of course, this does not always apply, for example if the work represents a milestone of some kind. One consequence of obsolescence is the stream of citations to my paper is short circuited. This will, in a sense, benefit them at my expense. Of course, I realize that my paper will eventually (hopefully) be generalized and become obsolete (i.e. no longer state-of-the-art).

Since you speak of "theorems," I gather you are working in mathematics. (This is corroborated by one of your other questions, where you identify yourself as working in applied mathematics.) I am also a (pure) mathematician, and the way you describe "obsolescence" is neither the way I think about mathematical results nor how I have heard other mathematicians talking about them. Maybe it is quite different in applied mathematics, but in pure mathematics there is not any prescribed lifespan on papers being read and cited. To try to quantify this, I just looked back over my last 10 accepted papers, and for each one identified the earliest cited paper. Of these ten papers, the latest one was published in 1976. (Moreover the 1976 paper came from a five page note with only a few citations.) In other words, in all of my recent papers I have cited papers that are more than 40 years old, and in fact usually older than that. In my department I have many colleagues who are 10-20 years older than I but who have a similar number of publications to me (publication pressures have risen in recent years). Most of these colleagues have higher total citation numbers than I do -- I think because their papers from 10, 20, 30...years ago continue to be cited. My most highly cited works were published in 2013, 2005, 2006, 2010 and 2003, respectively.

[Moreover, in mathematics, citation numbers are not (yet!) the ultimate metric of academic worth. Papers written on finite graphs tend to get more citations than papers written on admissible representations of p-adic groups because there are more people working on the former and many more people who know what the former are. I think most mathematicians realize this.]

So I have to wonder about the specific situation you are describing. In a different question, you mention a colleague of yours who worked on the same problem as you and came up with a result that was in some but not all ways more general, and then you published at least two papers together. I don't understand why this would "short circuit" your citations. Now you describe a situation in which your colleagues are working on generalizing one of your results, apparently without any new ideas. In this latter situation especially, I would expect that if they publish an improvement of your results using ideas essentially due to you, then that should augment your results in every way (including citations), not detract from it. (You are aware that senior mathematicians do this all the time, and the work of their students is usually viewed as an extension of their own work, I trust?)

Then you say:

I just rather prefer that it wasn't my coworkers who are working towards that goal (they even started while I was still drafting my paper).

If it gets to the point of an independently published generalization of your work, then I don't see how it makes any difference whatsoever if your coworkers were involved. However, before that happens the fact that it is your coworkers puts you in a much better situation: namely, in the worst case you have much more advance knowledge of what they are working on and can plan accordingly. In the best case you can pursue a collaboration with them in whatever way seems best to you.

If I may take a guess -- are you perhaps most upset by the fact that your coworkers have chosen to pursue these generalizations of your work without your involvement, so that they seem to be competing with you right under your nose? I could understand why that would be upsetting. If you feel that way, I think you should be much more proactive about collaborating with them.

Short answer, two possible approaches:

• collaborate with your coworkers. From what you write, it sounds like they may have already suggested and you may have been hesitant because you wanted unique ownership. Science is collaborative and you will both benefit from this collaboration




• keep being original, create new streams of research. Some academics enjoy new challenges, then get quickly bored and prefer variety (broadness of research areas to cover) to depth (being leading expert in a certain subfield). There is nothing wrong with that variety.

My feeling is that you are stuck in the middle. Just pick one of two routes and you will be happy again in no time 🙂

Ask yourself what goal you want to achieve. Do you want your colleagues to publicly apologize to you? Postpone their publications until yours gets enough citations? Abandon their work on the topic altogether? Include you in their paper as a co-author?

Unless you can define a specific goal which you deem achievable and are ethically OK with, the best advice I can give is to get yourself comforted by close friends over a beer, then get over it and move on.

If you feel that including you as a co-author could make sense, think about what you could contribute to colleagues' research (other than the paper you've already published), then speak with them about this possible collaboration as soon as possible.

One consequence of obsolescence is the stream of citations to my paper is short circuited. This will, in a sense, benefit them at my expense.

Possibly the opposite. Citations, IMO, tend to quote the base paper as well as the generalization.

This will, in a sense, benefit them at my expense. Of course, I realize that my paper will eventually (hopefully) be generalized and become obsolete (i.e. no longer state-of-the-art). I just rather prefer that it wasn't my coworkers who are working towards that goal (they even started while I was still drafting my paper).

You should look upon it as having been granted the privilege of having found some knowledge to humanity and having your work rewarded by inspiring others to extend it.

The vast majority of people will never experience discovering something like this and all too many people never have the luck to inspire others by their labors.

Historically (centuries past) it was not uncommon for scientists to deliberately keep discoveries to themselves to profit from them in some way. For example the dispute between Cardano and Tartaglia over the solution of a type of cubic equation. These days are (hopefully) gone and it's now a slightly better system of publishing as fast as possible and chasing citations (as they are a kind of bizarre currency). However ultimately you should try and look at the personal reward of discovery and sharing as your only rewards. Those are the only rewards you can be reasonably certain to get.

You have a small (?) place in the written history of the world. Be happy, most do not through no fault of their own.

You don't want to be part of the new project (I'd at least keep in touch with them if possible), so there's no gain in thinking about it.

Let this go and move on.

One consequence of obsolescence is the stream of citations to my paper is short circuited. This will, in a sense, benefit them at my expense.

Increasing the amount of knowledge not only benefits them but also the scientific community and humankind as a whole. This is very positive effect of obsolescence of scientific results.

Of course, I realize that my paper will eventually (hopefully) be generalized and become obsolete (i.e. no longer state-of-the-art). I just rather prefer that it wasn't my coworkers who are working towards that goal (they even started while I was still drafting my paper).

This sounds a bit like a missed chance for more cooperation between you and your coworkers and because of that possibly some waste of resources. Did they contact you and ask you for your further plans, maybe suggesting a further cooperation? Were they open about what they are working on? If not, your coworkers might simply have decided to leave you out of future developments. You could then try to compete with them and be faster or leave this particular field to them and do something else.

I did not experience direct competition from coworkers, but in cases of competition from other groups I always tried to be as fast as possible.

One lesson for the future could be that collaborations have a social dimension and that trust about future arrangements matters. Collaborations can be very long term and fruitful. It's probably a good idea to stick with those that worked well for you.