IDEAS home Printed from https://ideas.repec.org/a/spr/scient/v86y2011i1d10.1007_s11192-010-0249-x.html
   My bibliography  Save this article

Mathematics 1868–2008: a bibliometric analysis

Author

Listed:
  • Heinrich Behrens
  • Peter Luksch

    (FIZ Karlsruhe)

Abstract

This paper presents a bibliometric analysis of the literature published in the field of mathematics from 1868 to date. The data originate from the Zentralblatt MATH database. The increase rate of publications per year reflects the growth of the mathematics community and both can well be represented by exponential or linear functions, the latter especially after the Second World War. The distribution of publications follows Bradford′s law but in contrast to many other disciplines there is no strong domination of a small number of journals. The productivity of authors follows two inverse power laws of the Lotka form with different parameters, one in the range of low productivity and the other in the range of high productivity. The average productivity has changed only slightly since the year 1870. As far as multiple authorship is concerned the distribution of the number of authors per publication can be described quite well by a Gamma Distribution. The average number of authors per publication has been increasing steadily; while it was close to 1 up to the first quarter of the last century it has now reached a value of 2 in the last few years. This means that the percentage of single-authored papers has fallen from over 95% in the years before 1930 to about 30% today.

Suggested Citation

  • Heinrich Behrens & Peter Luksch, 2011. "Mathematics 1868–2008: a bibliometric analysis," Scientometrics, Springer;Akadémiai Kiadó, vol. 86(1), pages 179-194, January.
    • Handle: RePEc:spr:scient:v:86:y:2011:i:1:d:10.1007_s11192-010-0249-x
    DOI: 10.1007/s11192-010-0249-x
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s11192-010-0249-x
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.
    File URL: https://libkey.io/10.1007/s11192-010-0249-x?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Reed, William J., 2001. "The Pareto, Zipf and other power laws," Economics Letters, Elsevier, vol. 74(1), pages 15-19, December.
    2. A. Bookstein, 1990. "Informetric distributions, part I: Unified overview," Journal of the American Society for Information Science, Association for Information Science & Technology, vol. 41(5), pages 368-375, July.
    3. Helmut A. Abt, 2007. "The future of single-authored papers," Scientometrics, Springer;Akadémiai Kiadó, vol. 73(3), pages 353-358, December.
    4. Helmut A. Abt, 2007. "The publication rate of scientific papers depends only on the number of scientists," Scientometrics, Springer;Akadémiai Kiadó, vol. 73(3), pages 281-288, December.
    5. R. Bailón-Moreno & E. Jurado-Alameda & R. Ruiz-Baños & J. P. Courtial, 2005. "Bibliometric laws: Empirical flaws of fit," Scientometrics, Springer;Akadémiai Kiadó, vol. 63(2), pages 209-229, April.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Chung-Souk Han, 2011. "On the demographical changes of U.S. research doctorate awardees and corresponding trends in research fields," Scientometrics, Springer;Akadémiai Kiadó, vol. 89(3), pages 845-865, December.
    2. Qurat-ul Ain & Hira Riaz & Muhammad Tanvir Afzal, 2019. "Evaluation of h-index and its citation intensity based variants in the field of mathematics," Scientometrics, Springer;Akadémiai Kiadó, vol. 119(1), pages 187-211, April.
    3. Günter Krampen & Alexander Eye & Gabriel Schui, 2011. "Forecasting trends of development of psychology from a bibliometric perspective," Scientometrics, Springer;Akadémiai Kiadó, vol. 87(3), pages 687-694, June.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Dimosthenis Kifokeris & Yiannis Xenidis, 2021. "Game Theory-Based Minimization of the Ostracism Risk in Construction Companies," Sustainability, MDPI, vol. 13(12), pages 1-20, June.
    2. Abramo, Giovanni & D'Angelo, Ciriaco Andrea & Di Costa, Flavia, 2019. "Diversification versus specialization in scientific research: Which strategy pays off?," Technovation, Elsevier, vol. 82, pages 51-57.
    3. Rafael González-Val & Arturo Ramos & Fernando Sanz-Gracia & María Vera-Cabello, 2015. "Size distributions for all cities: Which one is best?," Papers in Regional Science, Wiley Blackwell, vol. 94(1), pages 177-196, March.
    4. González-Val, Rafael, 2019. "Lognormal city size distribution and distance," Economics Letters, Elsevier, vol. 181(C), pages 7-10.
    5. Fabio Fiorillo & Agnese Sacchi, 2012. "The Political Economy of the Standard Level of Services: The Role of Income Distribution," CESifo Working Paper Series 3696, CESifo.
    6. Mario V. Tomasello & Mauro Napoletano & Antonios Garas & Frank Schweitzer, 2017. "The rise and fall of R&D networks," Industrial and Corporate Change, Oxford University Press and the Associazione ICC, vol. 26(4), pages 617-646.
    7. Hajargasht, Gholamreza & Griffiths, William E., 2013. "Pareto–lognormal distributions: Inequality, poverty, and estimation from grouped income data," Economic Modelling, Elsevier, vol. 33(C), pages 593-604.
    8. Keiichi Kishi, 2016. "Technology Diffusion, Pareto Distribution, and Patent Policy," Discussion Papers in Economics and Business 16-31, Osaka University, Graduate School of Economics.
    9. Josh Yamamoto & Eitan Frachtenberg, 2022. "Gender Differences in Collaboration Patterns in Computer Science," Publications, MDPI, vol. 10(1), pages 1-21, February.
    10. Alex Coad, 2010. "The Exponential Age Distribution and the Pareto Firm Size Distribution," Journal of Industry, Competition and Trade, Springer, vol. 10(3), pages 389-395, September.
    11. de Wit, Gerrit, 2005. "Firm size distributions: An overview of steady-state distributions resulting from firm dynamics models," International Journal of Industrial Organization, Elsevier, vol. 23(5-6), pages 423-450, June.
    12. Ji Hyung Lee & Yuya Sasaki & Alexis Akira Toda & Yulong Wang, 2022. "Capital and Labor Income Pareto Exponents in the United States, 1916-2019," Papers 2206.04257, arXiv.org.
    13. Toda, Alexis Akira, 2019. "Wealth distribution with random discount factors," Journal of Monetary Economics, Elsevier, vol. 104(C), pages 101-113.
    14. Jess Benhabib & Alberto Bisin, 2018. "Skewed Wealth Distributions: Theory and Empirics," Journal of Economic Literature, American Economic Association, vol. 56(4), pages 1261-1291, December.
    15. repec:hal:wpspec:info:hdl:2441/f6h8764enu2lskk9p5487a6cm is not listed on IDEAS
    16. Nikolay K. Vitanov & Marcel Ausloos, 2015. "Test of two hypotheses explaining the size of populations in a system of cities," Journal of Applied Statistics, Taylor & Francis Journals, vol. 42(12), pages 2686-2693, December.
    17. Keith Head & Thierry Mayer & Mathias Thoenig, 2014. "Welfare and Trade without Pareto," American Economic Review, American Economic Association, vol. 104(5), pages 310-316, May.
    18. Wright, Ian, 2009. "Implicit Microfoundations for Macroeconomics," Economics - The Open-Access, Open-Assessment E-Journal (2007-2020), Kiel Institute for the World Economy (IfW Kiel), vol. 3, pages 1-27.
    19. Soo, Kwok Tong, 2005. "Zipf's Law for cities: a cross-country investigation," Regional Science and Urban Economics, Elsevier, vol. 35(3), pages 239-263, May.
    20. Mundt, Philipp & Alfarano, Simone & Milaković, Mishael, 2020. "Exploiting ergodicity in forecasts of corporate profitability," Journal of Economic Dynamics and Control, Elsevier, vol. 111(C).
    21. Massimiliano Zanin & David Papo & Miguel Romance & Regino Criado & Santiago Moral, 2016. "The topology of card transaction money flows," Papers 1605.04938, arXiv.org.

    More about this item

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:spr:scient:v:86:y:2011:i:1:d:10.1007_s11192-010-0249-x. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.