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Have there been any studies of publication rates in Mathematics?

We are trying to construct a workload model for the Faculty of Science and Engineering at my institution. Part of this involves assigning a fixed number of "points" for each published paper. It seems that our colleagues in some of the sciences publish many more papers than we do in Mathematics, which leaves us asking for the number of points per paper to be far higher in Mathematics than elsewhere. But we need to be able to back up our impressions with facts.

What I would like to do is to get some idea of how many papers one might expect a research mathematician to publish over, say, a five-year period. I recognize that there are a lot of problems here with the words "expect" and "research mathematician", not to mention problems with counting a 100-page paper on the same footing as a 5-page paper, or a paper in a "top" journal on the same footing as a paper in a not-so-top journal; I want to stay away from all those subjective and opinion-based issues.

I would like to know whether there are any publically-available figures along the following lines: pick a university where faculty are expected to be engaged in research; find out how many publications each member of the Math Department has had over (say) a five-year period; publish the median, or some other measure of the distribution of the publication numbers (not the mean, which could be skewed by a small number of members publishing a large number of papers).

I'm aware of the paper by Jerrold Grossman, Patterns of collaboration in mathematical research, SIAM News 35 (2002), but that's a study of all papers listed in Math Reviews, which includes people who published a paper or two and then left research mathematics for other fields. I'm really interested only in people who are employed by departments where publication in refereed journals is expected.

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    $\begingroup$ This whole business of ranking universities and people by assigning some number to them makes me sick. Honestly. $\endgroup$
    – Franz Lemmermeyer
    Oct 27, 2015 at 9:22
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    $\begingroup$ What do you want to do with such bibliometrics? -- As soon as you make anything depend on it, people will start "optimising" their activities accordingly to get good evaluations, and I am not convinced that this is helpful for anything or anybody, perhaps except for the inventors of the evaluation scheme ... . $\endgroup$
    – Stefan Kohl ♦
    Oct 27, 2015 at 10:00
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    $\begingroup$ A chemist friend of mine once told me that the standard in computational chemistry is: you set up a simulation, you get the computers cranking, and no matter what the output means you publish the numbers-there is your paper! Not to mention the shenanigans involved in cross-citing, which (thank God) is a much less pervasive practice in maths. The whole business of publication is more severely flawed in other disciplines, but for some reason that's the standard. $\endgroup$
    – user41593
    Oct 27, 2015 at 11:20
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    $\begingroup$ Measuring workload by number of papers will lead to the obvious result that people will publish as many small papers in low quality journals as possible. If possible, you should politely tell your dean that no reputable math department (actually no university) does this if it wants to remain so. $\endgroup$
    – user25199
    Oct 27, 2015 at 12:30
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    $\begingroup$ I do not vote to close this (at least not yet) but I think the question would be a lot better asked on Academia and generalized a bit. The motivation of the question seems to be (at least in part) to compare math to other disciplines. I thus think a broader picture could be more helpful. $\endgroup$
    – user9072
    Oct 27, 2015 at 13:24

6 Answers 6

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Here is the AMS culture statement on publication rates in mathematics. Even the best young mathematicians publish average of two or fewer articles per year.

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    $\begingroup$ This is much better than my answer. +1 $\endgroup$
    – Dan Romik
    Oct 28, 2015 at 4:34
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    $\begingroup$ And here is an updated version containing nearly the same content. $\endgroup$
    – R. van Dobben de Bruyn
    May 30, 2020 at 1:15
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    $\begingroup$ One further aspect that isn't talked about as much is the longevity and robustness of mathematical material: save for the occasional error, a result once proven will remain so, and cannot be challenged by progressing insights or competing schools of thought. (But it can be improved or forgotten.) Consequently, it is not uncommon for mathematicians to cite works from up to 50–60 years ago, which the "impact factor" method does not take into account. $\endgroup$
    – R. van Dobben de Bruyn
    May 30, 2020 at 1:29
  • $\begingroup$ Is this still relevant in 2023? $\endgroup$
    – cgb5436
    Sep 16, 2023 at 1:17
  • $\begingroup$ Just checked, and this was last updated in 2015. Hopefully they revisit this and continue to update it. Perhaps the community here can informally confirm or deny this if you ask as another question? Not sure if that would be ok, though... $\endgroup$
    – Jon Bannon
    Sep 16, 2023 at 12:18
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[extended comment not really answering the question, but an answer of sorts nonetheless; feel free to downvote!]

[edit: the thoughts below reflect my subjective opinion and are not meant to be interpreted as an expression of objective truth]

This question is, in a sense, flawed. You are asking about studies of a certain number $X$. Taken on its own this may be a reasonable question; the problem is that your stated motivation for why you are interested in $X$ is that you would like to (or your university would like to, and you seem willing to go along with it) use $X$ in a way that many reasonable mathematicians would agree is not just useless, but is in fact extremely harmful. How can anyone answer this with a straight face? Personally I would not answer even if I knew of such a study! There may be valid reasons to study $X$ and to be interested in it, but the motivation given for the question completely undermines the discussion.

With that said, it's important to emphasize that even across different areas within mathematics, there is a very large variation in

  1. $X=\,$the average rate of publication for a mathematician working in that area;

  2. $Y=\,$the average length of a publication;

  3. $Z=\,$the average number of coauthors of a paper;

  4. $W=\,$the average quality and impact of a paper (which are of course vaguely defined notions which there is currently no agreed upon way to quantify).

By agreeing to have your Faculty of Science and Engineering use $X$ as the measure of anything without making any attempt to take into account $Y$ and $Z$, let alone the much more intangible and ultimately most important parameter $W$, you would be allowing your university to create a hugely distorted image of your and your colleagues' research output. The fact that there will be some normalization factor that would ostensibly bring mathematics on par with other disciplines is completely irrelevant. So, as I said, although I'm sure it was well-intentioned, the motivation for the question is fatally flawed in my opinion. It may be worth having a discussion about average publication rates in the context of how to measure the productivity of mathematicians and whether it's a good idea to try to do so, but that would be a separate question that would need to be phrased in those terms.

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    $\begingroup$ You are quite quick and excessive in your judgment. $\endgroup$
    – user9072
    Oct 27, 2015 at 17:18
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    $\begingroup$ "use X in a way that any reasonable mathematician would agree is not just useless, but is in fact extremely harmful" is excessive in that you cannot know what any reasonable mathematician might think on the subject, except you decide that a deviating opinion on this matter makes a mathematician unreasonable. What's worse you cannot even know what the precise use would be a "workload model for the Faculty of Science and Engineering " can be all kinds of things. The proposed measure seems crude, but depending on what it should be used for it could be good enough. $\endgroup$
    – user9072
    Oct 27, 2015 at 17:28
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    $\begingroup$ Scientometrics is a pseudoscience. $\endgroup$
    – Zoran Skoda
    Oct 27, 2015 at 18:48
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    $\begingroup$ "...you seem willing to go along with it..." So, what do you suggest I do instead? Set myself on fire, in protest? I am trying to make the best of a bad situation. If you can't help, [censored]. $\endgroup$
    – Gerry Myerson
    Oct 28, 2015 at 2:18
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    $\begingroup$ @GerryMyerson I am truly sorry if you took offense to my answer. I was in fact trying to help by posting it, and believe that it contributes meaningfully to the discussion (and in that sense it is helpful) even if it didn't answer your actual question and had the unfortunate side effect of hurting your feelings, which I sincerely regret. As for what I suggest to do, others have made good comments about talking to your dean etc, and specifically I would say to make your best effort to convince the administration that what they are trying to do is utter folly. But you probably already knew that. $\endgroup$
    – Dan Romik
    Oct 28, 2015 at 3:02
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From an answer of mine on academia.stackexchange.com:

Italy introduced a few years ago a habilitation process which involves heavy bibliometric evaluation, and in the process they computed median values for all the professors in Italian universities for:

  • number of papers published in 10 years
  • citations per year
  • a sort of normalized H-index: the number h such that the person has h papers with score >=h, where a paper published Y years ago with C citations has score 4C/Y. (more precisely defined here (Italian) and here).

The medians are separate by discipline and academic role (associate and full professor only --- not for assistants, unfortunately). You can find them here: associate full, and a legend for the codes of the scientific disciplines is here. The documents are in Italian, but you can google-translate them (or guess the meaning of most words, it's not too difficult for an English speaker).

For instance, in computer science (01/B1) the medians for an associate professor are

  • 10 journal papers / 10 years,
  • 9.15 citations / year
  • "contemporary H-index" 5.

and for a full professor

  • 12 papers / 10 years
  • 14.8 citations / year
  • "contemporary H-index" 6.

The calculations are of course imperfect, but they are very interesting to browse and give an idea of how wildly these numbers vary across different fields. For instance, the typical professor in nuclear physics (02/A1) publishes 59.5 papers over 10 years and gets over 104 citations per year, while one in mathematical logic (01/A1) publishes 5 papers in 10 years and gets 1.74 citations per year.

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My impression is that some (scientific) fields tend to have many papers with very large number of authors, while mathematics papers tend to have fewer authors. (Although the number of co-authored math papers has been increasing, which has been documented by MathSciNet data.) Anyway, if your university is still discussing this, you might point out that less credit should be given for an N-person paper than for a 1-person paper. So maybe the way to assign "points" to a paper is to give a person 1/N points for an N-author paper. That might help math. Or, since some level of collaboration is to be encouraged, maybe use a weighting system that decreases in some other way, e.g., an N-person paper gets 1+2/N points or 1+3/N points.

A similar weighting system could be assigned to citations, you get 1/N of a citation for each time your N-author paper is cited!

Note that this wouldn't require you to get data about publication rates in different fields. It's a fairness argument about the amount of effort each individual is putting into their papers.

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    $\begingroup$ I don't think the lab sciences, where each paper can have 100 authors, would be very happy with this. $\endgroup$
    – Gerry Myerson
    Aug 26, 2016 at 21:13
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    $\begingroup$ @GerryMyerson Probably not. But maybe a somewhat weighted system: 5 points for papers with at most 3 authors, 3 points for papers with 4 to 10 authors, 1 point for papers with more than 10 authors. But the point should be made that if a paper has 100 authors, it's crazy to give each author more than a fraction of the credit for a paper with a single author. $\endgroup$
    – Joe Silverman
    Aug 26, 2016 at 22:12
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    $\begingroup$ @GerryMyerson Hmmm... On second thought, possibly I'm being unfair. I actually don't know if there are experimental scientists who spend, say, a year of their time working on a single paper that ends up having 100 authors. If they do, then yes, they deserve as much credit as a single author math paper. But if everyone who walks through the lab for a few hours gets their name on the paper, that would be a different story. $\endgroup$
    – Joe Silverman
    Aug 26, 2016 at 22:17
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The Performance Ranking of Scientific Papers for World Universities, as part of its scoring process, does count publications per university per discipline. However, when I looked at the current report for mathematics, I was unable to make sense of the number that they call "current articles," which presumably is some kind of measure of the number of papers published in the current year. It sounds like you want something like the number of publications per faculty member per year for each university, and it's not obvious to me how to derive that from the numbers reported by the Performance Ranking.

The Performance Ranking relies on the Thomson Reuters "Essential Science Indicators" (ESI), so I assume you could go directly to ESI and compile the numbers you want. However, I've never used ESI (they charge for their information) so I don't know how easy it is to extract the information you want. In principle, though, the data should be there.

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Perhaps you will find this site useful to find data to support your cause. The data comes from the SCOPUS database. Here you can compare various subject areas in terms of number of papers and citations per paper.

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