6
$\begingroup$

I am wondering about the most cited papers/books in Mathematics. I always had the impression that the number of citations in the mathematical community is several orders of magnitude below the number of citations in other scientific areas, such as chemistry, physics or biology. Nonetheless, there are some very well cited papers in mathematics. For example, Marco Gualtieri's thesis (of particular relevance in String Theory), which, according to Google Scholar, has 856 citations. To my biggest surprise, today I found that "Mathematical methods of classical mechanics" by V. I. Arnold has the astonishing number of 12934 citations, almost beating for example the most cited paper in String Theory, which if I am not mistaken is "The Large N Limit of Superconformal Field Theories and Supergravity" by Juan Maldacena, which has 13160 citations.

Thanks.

Improve this question
$\endgroup$
11
  • 5
    $\begingroup$ C. E. Shannon, A mathematical theory of communication, has 72774 citations according to Google Scholar. scholar.google.com/…. See also this Quora entry: quora.com/What-is-the-most-cited-paper-in-Mathematics $\endgroup$
    – Joel David Hamkins
    Commented Mar 14, 2015 at 14:19
  • 1
    $\begingroup$ For something more purely math: Hartshorne's "Algebraic Geometry" has 13k+. $\endgroup$
    – user9072
    Commented Mar 14, 2015 at 14:34
  • 10
    $\begingroup$ You cannot compare citations to books, theses, review articles,... to citations to research articles, almost by definition. Shannon's and Maldacena's are research papers, whereas Arnold's book and Gualtieri's thesis are in a different category. $\endgroup$
    – José Figueroa-O'Farrill
    Commented Mar 14, 2015 at 14:47
  • 8
    $\begingroup$ One problem with deciding this is that once a theorem is sufficiently widely known, it is often cited internally by name within a paper, but an explicit reference is not included in the bibiography of that paper. $\endgroup$
    – Geoff Robinson
    Commented Mar 14, 2015 at 15:37
  • 2
    $\begingroup$ @ThiKu it is the paper that one is requested to cite when one uses MAGMA. $\endgroup$
    – user9072
    Commented Mar 14, 2015 at 16:28

1 Answer 1

Reset to default
2
$\begingroup$

Apparently the most cited math article form the nineteen nineties had 379 citations. It was on a fast algorithm to solve large systems of linear equations. Here is a non-technical article by the author, Henk van der Vorst, on how the article achieved its popularity: 'How to write a frequently cited article'. http://www.staff.science.uu.nl/~vorst102/freqcited.pdf

I once attended a talk (with the same title) by him where he explained how he actively tried to convince people working in all kinds of industries to use his algorithm for solving their problems. (Linear algebra is everywhere as you know, once you learn how to recognize it.) I hoped the linked article is a transcript of that talk but I can't find the 'going to the industry' part in it - perhaps there is another article by Van der Vorst out there on the internet focusing more on that aspect of the story.

Improve this answer
$\endgroup$
9
  • 6
    $\begingroup$ I find that hard to believe. Hitchin's paper "Stable bundles and integrable systems" from 1987 has 620 citations, or again Hitchin's paper "Generalized Calabi-Yau manifolds" from the 2002 has 809 citations. So there are probably other papers from 90's with more citations than these that you mention. $\endgroup$
    – Bilateral
    Commented Mar 14, 2015 at 16:24
  • 1
    $\begingroup$ @S.S. where are those numbers from? At the moment the mentioned paper has more than 4k in Google Scholar. (GEMRES by Saad and Schultz has even 8k+, but is from the 80s) $\endgroup$
    – user9072
    Commented Mar 14, 2015 at 16:31
  • $\begingroup$ I personally found the number also somewhat hard to believe after reading the numbers in your question, perhaps we should send an email to this 'Institute for Scientific Information (ISI)' mentioned at the beginning of the article I linked to. $\endgroup$
    – Vincent
    Commented Mar 14, 2015 at 16:32
  • 2
    $\begingroup$ Vincent, it really depends what the source of the data is. The numbers from @S.S. seem to be Google Scholar, which includes not view "citations" that are not really citations, as it harvests all kinds of things and picks up references in things that are not even published (beyond being some pdf resembling a paper having been put up on the internet by somebody, or something like that). $\endgroup$
    – user9072
    Commented Mar 14, 2015 at 16:37
  • 8
    $\begingroup$ Google Scholar “citation” numbers are ridiculously inflated. Chances are a single citation in a paper will count as five if you put preprint versions of the paper on arXiv and on your institution website, and give talks about it on two workshops where you include the citation in the abstract. $\endgroup$
    – Emil Jeřábek
    Commented Mar 14, 2015 at 16:51

Not the answer you're looking for? Browse other questions tagged .