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Mathematics 1868–2008: a bibliometric analysis

Author

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  • 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
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    References listed on IDEAS

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    1. Helmut A. Abt, 2007. "The future of single-authored papers," Scientometrics, Springer;Akadémiai Kiadó, vol. 73(3), pages 353-358, December.
    2. 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.
    3. Reed, William J., 2001. "The Pareto, Zipf and other power laws," Economics Letters, Elsevier, vol. 74(1), pages 15-19, December.
    4. 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.
    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.
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    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.

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