# Do mathematicians really publish less often than (other) scientists?

I have heard from at least two mathematicians now, that mathematicians in general publish less per person per year than (other) scientists. This is anecdotal, so I looked around online and all I found, really, was this Reddit post; that's hardly evidence.

## The Question:

Do mathematicians publish less per person per year than (other) scientists?

Let's define "mathematician" as anyone who has ever published in a peer reviewed, academic mathematical journal. Feel free to use your own definition but please state it in your answers.

## Thoughts:

I would be surprised if they didn't, for reasons outlined in the Reddit post above. In summary:

• The comment, "mathematicians aren't allowed to publish their mistakes".
• Along the same lines, the subject is "not empirical", and so there's less emphasis on building evidence for & against hypotheses, other than computations.
• Meta-analyses are rare in mathematics (allegedly; I don't know).
• "The amount of material available": this one, I don't like. But the point is that scientists have more real world applications to work on than mathematicians.

There's more but you get the idea. There isn't much use in listing all the reasons why it might be true, if it's actually false.

I'm interested in the evidence, one way or another.

• What counting method is to be used? If it is a paper with 10 authors, do you count it as 1/10 of a paper for each of the authors? Commented Mar 4 at 1:37
• You need to divide by the square root of the number of authors, I would think, to account for the fact that more authors doesn't divide the amount of work evenly. But don't forget to sum up the number of pages rather than count papers. I would hate my 220-page maths paper to be found to be same as some chemist's three-page leaflet. Commented Mar 4 at 8:20
• You might want to specify what fields you are comparing to. For a biologist, for example, publishing once a year is already not bad. If you work with species that take a long time to mature and reproduce, it can take more than a year to even collect the data. Commented Mar 4 at 20:13
• Related/near-duplicate discussion on MathOverflow: Publication rates in Mathematics Commented Mar 5 at 6:44

Empirically it is true: Mathematicians publish less than, for example, computer scientists or chemists or physicists. But even within mathematics, there are substantial differences -- in pure mathematics, 1-2 papers per year is the norm, in applied mathematics it is 3-4. Of course, then there are other fields (for example in the liberal arts) where the standard is to publish books rather than journal articles, and how you want to compare that is probably a whole 'nother discussion.

I don't think it is useful to figure out why there are differences between mathematicians and others. At the end of the day, how much you publish comes down to how long it takes to work out the details in a paper. So if a field has meta-analyses, then the people who write these meta-analyses presumably publish less "original" work because they are busy doing the work for the meta-analysis. Conversely, in a field where you can't publish meta-analysis, you'd work on other things and publish those instead. I think it's probably also true that mathematicians do not work less than other scientists, and so the difference must simply come down to the fact that (i) it takes more time to get the material together for a paper, (ii) mathematics papers generally do not have as many authors as physics or computer science papers.

• @Buffy I believe you mean general relativity. I also think you may be underestimating the importance of the papers Einstein published "along the way" in 1907 and 1911. Sure, they didn't have the field equations, but the equivalence principle and the prediction of deflection of light by gravity are not small potatoes by any means. Commented Mar 3 at 19:30
• 1-2 papers a year is a high publishing rate compared to some fields. My group in molecular biology is generally regarded as publishing pretty well, but it takes us about 5 years to complete a paper (we may have 2 or 3 on the go at once). Commented Mar 3 at 23:58
• @Buffy I think pointing at a rather famous physicist's productivity from 120 years ago does not inform very much a discussion about the productivity of average mathematicians today :-) Commented Mar 4 at 1:31
• This answer entirely fits my own personal + anecdotal impressions — but on a question of the form “Is X commonly-believed thing really true?”, it would be really nice to have an answer backed up with some evidence.
– PLL
Commented Mar 4 at 8:39
• @WolfgangBangerth I agree that we should probably stop talking about Einstein as an example to follow, he was working more than a hundred years ago and the field of theoretical physics at that time was completely different.
– Tom
Commented Mar 4 at 20:13

This answer is written knowing mainly about differences in the two subjects in Germany. My definition of mathematician is "anyone associated with the department of mathematics at their university" - by your definition, I would be a mathematician because I once was co-author of a paper published in an AMS journal, although I see myself as a communications engineer and my official degree is "Dr.-Ing.".

I did my PhD in information theory; in my field, it was common to publish 3-5 papers per year as a PhD student. My brother was doing a PhD in mathematics, he was happy if he managed to publish 2 papers per year.

The main difference I noticed when digging deeper is that my my brother only counted journal articles as publications, conference contributions were not "publications" for him. In IT, on the other hand, all conference contributions were counted as publications. Sure enough, my brother did give talks at conferences, but those were not counted as publications, why, I do not know. On the other hand, if I had been counting journal papers only, I would have published 0-1 per year, the remaining 3-4 papers were conference papers.

Another big difference: a conference paper in IT was usually limited to five pages, a length that would have been considered short for a journal paper in both IT and mathematics. Each of those conference papers had to stand on its own, so if I wrote 3 papers on the same topic, the first page was typically spent defining symbols and parameters - of course, in a longer paper, I would have only defined them once, not thrice. The bibliography also would have a significant overlap. So I think it's pretty obvious that three papers with five pages each did not necessarily contain more "original" content than one paper with ten pages.

So my conclusion is: No, mathematicians don't publish less than other scientists, but the way they do it and the way they count their publications leads to smaller numbers, to a point where they can be pretty misleading.

As usual, the apparent sense of "publish" in the question is about "status-gate/keeping-passed" documents. Which I'd object to, as some times before, in the sense that it does not mean that people are not working, finding out new things.

At the same time, yes/no, most mathematicians (in my experience) do not imagine to write up a report of their last week's experiments, and make it into a "publication".

That is, the very concept of "publication" (at least in old-timey-math) is about significant progress.

(Oop, but, nowadays, apparently, lots of people in STEM fields have to pretend that they're making progress on a regular schedule, etc. Perhaps it's easier to pretend this in some experimental fields, but/and I have sympathy for those people...)

In summary, "number of publications" is a crazy metric for progress. Oop, but, well administrators irresistibly love numbers (and money).

• I feel like this could have been a few comments. It's appreciated though. Thanks. Commented Mar 4 at 22:55
• @Shaun, ah, yeah, could be a handful of comments, but they might be lost... and I do think the point I'm making, somewhat reframing your question, etc., does deserve some "permanent" presence. :) Commented Mar 4 at 22:56
• ... aaaaand the downvote (without comment) somewhat confirms my sense that the question does deserve some reframing. :) Commented Mar 5 at 21:30