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I was always wondering why is the impact factor of mathematical journals "often" lower than the impact factor of journals in other disciplines? I come up with some guesses that I would like to know your opinion about them.

  1. Mathematics papers are so hard to read and follow (or so specialized) that only a few people can read and apply their results.

  2. There are relatively a large number of subfields and branches of mathematics and only a few people are working in each branch.

  3. The number of journals and papers in mathematics (divided by the number of active mathematicians) is relatively higher than other disciplines.

  4. A mixture of these.

Please, share your insights about this issue.

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Why isn't the answer obviously "because mathematics papers are cited less often (and less quickly)"? – JeffE Jan 15 '13 at 0:58
@JeffE: That just reduces the question to "why are mathematics papers cited less often and less quickly?" It's clear that they are, and the question seems worthwile (if only to reassure mathematicians that the answer isn't necessarily "because they are less interesting or important"). – Anonymous Mathematician Jan 15 '13 at 1:20
Why do the Mars angels not sprinkle pixie dust on me every night ? – Suresh Jan 15 '13 at 6:12
up vote 19 down vote accepted

There are a lot of different factors, and I know of no reliable way to determine which is the best explanation. For example, one theory is that mathematics simply has less impact (in the non-technical sense) than most scientific fields. I don't believe this, but it's hard to give a principled refutation. The whole subject strikes me as a little silly, with lots of opinions and numbers with no clear meaning.

One important factor is clearly that mathematicians write fewer, often longer papers than most scientists. Another is the two-year cycle mentioned by walkmanyi (citations after two years do not count for impact factor, which is incompatible with both the time lag in mathematics publication and the time required to carry out research in mathematics in the first place).

Another factor is the size of the field. The highest impact factors should occur in an enormous field with some incredibly important research and also a ton of less important papers that cite the great ones. Mathematics is just not that large a field (compared with biology or medicine, certainly), and it furthermore fragments into a lot of subfields it's difficult to move between. When someone makes an amazing discovery in algebraic geometry, you aren't going to get a flood of mathematicians from other areas rushing in to take the next steps, because algebraic geometry requires a lot of background. I don't think that's a bad thing for mathematics as a whole (the things the would-be algebraic geometers are doing instead are probably as valuable as following the latest trends would be), but it cuts down on the opportunities for amassing citations quickly.

Ultimately, I doubt there's any conclusive or satisfying way to determine how much of a role each of these factors plays.

For some published commentary on impact factors in mathematics, see Nefarious Numbers by Arnold and Fowler and Impact Factor and How it Relates to Quality of Journals by Milman. The first paper focuses on the flaws of impact factors and their abuse/manipulation, while the second explains how impact factor calculations relate to mathematical publication practices (and some of the incentives for journal editors). Neither directly answers the question here, but they both shed some light on it.

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Size of the field: In my original answer I wanted to highlight this, but then decided not to as I cannot argue as IF is a ratio cited vs. published so it shouldn't be influenced by the size of the field. But if you are looking for arguments in this direction, there's quite some support in bibliometric maps of science. See e.g., here which is taken from here. There are more maps like that. Clearly, mathematics is a relatively small field in comparison to other scientific disciplines. – walkmanyi Jan 15 '13 at 9:16
In fact, it seems to me that size of the field should be related to the variability of the number of citations, rather to the the average number of citation by paper (see my answer). However, it makes me wonder whether the feeling that math journals have lesser IF than, say biology journals could be untrue, mostly based on the comparison of the highest IF journals in each field. This would make the size of the field a better explanation for that perception, in my opinion. – Benoît Kloeckner Apr 24 '15 at 7:15

why is the impact factor of mathematical journals "often" lower than the impact factor of journals in other disciplines?

Besides your observations 2 and 3, my take on this would stem from the observation that the pace of work in mathematics tends to be a longer shot than in disciplines, such as biology where often there would be several competing groups working on a very close subject. The impact factor is calculated as "recent", but in disciplines with slow pace of development, sooner than a paper gets cited, it already falls of the considered recent period (2, or 5 recent years).

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Rather than the "pace of work", I would put this down do the appalling culture, in Mathematics, of taking forever to peer-review journal papers. If it takes more than a year for a paper to get accepted, it takes more than two years for references to said paper to appear. – Pedro Jan 14 '13 at 23:57
@Pedro: I don't find it appalling. Journals simply aren't the primary means of communication in mathematics (preprints are). Instead, we've got a hybrid system of instantaneous communication of the latest results combined with a slow and careful refereeing process for long-term archiving. Of course not everyone's as quick or efficient as they could be, and editors are always trying to find ways to speed the process up, but there's nothing wrong with a system where it takes ten times as long to check the proofs in a math paper as to check that a biology paper uses a reasonable methodology. – Anonymous Mathematician Jan 15 '13 at 0:41

I must admit that I tend to disagree with the previous answers: while the description of the specifics of the mathematical community are accurate, I do not see why this should affect the impact factor (except for the time needed before an article is cited, whose influence is clear). In particular, size of the field does not have any impact per itself on the average impact factor of papers. In fact, papers are less cited mainly because papers cite less.

Let me back my point, first assuming we are looking in a field that is closed (only cites itself and is only cited by itself) and stationary (no evolution of the number of papers published or the average number of references per article). Consider the publication graph of a given year : it is a bipartite graph, whose vertices are papers published year 0 (first partition) and years -1 and -2 (second partition) and whose edges are citations from the first ones to the second ones. Then the (article) average of impact factors AIF in this domain is the ratio

AIF = (#citations from year 0 papers to year -1 and -2 ones)/(#year -1 and -2 papers)

which is equal to (#edges)/(#papers published in two years), since the field is assumed to be stationary. This is also twice the average number of references to the two preceding years that a paper in the fields has.

So the article average impact factor of a closed and stationary field is solely governed by the references habits in the field. In particular, this is not affected by the overall size of the field (e.g. math as opposed to biology).

Given the distribution of references, an expending field will tend to have bigger impact factor, as will a field that is often cited by other ones. I do not feel that speed of expansion is an important factor for math compared to other fields, but fondamental mathematics are probably seldom cited outside itself. This has little impact if one consider maths against the rest of the world, though, since math papers seldomly cited outside the field too.

Another factor can be the distribution of papers among journals: for example, if a field has only two journals, one very large and one very small that only gets the very top articles, then the (unweighted) journal average IF will be extremely high. I doubt this explain much of the difference between math and the other fields, since mathematics have a strong hierarchy of journals.

So, what we really have to explain is why math papers cite less papers in the two-years range than papers in (most) other fields. This will explain why they are less cited.

Then the answer seems quite clear: maths papers are often long to read, and take time to be digested. The core of a biology paper is usually easy to understand and such papers are more easy to cite. There is also a small subfield effect: mathematician can work on problems that involve few previous papers. This is different from the size of fields, because it is more about the degree of specialization.

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Hmm, interesting. I agree that math papers cite less within the two-year window for field-specific reasons, but I don't see any evidence they cite less otherwise. I guess what this suggests is that the distribution of citations per page in mathematics must simply be more uniform if it is less highly peaked? I agree that the average number of citations per paper can't scale with the size of the field, but I don't think that's what anyone observes. Instead, it's the number of citations per good paper, and that probably does scale. – Anonymous Mathematician Jan 15 '13 at 13:42
(I.e., I doubt the number of breakthroughs scales with the size of a field, thanks to diminishing returns. It presumably increases too, but a little more slowly, and all the other papers are citing the breakthroughs.) – Anonymous Mathematician Jan 15 '13 at 13:50
I fully agree with this answer, and want to add the point that mathematics has few review articles compared to a field like biology, for example. Review articles often contain hundreds of references and thus push impact factors greatly. – silvado Jan 15 '13 at 16:16

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