Are math papers getting longer?

A page of nonsenseAt the September 2021 meeting of the AMS Committee on Publications, Nick Trefethen asked whether Mathematical Reviews has seen an increase in the average length of papers that come through for indexing in MathSciNet.  I had not thought about that question, and there isn’t an easy query for page length in the Math Reviews database.  During the overnight break, I looked into the data for Transactions of the American Mathematical Society. Afterwards, I looked at two more journals, Mathematics of Computation and Annals of Mathematics.

This was not a random question on Trefethen’s part, he had written a letter to the editor of SIAM News on the topic, which was published in the July/August 2015 issue.  The letter was based on data collected by members of the Numerical Analysis Group at Oxford, of which Trefethen is the head. The average length of papers in the three SIAM journals SIAM Journal on Applied Mathematics (SIAP), SIAM Journal on Numerical Analysis (SINUM), and SIAM Journal on Scientific Computing (SISC) had doubled from 1975 to 2020.

Scatter plot of average page lengths of articles in primary SIAM journals

Average pages per article of three SIAM journals. Image from: Trefethen, Nick, Letter to the Editor: Why Have SIAM Journal Papers Grown So Long? SIAM News, Volume 48, Number 6, July / August 2015, p 2.

There is more on this topic on Trefethen’s blog, such as here.

The data for the Transactions of the AMS produce a graph very similar to the graphs for the SIAM journals, at least after things stabilized in the 1960s.

Scatter plot of average page lengths of articles in Transactions of the AMS from the 1920s to 2020The average number of pages in the years from 1965 to 1969 ranges from 13.5 to 16.8.  In the most recent five-year period, the average number of pages ranges from 28.8 to 31.7.

We can compute the average number of pages per article by decade, as in the following table, which shows that the average length of an article in Transactions has indeed doubled since the 1960s.

Transactions of the AMS
Decade #pgs #articles pgs/art
1920 4004 229 17.5
1930 8891 459 19.4
1940 9785 416 23.5
1950 14741 724 20.4
1960 28556 1735 16.5
1970 49678 2852 17.4
1980 46821 2500 18.7
1990 52421 2398 21.9
2000 56825 2422 23.5
2010 87778 3034 28.9
2020 9007 280 32.2

It is tempting to consider the question for the Proceedings of the AMS, but it has a page limit.  Assuming that the upper bound is mostly obeyed, it is unlikely that we will see the phenomenon in the Proceedings.  I am not aware of any strict page limit for the AMS journal Mathematics of Computation, however.  Let’s check it out.  Here is the plot for Math. of Comp. from 1960 to 2020:

Scatter plot of average page lengths of articles in the AMS journal "Mathematics of Computation" from the 1960s to 2020

Visually, the growth is rather clear.  As before, we can compute the average number of pages per article by decade, as in the following table:

Mathematics of Computation
Decade #pgs #articles pgs/art
1960 6600 683 9.7
1970 11165 1092 10.2
1980 14412 1062 13.6
1990 17626 1082 16.3
2000 20883 1107 18.9
2010 28274 1180 24.0
2020 3071 111 27.7

As with the SIAM journals, the Transactions of the AMS and Mathematics of Computation has also seen the average length of an article at least double since the 1960s.

What about Annals of Mathematics?  Well, here is the plot of the data for Annals:

For the Annals, the size of the articles prior to 1965 did not vary as much as we saw for Transactions.  Again, the growth is quite visible from the plot.  The table of the data for the Annals by decade shows consistent growth in the length of articles:

Annals of Mathematics
Decade #pgs #articles pgs/art
1930 8924 600 14.9
1940 9223 555 16.6
1950 12517 717 17.5
1960 12032 528 22.8
1970 11976 452 26.5
1980 12761 417 30.6
1990 14857 398 37.3
2000 22208 537 41.4
2010 27473 565 48.6
2020 3666 62 59.1

Going by decades, the average length of an article has more than doubled from the 1960s to the present.

So what is going on? There were no definitive answers during the discussion at the Committee on Publications meeting.  In his letter to SIAM News, Trefethen suggested that this is an indication of the professionalization of mathematics.  That is to say, 45 years ago, it was OK to write a paper that just presented an idea.  Now, an article represents a “piece of work”, explaining connections with other work.  The good thing about a piece of work is that it is less important for you to be part of the in-crowd to understand the paper.  The bad thing about a piece of work is that, in our time-crunched lives, we are more likely just to skim it, rather than to read it fully.

The phenomenon is curious, though, because it contradicts the supposed trend of “salami slicing” your work into several articles rather than one big article, aiming for the LPU (“Least Publishable Unit” or “publon”).  On the other hand, these six journals are not necessarily typical.


I am grateful to Nick Trefethen for asking the question, then encouraging my exploration of a very partial answer to it.  Thank you, also, to SIAM and SIAM News for so readily granting permission to reprint Trefethen’s original plot.

About Edward Dunne

I am the Executive Editor of Mathematical Reviews. Previously, I was an editor for the AMS Book Program for 17 years. Before working for the AMS, I had an academic career working at Rice University, Oxford University, and Oklahoma State University. In 1990-91, I worked for Springer-Verlag in Heidelberg. My Ph.D. is from Harvard. I received a world-class liberal arts education as an undergraduate at Santa Clara University.
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3 Responses to Are math papers getting longer?

  1. Ian D Gordon says:

    Edward, appreciate these observations, but I’m thinking that publishers as well as editors in the recent past have forgone page length as a limiter or filter on publishing good math of just even ideas. With manuscripts turned to PDFs and web documents they are exclusively ‘born digital’ and most often never see print paper. Without considerations for online or digital journal edition paper equivalents, page length and even journal editions and journals themselves are quickly going away as publishers, editors, researchers and librarians pivot to this new normal. One day students will wonder “What’s with article page length?” akin to the disappearance of print journals, books and maybe paper and pencils. Ian D. Gordon

  2. Felipe Voloch says:

    Have you tried to look at number of pages divided by number of authors? The number of authors has been growing as well and that might be the explanation.

  3. gwern says:

    The salami-slicing is easily explained; looking at journals with a long history and high prestige cannot take into account compositional effects like the efflorescence of paper mills and low-quality journals. That is, you cannot salami-slice the most prestigious journals because they will simply reject that and focus on quality and defensibility (as they can easily do given the overall growth while they remain the same size and publish fewer papers, if anything), which increasingly selects for long papers – while the slices go to all the other journals, particularly new ones. You’d need some field-wide metric (which of course brings in its own problems compared to a tight precise focus on a few old journals).

    I am also a bit skeptical that technological changes like TeX or digital publications really changed much for these journals. This is a smooth trend over a long time, with no particular bumps corresponding to the introduction of useful TeX ~1980, or PDFs+WWW ~1995. Were journals really discontinuing paper publication rapidly in, say, 1970?

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