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Mathematics 1868–2008: a bibliometric analysis


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.

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    Usually linear or nonlinear regression fits the parameters of a model to the data points (method of least squares). In this context the value R 2 is called the coefficient of determination and quantifies the goodness of a fit. R 2 is a fraction between 0.0 and 1.0 without any units. As closer R 2 is coming to 1 as better the fit is describing the data. In this paper the representation and fitting of the data has been carried out by the Software "Grapher 7 " of the company Golden Software, Inc, Golden, Colorado, USA.


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Correspondence to Peter Luksch.

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Behrens, H., Luksch, P. Mathematics 1868–2008: a bibliometric analysis. Scientometrics 86, 179–194 (2011).

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  • Doubling Time
  • Multiple Authorship
  • Yearly Paper
  • Exponential Growth Model
  • Small Correction Factor