Growth rates of modern science: A bibliometric analysis based on the number of publications and cited references

Many studies in information science have looked at the growth of science. In this study, we re-examine the question of the growth of science. To do this we (i) use current data up to publication year 2012 and (ii) analyse it across all disciplines and also separately for the natural sciences and for the medical and health sciences. Furthermore, the data are analysed with an advanced statistical technique - segmented regression analysis - which can identify specific segments with similar growth rates in the history of science. The study is based on two different sets of bibliometric data: (1) The number of publications held as source items in the Web of Science (WoS, Thomson Reuters) per publication year and (2) the number of cited references in the publications of the source items per cited reference year. We have looked at the rate at which science has grown since the mid-1600s. In our analysis of cited references we identified three growth phases in the development of science, which each led to growth rates tripling in comparison with the previous phase: from less than 1% up to the middle of the 18th century, to 2 to 3% up to the period between the two world wars and 8 to 9% to 2012.

💡 Research Summary

The paper revisits the long‑standing question of how rapidly science has expanded by employing up‑to‑date bibliometric data and a sophisticated statistical technique. Using the Web of Science (WoS) database, the authors construct two complementary time series covering the period from the mid‑17th century to 2012: (1) the annual count of source items, i.e., publications indexed as “articles, reviews, or proceedings” in WoS, and (2) the annual count of cited references extracted from those source items, which serves as a proxy for the volume of earlier scientific work that contemporary papers acknowledge. The dual‑approach is intended to capture both the direct output of modern science (source items) and the indirect, historical footprint of earlier research (cited references), thereby mitigating the well‑known under‑coverage of pre‑1900 literature in citation databases.

To identify periods with distinct growth dynamics, the authors apply segmented (piecewise) regression analysis to the cited‑reference series. This method automatically detects breakpoints where the slope of the logarithmic growth curve changes, allowing the data themselves to define “growth phases” rather than imposing arbitrary intervals. The analysis reveals three statistically robust segments. The first, spanning roughly 1650 to the mid‑18th century, shows an annual growth rate of less than 1 %. This modest increase reflects the infancy of modern scholarly communication, limited printing capacity, and the concentration of research within a small elite. The second segment, from the mid‑18th century through the inter‑war period, exhibits a growth rate of 2–3 % per year. This acceleration coincides with the Industrial Revolution, the establishment of research universities and national laboratories, and the emergence of systematic scientific funding. The third and most dramatic segment, covering the post‑World‑War II era up to 2012, displays an annual growth rate of 8–9 %. This period corresponds to the “big bang” of contemporary science, driven by breakthroughs in electronics, computing, molecular biology, and nanotechnology, as well as massive expansion of research infrastructure worldwide.

The authors repeat the segmented regression separately for natural sciences and for medical & health sciences. Both fields follow the same three‑phase pattern, but the absolute growth rates are slightly higher in the medical & health domain, likely due to the rapid commercialization of biomedical technologies and the demographic pressure of aging populations that fuels research demand. Correlation analysis shows a strong relationship between the number of source items and the number of cited references, yet in the most recent decade the ratio of references per paper declines modestly, suggesting a shift toward shorter articles, greater reliance on data repositories, and evolving citation practices.

Limitations are candidly discussed. WoS is biased toward English‑language, science‑technology journals, so non‑English and humanities publications are under‑represented. Cited references, while useful for reconstructing historical activity, do not capture uncited but influential works or gray literature such as technical reports and conference proceedings. Moreover, segmented regression assumes linear trends within each segment, potentially overlooking abrupt, non‑linear shocks such as wars, economic crises, or pandemics.

Despite these caveats, the study provides a comprehensive, quantitative portrait of scientific growth over more than three and a half centuries. Its findings have practical implications: policymakers can use the identified acceleration points to anticipate future resource needs, research managers can benchmark institutional performance against global trends, and publishers can adjust editorial strategies in response to changing citation behaviors. The authors suggest that future work should incorporate additional databases (e.g., Scopus, Google Scholar) and broader document types to refine growth estimates and to explore geographic and disciplinary variations in greater depth.