## Main

Although the past century witnessed an unprecedented expansion of scientific and technological knowledge, there are concerns that innovative activity is slowing18,19,20. Studies document declining research productivity in semiconductors, pharmaceuticals and other fields10,11. Papers, patents and even grant applications have become less novel relative to prior work and less likely to connect disparate areas of knowledge, both of which are precursors of innovation21,22. The gap between the year of discovery and the awarding of a Nobel Prize has also increased23,24, suggesting that today’s contributions do not measure up to the past. These trends have attracted increasing attention from policymakers, as they pose substantial threats to economic growth, human health and wellbeing, and national security, along with global efforts to combat grand challenges such as climate change25,26.

Numerous explanations for this slowdown have been proposed. Some point to a dearth of ‘low-hanging fruit’ as the readily available productivity-enhancing innovations have already been made19,27. Others emphasize the increasing burden of knowledge; scientists and inventors require ever more training to reach the frontiers of their fields, leaving less time to push those frontiers forward18,28. Yet much remains unknown, not merely about the causes of slowing innovative activity, but also the depth and breadth of the phenomenon. The decline is difficult to reconcile with centuries of observation by philosophers of science, who characterize the growth of knowledge as an endogenous process, wherein previous knowledge enables future discovery, a view captured famously in Newton’s observation that if he had seen further, it was by ‘standing on the shoulders of giants’3. Moreover, to date, the evidence pointing to a slowdown is based on studies of particular fields, using disparate and domain-specific metrics10,11, making it difficult to know whether the changes are happening at similar rates across areas of science and technology. Little is also known about whether the patterns seen in aggregate indicators mask differences in the degree to which individual works push the frontier.

We address these gaps in understanding by analysing 25 million papers (1945–2010) in the Web of Science (WoS) (Methods) and 3.9 million patents (1976–2010) in the United States Patent and Trademark Office’s (USPTO) Patents View database (Methods). The WoS data include 390 million citations, 25 million paper titles and 13 million abstracts. The Patents View data include 35 million citations, 3.9 million patent titles and 3.9 million abstracts. Subsequently, we replicate our core findings on four additional datasets—JSTOR, the American Physical Society corpus, Microsoft Academic Graph and PubMed—encompassing 20 million papers. Using these data, we join a new citation-based measure12 with textual analyses of titles and abstracts to understand whether papers and patents forge new directions over time and across fields.

## Measurement of disruptiveness

To characterize the nature of innovation, we draw on foundational theories of scientific and technological change2,29,30, which distinguish between two types of breakthroughs. First, some contributions improve existing streams of knowledge, and therefore consolidate the status quo. Kohn and Sham (1965)31, a Nobel-winning paper used established theorems to develop a method for calculating the structure of electrons, which cemented the value of previous research. Second, some contributions disrupt existing knowledge, rendering it obsolete, and propelling science and technology in new directions. Watson and Crick (1953)32, also a Nobel winner, introduced a model of the structure of DNA that superseded previous approaches (for example, Pauling’s triple helix). Kohn and Sham and Watson and Crick were both important, but their implications for scientific and technological change were different.

We quantify this distinction using a measure—the CD index12—that characterizes the consolidating or disruptive nature of science and technology (Fig. 1). The intuition is that if a paper or patent is disruptive, the subsequent work that cites it is less likely to also cite its predecessors; for future researchers, the ideas that went into its production are less relevant (for example, Pauling’s triple helix). If a paper or patent is consolidating, subsequent work that cites it is also more likely to cite its predecessors; for future researchers, the knowledge upon which the work builds is still (and perhaps more) relevant (for example, the theorems Kohn and Sham used). The CD index ranges from −1 (consolidating) to 1 (disruptive). We measure the CD index five years after the year of each paper’s publication (indicated by CD5, see Extended Data Fig. 1 for the distribution of CD5 among papers and patents and Extended Data Fig. 2 for analyses using alternative windows)33. For example, Watson and Crick and Kohn and Sham both received over a hundred citations within five years of being published. However, the Kohn and Sham paper has a CD5 of −0.22 (indicating consolidation), whereas the Watson and Crick paper has a CD5 of 0.62 (indicating disruption). The CD index has been validated extensively in previous research, including through correlation with expert assessments12,34.

## Declining disruptiveness

Across fields, we find that science and technology are becoming less disruptive. Figure 2 plots the average CD5 over time for papers (Fig. 2a) and patents (Fig. 2b). For papers, the decrease between 1945 and 2010 ranges from 91.9% (where the average CD5 dropped from 0.52 in 1945 to 0.04 in 2010 for ‘social sciences’) to 100% (where the average CD5 decreased from 0.36 in 1945 to 0 in 2010 for ‘physical sciences’); for patents, the decrease between 1980 and 2010 ranges from 78.7% (where the average CD5 decreased from 0.30 in 1980 to 0.06 in 2010 for ‘computers and communications’) to 91.5% (where the average CD5 decreased from 0.38 in 1980 to 0.03 in 2010 for ‘drugs and medical’). For both papers and patents, the rates of decline are greatest in the earlier parts of the time series, and for patents, they appear to begin stabilizing between the years 2000 and 2005. For papers, since about 1980, the rate of decline has been more modest in ‘life sciences and biomedicine’ and physical sciences, and most marked and persistent in social sciences and ‘technology’. Overall, however, relative to earlier eras, recent papers and patents do less to push science and technology in new directions. The general similarity in trends we observe across fields is noteworthy in light of ‘low-hanging fruit’ theories19,27, which would probably predict greater heterogeneity in the decline, as it seems unlikely fields would ‘consume’ their low-hanging fruit at similar rates or times.

## Linguistic change

The decline in disruptive science and technology is also observable using alternative indicators. Because they create departures from the status quo, disruptive papers and patents are likely to introduce new words (for example, words used to create a new paradigm might differ from those that are used to develop an existing paradigm)35,36. Therefore, if disruptiveness is declining, we would expect a decline in the diversity of words used in science and technology. To evaluate this, Fig. 3a,d documents the type-token ratio (that is, unique/total words) of paper and patent titles over time (Supplementary Information section 1). We observe substantial declines, especially in the earlier periods, before 1970 for papers and 1990 for patents. For paper titles (Fig. 3a), the decrease (1945–2010) ranges from 76.5% (social sciences) to 88% (technology); for patent titles (Fig. 3d), the decrease (1980–2010) ranges from 32.5% (chemical) to 81% (computers and communications). For paper abstracts (Extended Data Fig. 3a), the decrease (1992–2010) ranges from 23.1% (life sciences and biomedicine) to 38.9% (social sciences); for patent abstracts (Extended Data Fig. 3b), the decrease (1980–2010) ranges from 21.5% (mechanical) to 73.2% (computers and communications). In Fig. 3b,e, we demonstrate that these declines in word diversity are accompanied by similar declines in combinatorial novelty; over time, the particular words that scientists and inventors use in the titles of their papers and patents are increasingly likely to have been used together in the titles of previous work. Consistent with these trends in language, we also observe declining novelty in the combinations of previous work cited by papers and patents, based on a previously established measure of ‘atypical combinations’14 (Extended Data Fig. 4).

The decline in disruptive activity is also apparent in the specific words used by scientists and inventors. If disruptiveness is declining, we reasoned that verbs alluding to the creation, discovery or perception of new things should be used less frequently over time, whereas verbs alluding to the improvement, application or assessment of existing things may be used more often35,36. Figure 3 shows the most common verbs in paper (Fig. 3c) and patent titles (Fig. 3f) in the first and last decade of each sample (Supplementary Information section 2). Although precisely and quantitatively characterizing words as ‘consolidating’ or ‘disruptive’ is challenging in the absence of context, the figure highlights a clear and qualitative shift in language. In the earlier decades, verbs evoking creation (for example, ‘produce’, ‘form’, ‘prepare’ and ‘make’), discovery (for example, ‘determine’ and ‘report’) and perception (for example, ‘measure’) are prevalent in both paper and patent titles. In the later decades, however, these verbs are almost completely displaced by those tending to be more evocative of the improvement (for example, ‘improve’, ‘enhance’ and ‘increase’), application (for example, ‘use’ and ‘include’) or assessment (for example, ‘associate’, ‘mediate’ and ‘relate’) of existing scientific and technological knowledge and artefacts. Taken together, these patterns suggest a substantive shift in science and technology over time, with discovery and invention becoming less disruptive in nature, consistent with our results using the CD index.

## Conservation of highly disruptive work

The aggregate trends we document mask considerable heterogeneity in the disruptiveness of individual papers and patents and remarkable stability in the absolute number of highly disruptive works (Methods and Fig. 4). Specifically, despite large increases in scientific productivity, the number of papers and patents with CD5 values in the far right tail of the distribution remains nearly constant over time. This ‘conservation’ of the absolute number of highly disruptive papers and patents holds despite considerable churn in the underlying fields responsible for producing those works (Extended Data Fig. 5, inset). These results suggest that the persistence of major breakthroughs—for example, measurement of gravity waves and COVID-19 vaccines—is not inconsistent with slowing innovative activity. In short, declining aggregate disruptiveness does not preclude individual highly disruptive works.

## Alternative explanations

What is driving the decline in disruptiveness? Earlier, we suggested our results are not consistent with explanations that link slowing innovative activity to diminishing ‘low-hanging fruit’. Extended Data Fig. 5 shows that the decline in disruptiveness is unlikely to be due to other field-specific factors by decomposing variation in CD5 attributable to field, author and year effects (Methods).

Declining rates of disruptive activity are unlikely to be caused by the diminishing quality of science and technology22,37. If they were, then the patterns seen in Fig. 2 should be less visible in high-quality work. However, when we restrict our sample to articles published in premier publication venues such as Nature, Proceedings of the National Academy of Sciences and Science or to Nobel-winning discoveries38 (Fig. 5), the downward trend persists.

Furthermore, the trend is not driven by characteristics of the WoS and UPSTO data or our particular derivation of the CD index; we observe similar declines in disruptiveness when we compute CD5 on papers in JSTOR, the American Physical Society corpus, Microsoft Academic Graph and PubMed (Methods), the results of which are shown in Extended Data Fig. 6. We further show that the decline is not an artefact of the CD index by reporting similar patterns using alternative derivations13,15 (Methods and Extended Data Fig. 7).

Declines in disruptiveness are also not attributable to changing publication, citation or authorship practices (Methods). First, using approaches from the bibliometrics literature39,40,41,42,43, we computed several normalized versions of the CD index that adjusted for the increasing tendency for papers and patents to cite previous work44,45. Results using these alternative indicators (Extended Data Fig. 8a,d) were similar to those we reported in Fig. 2. Second, using regression, we estimated models of CD5 as a function of indicator variables for each paper or patent’s publication year, along with specific controls for field × year level—number of new papers/patents, mean number of papers/patents cited, mean number of authors or inventors per paper—and paper or patent-level—number of papers or patents cited—factors. Predictions from these models indicated a decline in disruptive papers and patents (Extended Data Fig. 8b,e and Supplementary Table 1) that was consistent with our main results. Finally, using Monte Carlo simulations, we randomly rewired the observed citation networks while preserving key characteristics of scientists’ and inventors’ citation behaviour, including the number of citations made and received by individual papers and patents and the age gap between citing and cited works. We find that observed CD5 values are lower than those from the simulated networks (Extended Data Fig. 8c,f), and the gap is widening: over time, papers and patents are increasingly less disruptive than would be expected by chance. Taken together, these additional analyses indicate that the decline in CD5 is unlikely to be driven by changing publication, citation or authorship practices.

## Growth of knowledge and disruptiveness

We also considered how declining disruptiveness relates to the growth of knowledge (Extended Data Fig. 9). On the one hand, scientists and inventors face an increasing knowledge burden, which may inhibit discoveries and inventions that disrupt the status quo. On the other hand, as previously noted, philosophers of science suggest that existing knowledge fosters discovery and invention3,6,7. Using regression models, we evaluated the relationship between the stock of papers and patents (a proxy for knowledge) within fields and their CD5 (Supplementary Information section 3 and Supplementary Table 2). We find a positive effect of the growth of knowledge on disruptiveness for papers, consistent with previous work20; however, we find a negative effect for patents.

Given these conflicting results, we considered the possibility that the availability of knowledge may differ from its use. In particular, the growth in publishing and patenting may lead scientists and inventors to focus on narrower slices of previous work18,46, thereby limiting the ‘effective’ stock of knowledge. Using three proxies, we document a decline in the use of previous knowledge among scientists and inventors (Fig. 6). First, we see a decline in the diversity of work cited (Fig. 6a,d), indicating that contemporary science and technology are engaging with narrower slices of existing knowledge. Moreover, this decline in diversity is accompanied by an increase in the share of citations to the 1% most highly cited papers and patents (Fig. 6a (i),d(i)), which are also decreasing in semantic diversity (Fig. 6a (ii),d (ii)). Over time, scientists and inventors are increasingly citing the same previous work, and that previous work is becoming more topically similar. Second, we see an increase in self-citation (Fig. 6b,e), a common proxy for the continuation of one’s pre-existing research stream47,48,49, which is consistent with scientists and inventors relying more on highly familiar knowledge. Third, the mean age of work cited, a common measure for the use of dated knowledge50,51,52, is increasing (Fig. 6c,f), suggesting that scientists and inventors may be struggling to keep up with the pace of knowledge expansion and instead relying on older, familiar work. All three indicators point to a consistent story: a narrower scope of existing knowledge is informing contemporary discovery and invention.

Results from a subsequent series of regression models suggest that use of less diverse work, more of one’s own work and older work are all negatively associated with disruption (Methods, Extended Data Table 1 and Supplementary Table 3), a pattern that holds even after accounting for the average age and number of previous works produced by team members. When the range of work used by scientists and inventors narrows, disruptive activity declines.

## Discussion

In summary, we report a marked decline in disruptive science and technology over time. Our analyses show that this trend is unlikely to be driven by changes in citation practices or the quality of published work. Rather, the decline represents a substantive shift in science and technology, one that reinforces concerns about slowing innovative activity. We attribute this trend in part to scientists’ and inventors’ reliance on a narrower set of existing knowledge. Even though philosophers of science may be correct that the growth of knowledge is an endogenous process—wherein accumulated understanding promotes future discovery and invention—engagement with a broad range of extant knowledge is necessary for that process to play out, a requirement that appears more difficult with time. Relying on narrower slices of knowledge benefits individual careers53, but not scientific progress more generally.

Moreover, even though the prevalence of disruptive works has declined, we find that the sheer number has remained stable. On the one hand, this result may suggest that there is a fixed ‘carrying capacity’ for highly disruptive science and technology, in which case, policy interventions aimed at increasing such work may prove challenging. On the other hand, our observation of considerable churn in the underlying fields responsible for producing disruptive science and technology suggests the potential importance of factors such as the shifting interests of funders and scientists and the ‘ripeness’ of scientific and technologicalknowledge for breakthroughs, in which case the production of disruptive work may be responsive to policy levers. In either case, the stability we observe in the sheer number of disruptive papers and patents suggests that science and technology do not appear to have reached the end of the ‘endless frontier’. Room remains for the regular rerouting that disruptive works contribute to scientific and technological progress.

Our study is not without limitations. Notably, even though research to date supports the validity of the CD index12,34, it is a relatively new indicator of innovative activity and will benefit from future work on its behaviour and properties, especially across data sources and contexts. Studies that systematically examine the effect of different citation practices54,55, which vary across fields, would be particularly informative.

Overall, our results deepen understanding of the evolution of knowledge and may guide career planning and science policy. To promote disruptive science and technology, scholars may be encouraged to read widely and given time to keep up with the rapidly expanding knowledge frontier. Universities may forgo the focus on quantity, and more strongly reward research quality56, and perhaps more fully subsidize year-long sabbaticals. Federal agencies may invest in the riskier and longer-term individual awards that support careers and not simply specific projects57, giving scholars the gift of time needed to step outside the fray, inoculate themselves from the publish or perish culture, and produce truly consequential work. Understanding the decline in disruptive science and technology more fully permits a much-needed rethinking of strategies for organizing the production of science and technology in the future.

## Methods

### WoS data

We limit our focus to research papers published between 1945 and 2010. Although the WoS data begin in the year 1900, the scale and social organization of science shifted markedly in the post-war era, thereby making comparisons with the present difficult and potentially misleading67,68,69. We end our analyses of papers in 2010 because some of our measures require several subsequent years of data following paper publication. The WoS data archive 65 million documents published in 28,968 journals between 1900 and 2017 and 735 million citations among them. In addition, the WoS data include the titles and the full text of abstracts for 65 and 29 million records, respectively, published between 1913 and 2017. After eliminating non-research documents (for example, book reviews and commentaries) and subsetting the data to the 1945–2010 window, the analytical sample consists of n = 24,659,076 papers.

### Patents View data

We limit our focus to patents granted from 1976, which is the earliest year for which machine-readable records are available in the Patents View data. As we did with papers, we end our analyses in 2010 because some measures require data from subsequent years for calculation. The Patents View data are the most exhaustive source of historical data on inventions, with information on 6.5 million patents granted between 1976 and 2017 and their corresponding 92 million citations. The Patents View data include the titles and abstracts for 6.5 million patents granted between 1976 and 2017. Following previous work12, we focused our attention on utility patents, which cover the vast majority (91% in our data) of patented inventions. After eliminating non-utility patents and subsetting the data to the 1976–2010 window, the analytical sample consists of n = 3,912,353 patents.

### Highly disruptive papers and patents

Observations (and claims) of slowing progress in science and technology are increasingly common, supported not only by the evidence we report, but also by previous research from diverse methodological and disciplinary perspectives10,11,18,19,20,21,22,23,24. Yet as noted in the main text, there is a tension between observations of slowing progress from aggregate data on the one hand, and continuing reports of seemingly major breakthroughs in many fields of science and technology—spanning everything from the measurement of gravity waves to the sequencing of the human genome—on the other. In an effort to reconcile this tension, we considered the possibility that whereas overall, discovery and invention may be less disruptive over time, the high-level view taken in previous work may mask considerable heterogeneity. Put differently, aggregate evidence of slowing progress does not preclude the possibility that some subset of discoveries and inventions is highly disruptive.

To evaluate this possibility, we plot the number of disruptive papers (Fig. 4a) and patents (Fig. 4b) over time, where disruptive papers and patents are defined as those with CD5 values >0. Within each panel, we plot four lines, corresponding to four evenly spaced intervals—(0, 0.25], (0.25, 0.5], (0.5, 0.75], (0.75, 1.00]—over the positive values of CD5. The first two intervals therefore correspond to papers and patents that are relatively weakly disruptive, whereas the latter two correspond to those that are more strongly so (for example, where we may expect to see major breakthroughs such as some of those mentioned above). Despite major increases in the numbers of papers and patents published each year, we see little change in the number of highly disruptive papers and patents, as evidenced by the relatively flat red, green and orange lines. Notably, this ‘conservation’ of disruptive work holds even despite fluctuations over time in the composition of the scientific and technological fields responsible for producing the most disruptive work (Fig. 4, inset plots). Overall, these results help to account for simultaneous observations of both major breakthroughs in many fields of science and technology and aggregate evidence of slowing progress.

### Relative contribution of field, year and author or inventor effects

Our results show a steady decline in the disruptiveness of science and technology over time. Moreover, the patterns we observe are generally similar across broad fields of study, which suggests that the factors driving the decline are not unique to specific domains of science and technology. The decline could be driven by other factors, such as the conditions of science and technology at a point in time or the particular individuals who produce science and technology. For example, exogenous factors such as economic conditions may encourage research or invention practices that are less disruptive. Similarly, scientists and inventors of different generations may have different approaches, which may result in greater or lesser tendencies for producing disruptive work. We therefore sought to understand the relative contribution of field, year and author (or inventor) factors to the decline of disruptive science and technology.

To do so, we decomposed the relative contribution of field, year and author fixed effects to the predictive power of regression models of the CD index. The unit of observation in these regressions is the author (or inventor) × year. We enter field fixed effects using granular subfield indicators (that is, 150 WoS subject areas for papers, 138 NBER subcategories for patents). For simplicity, we did not include additional covariates beyond the fixed effects in our models. Field fixed effects capture all field-specific factors that do not vary by author or year (for example, the basic subject matter); year fixed effects capture all year-specific factors that do not vary by field or author (for example, the state of communication technology); author (or inventor) fixed effects capture all author-specific factors that do not vary by field or year (for example, the year of PhD awarding). After specifying our model, we determine the relative contribution of field, year and author fixed effects to the overall model adjusted R2 using Shapley–Owen decomposition. Specifically, given our n = 3 groups of fixed effects (field, year and author) we evaluate the relative contribution of each set of fixed effects by estimating the adjusted R2 separately for the 2n models using subsets of the predictors. The relative contribution of each set of fixed effects is then computed using the Shapley value from game theory70.

Results of this analysis are shown in Extended Data Fig. 5, for both papers (top bar) and patents (bottom bar). Total bar size corresponds to the value of the adjusted R2 for the fully specified model (that is, with all three groups of fixed effects). Consistent with our observations from plots of the CD index over time, we observe that for both papers and patents, field-specific factors make the lowest relative contribution to the adjusted R2 (0.02 and 0.01 for papers and patents, respectively). Author fixed effects, by contrast, appear to contribute much more to the predictive power of the model, for both papers (0.20) and patents (0.17). Researchers and inventors who entered the field in more recent years may face a higher burden of knowledge and thus resort to building on narrower slices of existing work (for example, because of more specialized doctoral training), which would generally lead to less disruptive science and technology being produced in later years, consistent with our findings. The pattern is more complex for year fixed effects; although year-specific factors that do not vary by field or author hold more explanatory power than field for both papers (0.02) and patents (0.16), they appear to be substantially more important for the latter than the former. Taken together, these findings suggest that relatively stable factors that vary across individual scientists and inventors may be particularly important for understanding changes in disruptiveness over time. The results also confirm that domain-specific factors across fields of science and technology play a very small role in explaining the decline in disruptiveness of papers and patents.

### Alternative bibliometric measures

Several recent papers have introduced alternative specifications of the CD index12. We evaluated whether the declines in disruptiveness we observe are corroborated using two alternative variations. One criticism of the CD index has been that the number of papers that cite only the focal paper’s references dominates the measure13. Bornmann et al.13 proposes $${{\rm{DI}}}_{l}^{{\rm{nok}}}$$ as a variant that is less susceptible to this issue. Another potential weakness of the CD index is that it could be very sensitive to small changes in the forward citation patterns of papers that make no backward citations15. Leydesdorff et al.15 suggests DI* as an alternate indicator of disruption that addresses this issue. Therefore, we calculated $${{\rm{DI}}}_{l}^{{\rm{nok}}}$$ where l = 5 and DI* for 100,000 randomly drawn papers and patents each from our analytic sample. Results are presented in Extended Data Fig. 7a (papers) and b (patents). The blue lines indicate disruption based on Bornmann et al.13 and the orange lines indicate disruption based on Leydesdorff et al.15. Across science and technology, the two alternative measures both show declines in disruption over time, similar to the patterns observed with the CD index. Taken together, these results suggest that the declines in disruption we document are not an artefact of our particular operationalization.

### Robustness to changes in publication, citation and authorship practices

We also considered whether our results may be attributable to changes in publication, citation or authorship practices, rather than by substantive shifts in discovery and invention. Perhaps most critically, as noted in the main text, there has been a marked expansion in publishing and patenting over the period of our study. This expansion has naturally increased the amount of previous work that is relevant to current science and technology and therefore at risk of being cited, a pattern reflected in the marked increase in the average number of citations made by papers and patents (that is, papers and patents are citing more previous work than in previous eras)44,45. Recall that the CD index quantifies the degree to which future work cites a focal work together with its predecessors (that is, the references in the bibliography of the focal work). Greater citation of a focal work independently of its predecessors is taken to be evidence of a social process of disruption. As papers and patents cite more previous work, however, the probability of a focal work being cited independently of its predecessors may decline mechanically; the more citations a focal work makes, the more likely future work is to cite it together with one of its predecessors, even by chance. Consequently, increases in the number of papers and patents available for citing and in the average number of citations made by scientists and inventors may contribute to the declining values of the CD index. In short, given the marked changes in science and technology over our long study window, the CD index of papers and patents published in earlier periods may not be directly comparable to those of more recent vintage, which could in turn render our conclusions about the decline in disruptive science and technology suspect. We addressed these concerns using three distinctive but complementary approaches—normalization, regression adjustment and simulation.

#### Verification using normalization

First, following common practice in bibliometric research39,40,41,42,43, we developed two normalized versions of the CD index, with the goal of facilitating comparisons across time. Among the various components of the CD index, we focused our attention on the count of papers or patents that only cite the focal work’s references (Nk), as this term would seem most likely to scale with the increases in publishing and patenting and in the average number of citations made by papers and patents to previous work13. Larger values of Nk lead to smaller values of the CD index. Consequently, marked increases in Nk over time, particularly relative to other components of the measure, may lead to a downward bias, thereby inhibiting our ability to accurately compare disruptive science and technology in later years with earlier periods.

Our two normalized versions of the CD index aim to address this potential bias by attenuating the effect of increases in Nk. In the first version, which we call ‘Paper normalized’, we subtract from Nk the number of citations made by the focal paper or patent to previous work (Nb). The intuition behind this adjustment is that when a focal paper or patent cites more previous work, Nk is likely to be larger because there are more opportunities for future work to cite the focal paper or patent’s predecessors. This increase in Nk would result in lower values of the CD index, although not necessarily as a result of the focal paper or patent being less disruptive. In the second version, which we call ‘field × year normalized’, we subtract Nk by the average number of backward citations made by papers or patents in the focal paper or patent’s WoS research area or NBER technology category, respectively, during its year of publication (we label this quantity $${N}_{{\rm{b}}}^{{\rm{m}}{\rm{e}}{\rm{a}}{\rm{n}}}$$). The intuition behind this adjustment is that in fields and time periods in which there is a greater tendency for scientists and inventors to cite previous work, Nk is also likely to be larger, thereby leading to lower values of the CD index, although again not necessarily as a result of the focal paper or patent being less disruptive. In cases in which either Nb or $${N}_{{\rm{b}}}^{{\rm{m}}{\rm{e}}{\rm{a}}{\rm{n}}}$$ exceed the value of Nk, we set Nk to 0 (that is, Nk is never negative in the normalized measures). Both adaptations of the CD index are inspired by established approaches in the scientometrics literature, and may be understood as a form of ‘citing side normalization’ (that is, normalization by correcting for the effect of differences in lengths of references lists)40.

In Extended Data Fig. 8, we plot the average values of both normalized versions of the CD index over time, separately for papers (Extended Data Fig. 8a) and patents (Extended Data Fig. 8d). Consistent with our findings reported in the main text, we continue to observe a decline in the CD index over time, suggesting that the patterns we observe in disruptive science and technology are unlikely to be driven by changes in citation practices.

#### Verification using regression adjustment

Second, we adjusted for potential confounding using a regression-based approach. This approach complements the bibliometric normalizations just described by allowing us to account for a broader array of changes in publication, citation and authorship practices in general (the latter of which is not directly accounted for in either the normalization approach or the simulation approach described next), and increases the amount of previous work that is relevant to current science and technology in particular. In Supplementary Table 1, we report the results of regression models predicting CD5 for papers (Models 1–4) and patents (Models 5–8), with indicator variables included for each year of our study window (the reference categories are 1945 and 1980 for papers and patents, respectively). Models 1 and 4 are the baseline models, and include no other adjustments beyond the year indicators. In Models 2 and 5, we add subfield fixed effects (WoS subject areas for papers and NBER technology subcategories for patents). Finally, in Models 3–4 and 7–8, we add control variables for several field × year level—number of new papers orpatents, mean number of papers or patents cited, mean number of authors or inventors per paper—and paper- or patent-level—number of papers or patents cited—characteristics, thereby enabling more robust comparisons in patterns of disruptive science and technology over the long time period spanned by our study. For the paper models, we also include a paper-level control for the number of unlinked references (that is, the number of citations to works that are not indexed in WoS). We find that the inclusion of these controls improves model fit, as indicated by statistically significant Wald tests presented below the relevant models.

Across all eight models shown in Supplementary Table 1, we find that the coefficients on the year indicators are statistically significant and negative, and growing in magnitude over time, which is consistent with the patterns we reported based on unadjusted CD5 values index in the main text (Fig. 2). In Extended Data Fig. 8, we visualize the results of our regression-based approach by plotting the predicted CD5 values separately for each of the year indicators included in Models 4 (papers) and 8 (patents). To enable comparisons with raw CD5 values shown in the main text, we present the separate predictions made for each year as a line graph. As shown in the figure, we continue to observe declining values of the CD index across papers and patents, even when accounting for changes in publication, citation and authorship practices.

#### Verification using simulation

Third, following related work in the Science of Science14,71,72,73, we considered whether our results may be an artefact of changing patterns in publishing and citation practices by using a simulation approach. In essence, the CD index measures disruption by characterizing the network of citations around a focal paper or patent. However, many complex networks, even those resulting from random processes, exhibit structures that yield non-trivial values on common network measures (for example, clustering)74,75,76. During the period spanned by our study, the citation networks of science and technology experienced significant change, with marked increases in both the numbers of nodes (that is, papers or patents) and edges (that is, citations). Thus, rather than reflecting a meaningful social process, the observed declines in disruption may result from these structural changes in the underlying citation networks.

To evaluate this possibility, we followed standard techniques from network science75,77 and conducted an analysis in which we recomputed the CD index on randomly rewired citation networks. If the patterns we observe in the CD index are the result of structural changes in the citation networks of science and technology (for example, growth in the number of nodes or edges) rather than a meaningful social process, then these patterns should also be visible in comparable random networks that experience similar structural changes. Therefore, finding that the patterns we see in the CD index differ for the observed and random citation networks would serve as evidence that the decline in disruption is not an artefact of the data.

We began by creating copies of the underlying citation network on which the values of the CD index used in all analyses reported in the main text were based, separately for papers and patents. For each citation network (one for papers, one for patents), we then rewired citations using a degree-preserving randomization algorithm. In each iteration of the algorithm, two edges (for example, A–B and C–D) are selected from the underlying citation network, after which the algorithm attempts to swap the two endpoints of the edges (for example, A–B becomes A–D, and C–D becomes C–B). If the degree centrality of A, B, C and D remains the same after the swap, the swap is retained; otherwise, the algorithm discards the swap and moves on to the next iteration. When evaluating degree centrality, we consider ‘in-degree’ (that is, citations from other papers or patents to the focal paper or patent) and ‘out-degree’ (that is, citations from the focal paper or patent to other papers or patents) separately. Furthermore, we also required that the age distribution of citing and cited papers or patents was identical in the original and rewired networks. Specifically, swaps were only retained when the publication year of the original and candidate citations was the same. In light of these design choices, our rewiring algorithm should be seen as fairly conservative, as it preserves substantial structure from the original network. There is no scholarly consensus on the number of swaps necessary to ensure the original and rewired networks are sufficiently different from one another; the rule we adopt here is 100 × m, where m is the number of edges in the network being rewired.

Following previous work14, we created ten rewired copies of the observed citation networks for both papers and patents. After creating these rewired citation networks, we then recomputed CD5. Owing to the large scale of the WoS data, we base our analyses on a random subsample of ten million papers; CD5 was computed on the rewired network for all patents. For each paper and patent, we then compute a z score that compares the observed CD5 value to those of the same paper or patent in the ten rewired citation networks. Positive z scores indicate that the observed CD5 value is greater (that is, more disruptive) than would be expected by chance; negative z scores indicate that the observed values are lesser (that is, more consolidating).

The results of these analyses are shown in Extended Data Fig. 8, separately for papers (Extended Data Fig. 8c) and patents (Extended Data Fig. 8f). Lines correspond to the average z score among papers or patents published in the focal year. The plots reveal a pattern of change in the CD index over and beyond that ‘baked in’ to the changing structure of the network. We find that on average, papers and patents tend to be less disruptive than would be expected by chance, and moreover, the gap between the observed CD index values and those from the randomly rewired networks is increasing over time, which is consistent with our findings of a decline in disruptive science and technology.

Taken together, the results of the foregoing analyses suggest that although there have been marked changes in science and technology over the course of our long study window, particularly with respect to publication, citation and authorship practices, the decline in disruptive science and technology that we document using the CD index is unlikely to be an artefact of these changes, and instead represents a substantive shift in the nature of discovery and invention.

### Regression analysis

We evaluate the relationship between disruptiveness and the use of previous knowledge using regression models, predicting CD5 for individual papers and patents, based on three indicators of previous knowledge use—the diversity of work cited, mean number of self-citations and mean age of work cited. Our measure of the diversity of work cited is measured at the field × year level; all other variables included in the regressions are defined at the level of the paper or patent. To account for potential confounding factors, our models included year and field fixed effects. Year fixed effects account for time variant factors that affect all observations (papers or patents) equally (for example, global economic trends). Field fixed effects account for field-specific factors that do not change over time (for example, some fields may intrinsically value disruptive work over consolidating ones). In contrast to our descriptive plots, for our regression models, we adjust for field effects using the more granular 150 WoS ‘extended subjects’ (for example, ‘biochemistry and molecular biology’, ‘biophysics’, ‘biotechnology and applied microbiology’, ‘cell biology’, ‘developmental biology’, ‘evolutionary biology’ and ‘microbiology’ are extended subjects within the life sciences and biomedicine research area) and 38 NBER technology subcategories (for example, ‘agriculture’, ‘food’, ‘textile’; ‘coating’; ‘gas’; ‘organic’; and ‘resins’ are subcategories within the chemistry technology category).

In addition, we also include controls for the ‘mean age of team members’ (that is, ‘career age’, defined as the difference between the publication year of the focal paper or patent and the first year in which each author or inventor published a paper or patent) and the ‘mean number of previous works produced by team members’. Although increases in rates of self-citations may indicate that scientists and inventors are becoming more narrowly focused on their own work, these rates may also be driven in part by the amount of previous work available for self-citing. Similarly, although increases in the age of work cited in papers and patents may indicate that scientists and inventors are struggling to keep up, they may also be driven by the rapidly aging workforce in science and technology78,79. For example, older scientists and inventors may be more familiar with or more attentive to older work, or may actively resist change80. These control variables help to account for these alternative explanations.

Supplementary Table 3 shows summary statistics for variables used in the ordinary-least-squares regression models. The diversity of work cited is measured by normalized entropy, which ranges from 0 to 1. Greater values on this measure indicate a more uniform distribution of citations to a wider range of existing work; lower values indicate a more concentrated distribution of citations to a smaller range of existing work. The tables show that the normalized entropy in a given field and year has a nearly maximal average entropy of 0.98 for both science and technology. About 16% of papers cited in a paper are by an author of the focal paper; the corresponding number for patents is about 7%. Papers tend to rely on older work and work that varies more greatly in age (measured by standard deviation) than patents. In addition, the average CD5 of a paper is 0.04 whereas the average CD5 of a patent is 0.12, meaning that the average paper tends to be less disruptive than the average patent.

We find that using more diverse work, less of one’s own work and older work tends to be associated with the production of more disruptive science and technology, even after accounting for the average age and number of previous works produced by team members. These findings are based on our regression results, shown in Extended Data Table 1. Models 6 and 12 present the full regression models. The models indicate a consistent pattern for both science and technology, wherein the coefficients for diversity of work cited are positive and significant for papers (0.159, P < 0.01) and patents (0.069, P < 0.01), indicating that in fields in which there is more use of diverse work, there is greater disruption. Holding all other variables at their means, the predicted CD5 of papers and patents increases by 303.5% and 1.3%, respectively, when the diversity of work cited increases by 1 s.d. The coefficients of the ratio of self-citations to total work cited is negative and significant for papers (−0.011, P < 0.01) and patents (−0.060, P < 0.01), showing that when researchers or inventors rely more on their own work, discovery and invention tends to be less disruptive. Again holding all other variables at their means, the predicted CD5 of papers and patents decreases by 622.9% and 18.5%, respectively, with a 1 s.d. increase in the ratio. The coefficients of the interaction between mean age of work cited and dispersion in age of work cited is positive and significant for papers (0.000, P < 0.01) and patents (0.001, P < 0.01), suggesting that—holding the dispersion of the age of work cited constant—papers and patents that engage with older work are more likely to be disruptive. The predicted CD5 of papers and patents increases by a striking 2,072.4% and 58.4%, respectively, when the mean age of work cited increases by 1 s.d. (about nine and eight years for papers and patents, respectively), again holding all other variables at their means. In summary, the regression results suggest that changes in the use of previous knowledge may contribute to the production of less disruptive science and technology.

### Reporting summary

Further information on research design is available in the Nature Portfolio Reporting Summary linked to this article.