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Do you know readers of your papers ?

Or - is it true that if paper is not groundbreaking no one (except very few people, working very closely and hence known for you) will read it ?

If it is so - you can write "from expert to experts" concentrating on details. If it not so - it is better to include more introduction, background, motivation, examples.

"Definition" READER is any person looking at yours paper will extract something useful for him. That is why it is difficult to measure by citations number - many papers are cited but not "readed" and vice versa.

Some quote:

"Gowers Says:
November 7, 2011 at 3:21 pm ... I once heard that the average number of readers of a mathematics paper is less than 1."

I heard the same from other people - this is based on impact factor which they say averagely less than 1 for most of math journals.

To my taste "ideal" paper should be written in such a way that just "undergrad" can understand it. But that would of course require enormous efforts and size. Which is unjustified if you know that no one will read it :)

Practical situation - I am now writing a paper, which I am almost sure some 5 experts (whom I know) will look. The whole number of experts worked quite closely around the topic in last 10 years is may be bigger - 10-20 (depends on word "closely"). But different people has different tastes and interests, so I am not sure all of them will look, moreover I feel from previous experience many will not.

On the other hand, I feel, that some questions discussed in the paper are at least understandable for any undergraduate (and hopefully interesting). So potential number of readers is much bigger - that is why I am spending time to write it as readable as I can do. But it takes much time. It does not seems to me worth to spend so much time if I know that only those 5 experts (whom I know) will look on it.

Should I spend this time - or just put formulations of the theorems and write "obviously" ? :) (For experts this would be Okay :)

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closed as off topic by Felipe Voloch, Loop Space, Mark Meckes, Andrés E. Caicedo, Andy Putman Feb 6 '12 at 16:19

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I know a few of them ;-) --- but even if you were to chase citations to your paper (say via google scholar), does not mean that the people citing your paper actually read it. for that matter, given sometimes the errors in papers, it is not entirely convincing if the author himself has ever fully read his own paper! – Suvrit Feb 6 '12 at 13:51
To complement Suvrit’s comment, many (most?) people reading the paper will not cite it. (In order not to pronounce judgments about sizes of sets allegedly included in a singleton, let me reformulate it as: you cite only a fraction of papers you read.) – Emil Jeřábek Feb 6 '12 at 14:05
Papers often acquire new readers a long time after they're written, and for reasons that might not be evident at first. If you aim your writing at only the (known) experts, you're likely to prevent the later development of a wider readership. Also, unless your memory is a lot better than mine, those "obviously ..." statements might not seem so obvious, even to you, when someone comes along with a question 10 years later. I would advise you to write so as to be understandable for graduate students in your field; if you can reach undergraduates too, so much the better. – Andreas Blass Feb 6 '12 at 14:22
The usual publishing process should ensure that at least two referees read the paper from beginning to end... – Federico Poloni Feb 6 '12 at 15:08
2 in my experience as a referee I damn well do – Yemon Choi Feb 6 '12 at 22:10

I guess we all have been the readers of our first math paper, when we were students, and that we all regretted it was not written so clearly.

At least twice, in the past, some young Ph.D. students told me that my papers helped them a lot in understanding some topics that they hadn't found clearly stated elsewhere. To me this was enough to think that the time devoted to writing was well spent. But I understand perfectly well that for some others this may be of no satisfaction.

I guess that your question can be answered only by yourself. What do YOU prefer? More readers that can profit from your papers in different ways, not only for the original new math but also for the overview on a subject, or do you prefer less readers per paper and more time to devote to research? I think this balance is very personal, extremes are rare but nevertheless exist with their ups and downs (people that write math in a way in which is incomprehensible even for themselves and people that devote so much time to polishing their papers that you doubt they're doing research at all).

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As a young researcher I like this answer very much. Indeed, I should add that it happen very often that I read some paper not because I'm interested in its main result, but because it has a clear and well written introduction/background section giving some nice philosophical and technical overview of some theory I'm interested in. – Adrien Feb 6 '12 at 15:02
@Nicola 1) You answer is wonderful 2) You write "two young guys..." actually this a kind of statistics I want to know. For you 2, for me zero, but what is a distribution ? – Alexander Chervov Feb 6 '12 at 17:55
Thanks both. 2 and 0 are the numbers we know of. When I was doing my PhD I read so many papers on topics I've never really worked on... – Nicola Ciccoli Feb 6 '12 at 19:09
@Nicola Unfortunately we will not know more numbers since they close question. "When I was doing my PhD I read so many... " Me too :) However I was probably extracting nothing from the majority of that papers, so probably does not correspond to my meaning for "read". – Alexander Chervov Feb 6 '12 at 21:18

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