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.
Abt, H. A. (2007a). The publication rate of scientific papers depends only on the number of scientists. Scientometrics, 73, 281–288.
Abt, H. A. (2007b). The future of single-authored papers. Scientometrics, 73, 353–358.
Ajiferuke, I., Burrell, Q. L., & Tague, J. (1988). Collaborative coefficient: A single measure of the degree of collaboration in research. Scientometrics, 14(5–6), 421–433.
Bailón-Moreno, R., Jurado-Almeda, E., Ruiz-Banos, R., & Courtial, J. P. (2005). Bibliometric laws: Empirical flaws of fit. Scientometrics, 63, 209–229.
Barth, A., & Marx, W. (2008). Mapping high temperature superconductors—a scientometric approach. Journal of Superconductivity and Novel Magnetism, 21, 113–128.
Behrens, H., & Genz, H. (2008). Von den ersten Periodika zur Paper-Flut. Physik Journal, 7, 28–31.
Behrens, H., & Lankenau, I. (2006). Wissenschaftswachstum in wichtigen naturwissenschaftlichen Disziplinen vom 17. Bis zum 21. Jahrhundert. Berichte zur Wissenschaftsgeschichte, 29, 89–108.
Behrens, H., & Luksch, P. (2006). A bibliometric study in crystallography. Acta Crystallographica B, 62, 993–1001.
Bookstein, A. (1990). Informetric distributions, part I: Unified overview. Journal of the American Society for Information Science, 41, 368–375.
Bradford, S. C. (1934). Sources of information on specific subjects. Engineering, 137, 85–86.
Furner, J. (2003). Little book, big book: Before and after little science, big science: A review article, Part I and II. Journal of Librarianship and Information, 35, 115–125. (189–201).
Glänzel, W. (2002). Co-authorship patterns and trends in the sciences (1980–1998), a bibliometric study with implications for database indexing and search strategies. Library Trends, 50(3), 461–473.
Leimkühler, F. F. (1967). The Bradford distribution. Journal of Documentation, 23, 197–207.
Lotka, A. J. (1926). The frequency distribution of scientific productivity. Journal of the Washington Academy of Sciences, 16, 317–323.
May, K. O. (1966). Quantitative growth of the mathematical literature. Science, 154, 1672–1673.
Perline, R. (2005). Strong, weak, and false inverse power laws. Statistical Science, 20, 68–88.
Person, O., Glänzel, W., & Daniel, R. (2004). Inflationary bibliometric values: The role of scientific collaboration and the need for relative indicators in evaluative studies. Scientometrics, 60, 421–432.
Price, D. J. D. (1963). Little science, big science. New York: Columbia University Press.
Price, D. D., & Gürsey, S. (1976). Studies in scientometrics. Part 1. Transience and continuance in scientific authorship. International Forum on Information, and Documentation, 1(2), 17–24.
Rao, I. K. R. (1995). A stochastic approach to analysis of distribution of papers in mathematics: Lotka’s law revisited. In M. Koenig & A. Bookstein (Eds.), Proceedings of the International Society for Scientometrics and Informetrics, pp. 455–464.
Reed, W. J. (2001). The Pareto, Zipf and other power laws. Economics Letters, 74, 15–19.
Rousseau, R. (1994). Bradford curves. Information Processing and Management, 30(2), 267–277.
Saxena, A., Gupta, B. M., & Jauhari, M. (2001). Forecasting growth of literature: All models are wrong, some are useful. In M. Davis & C. S. Wilson (Eds.), Proceedings of the International Conference on Scientometrics and Informetrics, Sydney Australia, pp. 647–653.
Wagner-Döbler, R. (1995). Where has the cumulative advantage gone? Some observations about the frequency distribution of scientific productivity, of duration of scientific participation, and of speed of publication. Scientometrics, 32, 123–132.
Wagner-Döbler, R. (1996). Two components of a casual explanation of Bradford′s law. Journal of Information Science, 22, 125–132.
Wagner-Döbler, R. (1997a). Science-technology coupling: The case of mathematical logic and computer science. Journal of the American Association for Information Science, 48, 171–183.
Wagner-Döbler, R. (1997b). Wachstumszyklen technisch-wissenschaftlicher Kreativität. Eine quantitative Studie unter besonderer Beachtung der Mathematik. Frankfurt am Main/New York: Campus Verlag.
Wagner-Döbler, R., & Berg, J. (1995). The dependence of Lotka′s Law on the selection of time periods in the development of scientific areas and authors. Journal of Documentation, 51, 28–43.
Wagner-Döbler, R., & Berg, J. (1996). Nineteenth-century mathematics in the mirror of its literature. A quantitative approach. Historia Mathematica, 23, 288–318.
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Behrens, H., Luksch, P. Mathematics 1868–2008: a bibliometric analysis. Scientometrics 86, 179–194 (2011). https://doi.org/10.1007/s11192-010-0249-x
- Doubling Time
- Multiple Authorship
- Yearly Paper
- Exponential Growth Model
- Small Correction Factor