Introduction

Scientific research demonstrates a trend of integrating multidisciplinary knowledge (Porter & Rafols, 2009; Zhou et al., 2022). The development of scientific research since the 1960s has led to an increase in interdisciplinary research and proved its effectiveness in solving critical issues in society (Schmidt, 2008). Interdisciplinary research produces successful scientific breakthroughs and influences economic and social needs (Rafols & Meyer, 2010). Theories of knowledge production, such as big science (Price et al., 1986), post-normal science, and ‘Mode 2’ (Hessels & van Lente, 2008), recognize the importance of interdisciplinarity in the development of science.

‘Interdisciplinary’ can be defined based on either knowledge linkage or team cooperation (Stokols et al., 2008; Wagner et al., 2011). The process of integrating different bodies of knowledge is the key aspect of interdisciplinary research (National Academy of Sciences, 2004). Hence, knowledge integration is considered the core feature of interdisciplinary research. Scientific research is a process of knowledge recombination resulting in new knowledge output. Studies on interdisciplinary research focus on the measures of interdisciplinarity and their impacts on scientific research (Leydesdorf, 2007; Leydesdorff & Rafols, 2011; Leydesdorff et al., 2019; Rafols & Meyer, 2010; Stirling, 2007; Uzzi et al., 2013; Wagner et al., 2011; Yegros-Yegros et al., 2015; Zhang et al., 2021; Zwanenburg et al., 2022), characteristics of knowledge exchange in a specific field or over a period of time (Barthel & Seidl, 2017; Chang & Huang, 2012; Larivière et al., 2012; Liu & Rousseau, 2012; Truc, 2022; Yan et al., 2013), and interdisciplinary research policies (Bromham et al., 2016; Petersen et al., 2021). However, an in-depth exploration of the dynamics and characteristics of knowledge integration in the development of science across different fields and in a long history remains underexplored, which limits our understanding of the trends and patterns in the development of science throughout history.

Herein, we investigated 2 research questions: first, ‘what are the dynamics of interdisciplinarity of scientific breakthroughs?’ and second, ‘what are the characteristics of knowledge structure of the breakthrough achievements?’ The investigation is based on analysis of the key publications of the Nobel Prize in natural science, namely, Chemistry, Physics, and Physiology or Medicine, and their reference data: Nobel Prize-winning research (hereinafter ‘Nobel-winning research’) is a noteworthy topic of investigation because it represents the most important original scientific research achievements (Shelton & Holdridge, 2004). Academia is increasingly interested in the analysis of Nobel Prizes, focusing on three aspects: the characteristics of laureates, including their achievements; the knowledge production process, including the generation and dissemination of revolutionary ideas; and the evaluation of research quality (Hansson & Schlich, 2015; Luttenberger, 1996). In-depth exploration of the disciplinary characteristics and dynamics of knowledge integration of Nobel-winning research can help us understand the laws of scientific research and discipline development and may lead to enlightened policy implications.

This study contributes to the related research in the following three aspects. First, by systematically examining the dynamics and characteristics of knowledge integration in Nobel-winning research pertaining to natural science in the long run, we demonstrate that scientific breakthroughs typically result from a novel combination of a larger amount of distant knowledge but in fewer disciplines, thus acquiring a better understanding of the development of natural science in the past 120 years.

Second, by distinguishing the three aspects of diversity in variety, balance, and disparity in Chemistry, Physics, and Physiology or Medicine over a long time, we are able to identify the different development trends across the three fields and provide new evidence on the dynamics between balance and scientific breakthroughs over a long time period, thus obtaining a more comprehensive understanding of the overall degree of integration between different knowledge components in scientific breakthroughs across different fields and of the relationship between distinct and comprehensive characteristics of interdisciplinarity and the quality of scientific research. These findings also demonstrate the need to analyse the three aspects of diversity separately to precisely understand the characteristics of interdisciplinarity.

Third, unlike most extant research on interdisciplinarity, this study addresses the feature of knowledge combination in a network and the interconnection of knowledge as an important perspective to understand the interdisciplinary nature, in addition to diversity analysis. By combining bibliometrics and social network analysis (SNA) approaches to simultaneously analyse the diversity and coherence dimensions of interdisciplinarity, we are able to better capture the large-scale breadth of the knowledge base of scientific breakthroughs and the novelty of their knowledge integration. We reveal that the interdisciplinary nature of scientific breakthroughs features a trend of increasing diversity and coherence concurrently, albeit to a different degree across the three fields, thus completing the understanding of the interdisciplinary characteristics of scientific breakthroughs.

The remainder of this paper is organized as follows. “Literature review” section reviews the literature on interdisciplinary research and the Nobel Prize. “Research design” section proposes the research design. “Empirical results” section presents the empirical results and discusses the research findings, and “Conclusions” section provides the conclusion and discussion.

Literature review

Dynamics of interdisciplinary research

Scientific research has undergone remarkable changes in the integration of interdisciplinary knowledge. Porter & Rafols (2009) documented a 50% increase in the number of disciplines and references per article and a 75% increase in the number of co-authors from 1975–2005 in natural science research. Similarly, the average number of disciplines of Nature publications increased from 1–2 to 9 from 1900–2017 (Gates et al., 2019). The number of references per article in Economics and Business, and Political Science have increased more than threefold from 1960–2009, while other social science disciplines have achieved more than 200% growth (Zhou et al., 2022). However, the degree of interdisciplinarity varies across disciplines. For example, interdisciplinarity in the field of biology is relatively high, while it is relatively low in physics and mathematics (Porter & Rafols, 2009; Yan et al., 2013).

A higher level of interdisciplinarity typically improves the originality or novelty of scientific research, resulting in the spread of interdisciplinary research. Highly cited papers in more than 90% of NSF (National Science Foundation)-supported disciplines have a higher level of interdisciplinarity than others (Chen et al., 2015). The increase in the effective number of disciplines was associated with an approximately 20% increase in the research impact (Okamura, 2019). Highly cited papers generally exhibit higher variety and disparity and lower balance. The effect of variety on citation impact is most significant, followed by disparity and balance (Chen et al., 2021a). Researchers conducting interdisciplinary studies demonstrate a high degree of cognition of complexity, internalize knowledge of multiple disciplines, and can observe and comprehensively understand the connections between phenomena involving multiple disciplines. This increases the possibility of major scientific discoveries (Alexander et al., 2013). Uzzi et al. (2013) reported that the most influential papers, measured by the top 5% citations, featured a combination of novel and well-established science. Balancing atypical knowledge with conventional knowledge is a crucial link between innovativeness and impact. However, cognitive and collaborative challenges associated with interdisciplinary research and/or hurdles in the review process might reduce scientists’ productivity (Leahey et al., 2015).

Measures of interdisciplinary research

Two approaches are used to measure interdisciplinarity: bibliometric and SNA. Bibliometric analysis extracts data representing the disciplines in scientific literature, such as discipline classification and co-authors (Morillo et al., 2001; Wagner et al., 2011; Wang et al., 2015). Indicators are constructed from two recognized key attributes, namely, diversity and coherence. Diversity measures the differences in the bodies of integrated knowledge, typically divided into three dimensions: variety, balance, and disparity/similarity (Leydesdorff et al., 2019; Porter et al., 2007; Stirling, 2007); coherence measures the intensities of the relations between these bodies of knowledge (Nesta & Saviotti, 2005; Rafols & Meyer, 2010). Integrated indicators to measure comprehensive aspects of diversity have been proposed, including Simpson’s diversity (Simpson, 1949), Shannon entropy (Shannon, 1948), Brillouin’s diversity (Brillouin, 1956), Rao-Stirling (Rafols & Meyer, 2010), Hill index (Zhang et al., 2016), and DIV indices (Leydesdorff et al., 2019). Each measure has its advantages and disadvantages; however, none were able to uniformly measure the degree of interdisciplinarity (Zwanenburg et al., 2022).

Interdisciplinary research is considered a knowledge integration process characterized by high cognitive heterogeneity and intense relational structures. SNA is capable of analysing the magnitude of interdisciplinarity by assuming that the location of a subject category in a network can indicate its degree of interdisciplinarity. Betweenness centrality, clustering coefficient, and average similarity of networks are used to measure the interdisciplinarity of journals (Leydesdorf, 2007; Leydesdorff et al., 2018; Rafols et al., 2012). Recent studies have evaluated the validity and consistency of these bibliometrics and SNA indicators, highlighting the inconsistencies between these measures (Wang & Schneider, 2020; Zwanenburg et al., 2022). Nevertheless, these indicators provide a good platform for more effective and coherent interdisciplinarity measurement, and network-based discipline classification or grouping remains in development. Furthermore, attention should be focused on emphasized definitions and implied assumptions (Zwanenburg et al., 2022).

Interdisciplinarity in Nobel-winning research

Nobel-winning research is characterized by a wider knowledge span in the process of knowledge production and combination. Nobel-winning publications exhibit remarkable boundary-spanning traits and exceptional abilities to connect disparate and topically diverse clusters of research papers (Sebastian & Chen, 2021). Furthermore, these papers have significantly changed the existing knowledge space structure. Nevertheless, Nobel-winning publications cite a large number of journals with relatively low impact factors. For example, the most ground-breaking scientific work in physics is not necessarily published in the journals with the highest impact factor (Bjørk, 2020; Liang et al., 2019). Methods are the most popular article type that are integrated in the process of knowledge combination. Recent Nobel-winning research focused more on earlier knowledge due to an increasing citation time lag (Liang et al., 2019).

Regarding team cooperation, Nobel laureates are particularly positioned in the activities of scientific knowledge combination (Tong & Ahlgren, 2017). The laureates are generally located in the bridge position of the co-authored network when compared with a group of matched scientists and act as ‘structural holes’, which is a state that is more likely to increase social capital for the network (Wagner et al., 2015). The laureates are positioned closer to the edge of multiple nonbiomedical disciplines than other biomedical researchers. On average, the co-authoring steps of the laureates and interdisciplinary researchers (at least one) are approximately 2.8 (Chris, 2015). Nobel laureates are more loyal to the cooperation that they initiated prior to winning the prize. There is less collaboration with new co-authors post-award than pre-award; the greater the intensity of pre-award cooperation and the longer the period of pre-award collaboration, the higher the probability of remaining in the co-author network after the award (Chan et al., 2015). However, evidence supporting a positive relationship between the longevity of collaborative relationships and creativity is lacking. Scientific collaboration involves conceptual complementarities that may erode over repeated interactions (Chan et al., 2016). Nobel laureates form a distinct group in the network with greater numbers of Nobel laureate ancestors, descendants, mentees/grand mentees, and local academia (Chariker et al., 2017). The international collaboration in the closely related Nobel Prize research themes, such as Ribozyme, Ozone, and Fullerene, demonstrates an increasing trend with a large share of publications with at least 2 countries (Tong & Ahlgren, 2017).

The dissemination of the Nobel-winning research reveals a pattern of scientific paradigm change and interdisciplinary development of knowledge production (Mazloumian et al., 2011; Szell et al., 2018). Hence, the single-field nature of Nobel Prize selection in an interdisciplinary context has been challenged (Mukhopadhyay, 2009). Landmark papers of Nobel Prize laureates caused an increase in forward citation of their previous publications, thereby drawing the attention of the scientific community and presenting the Matthew effect, that is, the ‘rich-get-richer’ effect in publication citation bias proposed by Merton (1968). This further led to a sudden paradigm shift (Mazloumian et al., 2011). Three types of citation accumulation curves of achievements were identified: concave, convex, and straight curves (Liu & Rousseau, 2014), representing different types of dynamics between old ideas and new opinions. A concave curve reveals a major conflict between the new ideas and old knowledge systems, causing strong interest and increased citations. A convex curve occurs when an originally underestimated new idea rapidly spreads after its value is increasingly recognized. The evolution of instrument types from bounded to linked to extension, by analysing instrument-related physics awards, gradually generated a form of scientific knowledge, e.g., instrument knowledge (Marcovich & Shinn, 2017).

Despite an increasing interest in analysing Nobel achievements, there is limited understanding of interdisciplinarity features in Nobel-winning research, especially their characteristics of knowledge integration (Gingras & Wallace, 2010; Turki et al., 2020). Furthermore, an understanding of the dynamics and characteristics of scientific breakthroughs in terms of interdisciplinary knowledge combination is inadequate. The present study bridges the gap by analysing the dynamics and characteristics of interdisciplinary knowledge integration of Nobel-winning research and their reference data in the past 120 years via a combination of bibliometrics and SNA approaches.

Research design

Sample selection and data sources

The data were extracted from three sources: (1) the official website of the Nobel Prize (nobelprize.org), which provides information on Nobel laureates, including a description of their key contributions and publicationsFootnote 1; (2) a dataset of the publication records of the Nobel laureates awarded during 1901 to 2016, constructed by Li et al. (2019), which retrieved information from multiple sources, including the laureates’ resumes, university websites, Wikipedia, and Microsoft Academic Graph, and manual processing and algorithmic disambiguation; and (3) Web of Science (WoS), for reference data of the key publications.

First, we obtained data pertaining to all laureates in Chemistry, Physics, and Physiology or Medicine from 1901–2020, comprising 186, 216, and 222 laureates, respectively, from the official website. We combined Physiology or Medicine into one research field in the following analysis by following the classification of the Nobel Prize. Subsequently, key publications were extracted from the official website for the Nobel laureates awarded during 2017 to 2020 and from the dataset of the publication records constructed by Li et al. (2019) (data source (2)) for the award period from 1901 to 2016. The 2 datasets were integrated using the laureates’ names. Finally, we collected the reference information cited by these key publications from WoS, which generated a total of 835 key publications and 10,894 references. Laureates whose key publications were not able to be identified or retrieved were excluded from the analysis. Table 1 presents the detailed sample information.

Table 1 Sample Information
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The key publications published after the 1950s account for a relatively high proportion of awards publications, with 69.58%, 58.37%, and 69.84% in the fields of Chemistry, Physics, and Physiology or Medicine, respectively. This might be because expenditures on basic research greatly increased in developed countries post-World War II due to improvements in the scientific research environment, and many research papers accumulated during the War were later published, leading to a boost in scientific achievements. This general trend is consistent with Larivière et al. (2010)’s finding, which demonstrated that scientific publications exponentially increased in the golden age of scientific development from 1945–1975 in the West and subsequently slowed down after the 1980s.

Methods and variables

To comprehensively investigate the integration of interdisciplinary knowledge, we constructed an analytical framework consisting of the 2 dimensions of diversity and coherence to analyse the interdisciplinary trends and characteristics of Nobel-winning research by using a combination of bibliometrics and the SNA approach. The two approaches essentially correspond to a distinction between node-level and network-level analyses. The former is used to analyse diversity indicators, while the latter is used to analyse the coherence dimension. We address interdisciplinary knowledge as a process of knowledge combination and integration; it is then necessary to understand to what extent specific topics, concepts, tools, data, etc., used in a research process are related. Hence, the use of both approaches can better capture the two aspects of interdisciplinary knowledge integration: the large-scale breadth of the knowledge base of scientific research and the novelty of their knowledge integration. Table 2 presents the conceptual framework of diversity and coherence indices.

Table 2 Summary of the conceptual framework
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(1) Diversity refers to the number, balance, and degree of difference between the combined knowledge (Ávila-Robinson et al., 2021; Chen et al., 2021a, 2021b; Leydesdorff & Rafols, 2011); diversity is measured based on the three dimensions of variety, balance, and disparity. For bibliometric indicators, we included 5 measures that have frequently been used in the literature. Variety is measured by the number of references and disciplines. The greater the average references and average disciplines are, the higher the variety. Based on the information on the laureate’s name, prize year, title, publication year, and journal name, we collected the bibliographic data of references of Nobel-winning research in the core collection of the WoS database, i.e., the number of references (Ri) and retrieved references for each key publication. We used SC (subject category) in WoS as a discipline classification. The average references (R) is the average number of references (Ri) for all key publications, as shown in Eq. (1). The average discipline (S) is the average number of SCs involved in references for all key publications, as shown in Eq. (2). Table 5 in Appendix shows the number of publications per discipline category for the three time periods.

The balance of interdisciplinarity is measured by the complementary value of the Gini coefficient (1 − Gini) and information entropy. The Gini coefficient ranges from 0, indicating perfect equality, to 1, perfect inequality. A larger value corresponds to a lower balance, indicating that knowledge integration is more concentrated in a few disciplines. A lower Gini coefficient corresponds to a higher balance, indicating that knowledge integration is more dispersed in more disciplines. The information entropy increases with the number of discipline categories and the evenness of probability distributions.

Disparity is measured by the average distance of disciplines, as shown in Eq. (5). A larger disparity represents a greater knowledge distance between disciplines. The benchmark value of the cosine similarity matrix for all disciplines is extracted from Leydesdorff et al. (2019) based on an estimation of citation data of 11,487 journals contained in the Journal Citation Reports 2016 (available at https://www.leydesdorff.net/software/mode2div/). We then adapt it to the reference data of Nobel-winning research by extracting relevant matrix elements.

(2) Coherence refers to interconnection between combined knowledge. This concept can be measured by the extent to which publication networks form an intense structure; a more clustered network corresponds to a higher level of knowledge connection. We adopted network density, derived from the SNA approach, to measure coherence instead of using the mean linkage strength and mean path length of the network, as Rafols and Meyer (2010) proposed. This is more suitable because it measures the closeness of the connection between the points in a network, taking into account the inclusiveness and sum of the degrees of each point of the graph; hence, the overall integration degree between different knowledge components in a disciplinary network can be measured (Chen et al., 2021b).

The discipline co-occurrence network is constructed based on a co-occurrence matrix using the SCs of references. The rows and columns of the co-occurrence matrix are SCs, and the elements of the matrix represent the co-occurrence frequency of every two disciplines. Subsequently, the network graph is drawn using UCINET-NetDraw based on the constructed matrix. In the network, each block (node) represents one SC, and the connection means that the two disciplines appear in the SC logo of one reference simultaneously. The thickness of the connection indicates the co-occurrence frequency of the two disciplines, and the size of the block indicates the betweenness centrality of the discipline.

In addition to measuring the overall interconnection of integrated disciplines in Nobel-winning research using the indicator of network density, we adopt other SNA indicators and methods, such as betweenness centrality, the co-occurrence of disciplines, and discipline network diagrams, to analyse the key bridging disciplines of knowledge combination and the connectional structure of disciplines to obtain an in-depth understanding of the characteristics of knowledge combination in Nobel-winning research. We use the betweenness centrality of nodes to analyse the role of disciplines in the communication between different knowledge fields. The Freeman betweenness centrality is calculated using Eq. (7):

$$\text{BC}\left({v}\right)=\sum_{{s}\ne {v}\ne {t}}\frac{{{d}}_{\mathrm{st}}\left({v}\right)}{{{d}}_{\mathrm{st}}},$$
(7)

where \({d}_{\mathrm{st}}(v)\) is the number of shortest paths through v from point s to point t, and \({d}_{\mathrm{st}}\) is the total number of paths from s to t. The larger the value, the stronger the mediation effect.

To obtain comparable results across different networks, we further calculate weighted betweenness centrality, i.e., the relative Freeman betweenness centrality (RBC) as Eq. (8).

$$\mathrm{RBC}\left({v}\right)=\frac{2\mathrm{BC}({v})}{{{n}}^{2}-3n+2},$$
(8)

where n is the number of nodes. Its value range is [0,1].

Following Leydesdorf (2007), we consider the journal or discipline as interdisciplinary if a journal or discipline is at the intermediate position between other journals or disciplines. Publications in such journals functioned as communication channels for other journals or disciplines (Silva et al., 2013).

Empirical results

Descriptive analysis

Based on the conceptual framework in Table 2, we estimated the varieties of key publications by Nobel laureates with an interval of a decade from 1887–2012. Disciplines were classified by the subject categories (SC) in the WoS database. The amount of knowledge and disciplines integrated in Nobel-winning research in natural science has been increasing for the past 120 years. As illustrated in Fig. 1, both the average number of references and the number of disciplines involved in the three fields present an upwards trend. The average number of references is approximately 1.58, 1.99, and 2.01 times for Chemistry, Physics, and Physiology or Medicine, respectively, in the mid-twentieth century than in the 2000s. Furthermore, the average disciplines are approximately 2.66, 3.00, and 1.97 times for Chemistry, Physics, and Physiology or Medicine, respectively, in the same time period.

Fig. 1
figure 1

Average references and disciplines of Nobel-winning research from 1901–2020 (award period)

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Based on the trend change in the average references and distribution of the disciplines of these publications, we divided the development of natural sciences in terms of interdisciplinarity into three periods: the 1900s–1940s, 1950s–1970s, and 1980s and beyond (hereinafter 1900–‘40s, 1950s–‘70s, and 1980s–, respectively). We further analysed the interdisciplinary properties of the Nobel-winning research based on the three time periods.

Interdisciplinary dynamics and characteristics

Variety analysis

The estimations of diversity and coherence indices for the three fields across the three time periods are presented in Table 3. The varieties of the Nobel-winning research have dramatically increased over the three periods. During the three periods in the 1900s–‘40s, 1950s–‘70s, and 1980s and beyond, the average references are approximately 11, 25, and 35 for all Nobel-winning research, and average disciplines are approximately 3, 5, and 8. The highest increase occurs in the field of chemistry, 3.42 and 3.40 times that of the 1900s–‘40s in the following two periods. This might be because chemistry integrated a larger amount of knowledge in the field of life sciences and biomedicine in later stages,Footnote 2 and this field accounts for 49.67% of discipline categories in the WoS classification system. There are five major categories, 151 middle categories, and 252 subcategories in the discipline classification system of WoS released in 2013. Seventy-five out of 151 middle categories belong to the major categories of life sciences and biomedicine.

Table 3 Interdisciplinary indicators along the three periods
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The amount of knowledge integrated by the Nobel achievements is equivalent to or more than the overall level of the corresponding field during the same period estimated by Larivière et al. (2010)Footnote 3; however, the number of integrated disciplines does not follow a similar trend. The differences between Nobel-winning research in physiology or medicine and medical (MED) publications in Larivière et al. (2010) are 0, 7, and 8, respectively. The differences between Nobel-winning research in Chemistry, Physics, and natural science and engineering (NSE) publications reported by Larivière et al. (2010) are 0, 11, and 10. Therefore, the amount of knowledge integrated in Nobel-winning research has apparently been higher than the average level of general scientific research in the same period since the 1950s.

However, Nobel-winning research is not particularly prominent in terms of the number of integrated disciplines. Table 4 compares the variety of indices between key Nobel publications and general publications, as estimated by Porter and Rafols (2009). This reveals that Nobel achievements in physiology or medicine have a lower number of integrated disciplines than general publications from 1975–2005 (− 0.6 to − 2.49), suggesting that Nobel-winning achievements feature a higher level of knowledge concentration and are grounded in deep expertise in specialized disciplines. This is consistent with the findings for Nature publications from 1869–2019 reported by Gates et al. (2019) and for Nobel-winning publications from 1900–2016 reported by Li et al. (2022). The former contends that Nature publication only references 9 disciplines, while a currently published typical article references 11 disciplines. The latter finds that the diversity of references cited in Nobel-winning publications is generally lower than that in conventional articles from the same field or on the same topic.

Table 4 Comparison of Nobel key publications with general publications in terms of average disciplines
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Balance analysis

The variety and balance of knowledge integration in the field of natural science improves as information entropy (H) increases across the three time periods; however, the three fields follow different trends (Table 3), consistent with the 1-Gini. Both Chemistry and Physics follow an up-down-up development trend in terms of the concentrated degree of integrated disciplines, while Physiology or Medicine presents an up-down development trend. This implies that the distribution of the integrated disciplines in Chemistry and Physics shifts from centralization to decentralization. Conversely, the distribution of the disciplines in Physiology or Medicine initially disperses and subsequently becomes more concentrated.

This may be related to the development stage of the discipline and within-the-field knowledge breakthroughs. For most of the twentieth century, Physics and Chemistry were mainly at the stage of their own in-depth development; hence, knowledge production continuously developed within specific fields. Subsequently, as the discipline matured, the concepts, theories, tools, and methods of these 2 disciplines disseminated to other disciplines, contributing to discipline development (Schrödinger, 1944). Since the 1950s–‘60s, due to important discoveries and pioneering works in particle physics, including the detection of cosmic neutrinos, astronomy, and astrophysics, a new research area, ‘astroparticle physics’, emerged and rapidly developed (Sun & Latora, 2020). The discipline with the highest frequency in Physics had shifted from physics to astronomy and astrophysics in the 1980s. Moreover, optics knowledge is widely cited, reflecting an interdisciplinary trend within the field of Physics.

The Physiology or Medical field demonstrates a trend of focusing on biochemistry and molecular biology (hereinafter BMB). Since the twentieth century, biochemistry has gradually influenced the advance of the medical revolution driven by Pasteur's work, evolving from the preparation of bacterial vaccines or immune sera based on a biological perspective to exploring the chemical mechanism of these therapies. Furthermore, these studies merge with research on chemically based metabolic diseases, for example, certain nutritional deficiencies. Biochemistry links these 2 streams of work (Bernal, 2010). Meanwhile, since the emergence of molecular biology, molecular-level studies on life phenomena have gradually become the mainstream research direction in the medical field and generated several new research topics in the treatment of human diseases and drug development (Zhou, 2005).

Disparity analysis

The disparity index reveals an increasing trend across the three time periods for both a single field and overall disciplines. However, the trend slowed from the 1950s to the 1980s–2010s, especially in the fields of Chemistry and Physiology or Medicine, implying that integrating long-distance knowledge was challenging.

Except for chemistry, physics and BMB were the main disciplines integrated in the field of Chemistry during the 1900s–‘40s. This can be seen from the discipline frequency statistics of the references shown in Appendix Table 5. Subsequently, biophysics, electrochemistry, cell biology, virology, engineering, microscopy, spectroscopy, etc., which were emerging cross-disciplines, and biological science, engineering, and instrumentation disciplines, were gradually incorporated into the knowledge integration process. After the 1980s, environmental science and ecology as well as water resources emerged in the knowledge network. Although BMB became more prominent in the knowledge network in this period, it was generally considered an expansion of chemical research rather than a revolution in the theory or method of chemistry itself.

Multidisciplinary sciences and metallurgy and metallurgical engineering were the main disciplines integrated into the field of Physics during 1900–‘40s. Subsequently, engineering, nuclear science& technology were gradually incorporated into the knowledge integration process. After the 1980s, optics and computer science emerged in the knowledge network. The disciplines of knowledge integration in physical research are relatively few and concentrated, so the knowledge distance in this field is relatively short.

In the field of Physiology or Medicine, physiology, BMB, and research and experimental medicine were the main integrated disciplines during the 1900s–‘40s. Subsequently, in addition to more medical disciplines, engineering, crystallography, instruments and instrumentation were gradually incorporated into the process of knowledge integration. After 1980, there were no particularly important long-distance disciplines, and the frequency of the original disciplines increased. This implies that the process of knowledge production in Physiology or Medicine entered a more mature and specialized development stage.

Coherence analysis

Coherence, measured by overall network density, increased across the three time periods, while the three fields demonstrated various magnitudes, indicating a more intense connection among overall integrated knowledge (Table 3). The network density in the knowledge network of Chemistry and Physiology or Medicine is constantly increasing. It is observable that the disciplines included in the knowledge network of these two fields are gradually becoming interconnected, presenting a higher level of coherence. The knowledge network of Physics presents the lowest density and the slowest growth rate. This mainly because other disciplines integrated into the knowledge network of Physics are dominantly connected with physics, and connections between them are absent.

The number of integrated disciplines increased from 16 to 44 in the knowledge network of Chemistry across the three periods, among which the number of disciplines connected with at least one discipline increased from 7 to 35, an increase of 4 times, and the network density increased from 0.13 to 0.58. The number of integrated disciplines increased from 16 to 44 in the knowledge network of Physiology or Medicine across the three periods, among which the number of disciplines connected with at least one discipline increased from 13 to 45, an increase of 2 times, and the network density increased from 0.11 to 0.60, presenting the highest increase in terms of knowledge coherence. The number of integrated disciplines increased from 9 to 18 in the knowledge network of Physics across the three periods, among which the number of disciplines connected with at least one discipline increased from 6 to 18, an increase of 2 times, and the network density increased from 0.17 to 0.23. Hence, network density can properly capture the level of knowledge coherence in an integrated knowledge network.

Additionally, bridging disciplines that facilitate knowledge exchange have shifted in the knowledge network (Figs. 2, 3, and 4). Chemistry and Physiology or Medicine have experienced a more prominent shift, while Physics has remained relatively stable. Bridging disciplines in Chemistry have shifted from physics, BMB, and chemistry to BMB dominance. Bridging disciplines in Physics have shifted from the absolute centre of physics to the dual centre of physics and engineering; however, the relationship between physics and other subjects has remained the main connection. This explains the lower density of Physics networks in 1950s–‘70s. Bridging disciplines in Physiology or Medicine have gradually shifted from microbiology, immunology, and physiology to BMB, cell biology, neuroscience and neurology, genes and genetics.

Fig. 2
figure 2

Disciplinary networks of Nobel-winning research in Chemistry, Physics, and Physiology or Medicine (from top to bottom) in the 1900s–‘40s

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Fig. 3
figure 3

Disciplinary networks of Nobel-winning research in Chemistry, Physics, Physiology or Medicine (from top to bottom) in the 1950s–‘70s

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Fig. 4
figure 4

Disciplinary networks of Nobel-winning research in Chemistry, Physics, Physiology or Medicine (from top to bottom) in the 1980s–

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Source: Illustrated based on the co-occurrence matrix of the disciplines involved in the references. The size of the square indicates the betweenness centrality of the disciplines, and the thickness of the line indicates the frequency of co-occurrence between disciplines (similar rules apply to both Figs. 3 and 4).

The main bridging disciplines for the three fields can be divided into two categories: basic disciplines and engineering technology disciplines. First, combining the BC and RBC results shown in Table 6 of the Appendix, it is arguable that chemistry, physics, and BMB are basic disciplines with relatively large intermediate centrality in the three fields across three periods, especially after the 1950s. These disciplines have the most basic research objects, strong universality of concepts and theories, and high maturity of methods or tools. Their development and knowledge diffusion will have a great impact on other disciplines. For example, in Chemistry, the award-winning achievements before 1960 were awarded to the three fields of physical chemistry, organic chemistry, and inorganic, analytical, and radiochemistry on an equal basis. Among them, radiochemistry and physical chemistry, led by chemical thermodynamics, won many awards, reflecting their primary importance in chemistry and the new academic development introduced by the progress of physics (Noboru, 2018). Physics is one of the main disciplines of knowledge integration in Chemistry. After more than half a century, biochemistry emerged to play a more important role in Chemistry. Since then, the number of awards in biochemistry and molecular biology has increased dramatically, and achievements in biochemistry and molecular biology have won both the Chemistry and Physiology or Medicine Prizes.

Second, engineering technology disciplines, such as engineering, instruments and instrumentation, computer science, etc., show increasingly high betweenness centrality in the knowledge network, especially in the fields of Chemistry and Physics (Fig. 4 and Appendix Table 6). Their functions have evolved from simply applying and measuring to driving the formation of new knowledge as well as extensively linking more material disciplines (as an intermediary). This is more prominent in Physics, as instruments evolved in a pattern of “bounded-linked-extension” in prize-winning achievements from 1901 to 2012 (Marcovich & Shinn, 2017), reflecting the promise and power of instrumentation in experimental and theoretical explorations.

Robustness checks

To check the robustness of the results on diversity analysis, we conduct econometric analyses on the dynamics of diversity indicators at the publication levels by including the controls at the publication level. Following Zhou et al. (2022), we build a linear model as shown in Eq. (9) to control the relevant factors that may influence the interdisciplinary levels. In this way, we intend to control the systematic change in scientific publications to a certain degree.

$${Div}_{i}={\mathrm{Time}}_{{i}}+{Team}_{i}+{\mathrm{Refn}}_{i}{+\mathrm{Refa}}_{i}+{\varepsilon }_{i},$$
(9)

where \({Div}_{i}\) represents the estimated diversity indicators for each publication i, namely, number of disciplines, Shannon information entropy, 1-gini coefficients, and disparity index; \({\mathrm{Time}}_{{i}}\) is a categorial variable, with 0, 1, and 2 representing publications in the period of 1900–1949, 1950–1979, or 1980–2012, respectively. The coefficients of \({\mathrm{Time}}_{{i}}\) represent the after controlling the publication. The control variables include the number of authors (\({\mathrm{Team}}_{i}\)), number of references (\({\mathrm{Refn}}_{i}\)), and age of references (\({\mathrm{Refa}}_{i}\)). Those controls are selected by considering the data availability and relevant literatures. The results are shown in Table 5. The detailed estimation results are shown in Tables 8, 9, 10 in Appendix.

Table 5 Robustness checks: OLS estimation results for diversity indicators
Full size table

The results generally confirm the robustness of the main estimation. As shown in Table 5, most of the controlled coefficients have significant signs consistently with the raw results, with slightly smaller magnitudes. The results on variety and disparity indicators are more consistent with results of pooled samples, except for insignificant results on the increases in number of references and disciplines in Physics during the 1950s–‘70s, as well as the controlled average distance of knowledge in Physiology or Medicine in the 1980s–.

While some results on balance indicators are not consistent with those of pooled samples, the two indicators of information entropy and 1 − Gini coefficient do not change uniformly. Inconsistent with previous result, the 1 − Gini coefficient in Physics further decreases during 1980s–; the raw and controlled changes in information entropy indicator in Physiology or Medicine during the 1980s– further increases. The controlled change in 1 − Gini coefficient during 1950s–‘70s is not significant in Chemistry. The raw results on balance and disparity results are not identical to those of the pooled sample, as they are not a linear combination.

Conclusions

This study analysed the interdisciplinary dynamics and characteristics in natural science from the perspective of knowledge integration using Nobel-winning research and their references data. This corresponds to 585 laureates in Chemistry, Physics, and Physiology or Medicine awarded from 1901 to 2020, 835 key publications published from 1887 to 2012, and 10,894 citation publications. The main findings, their policy implications, and research limitations are as follows.

Research findings and discussions

Interdisciplinary knowledge integration is an essential feature of original scientific breakthroughs, although influential achievements typically result from a novel combination of a larger amount of distant knowledge but in fewer disciplines. Nobel achievements in natural sciences are increasingly presented as the outcome of high-level knowledge integration both in their own discipline and with other disciplines. The number of references and disciplines per article of the achievements in the three fields has increased over the past 120 years. However, the number of integrated disciplines is not significant when compared to general publications at a comparable stage and is mainly focused on a few disciplines. While the disparity indicator shows that distant disciplines are gradually integrated into the scope of knowledge production in the three fields, the overall distribution of disciplines presents an increasing trend of concentration as it becomes less balanced. These three aspects of findings demonstrate that scientific breakthroughs require a novel combination of profound knowledge within narrow knowledge domains. Hence, this study complements Chen et al. (2021b)’s finding by demonstrating that scientific breakthroughs broadly feature a high concentration degree and a low level of balance across three fields over a long time. Meanwhile, in line with Uzzi et al. (2013) and Li et al. (2022), influential scientific achievements result from a combination of profound knowledge and innovative thinking that may be disseminated from other fields.

(2) The development of various disciplines in natural science has followed different dynamics of interdisciplinary processes for more than 120 years, as the characteristics of the three fields in variety, balance and disparity show different trends. First, the concentration dynamics of integrated disciplines vary across the three fields. Both Chemistry and Physics experienced a dynamic shift from centralization to decentralization in terms of the balance degree of integrated disciplines, while the distribution of the integrated disciplines in Physiology or Medicine initially dispersed and subsequently became more concentrated. Initially, Chemistry and Physics mainly integrated two to three disciplines, and then, during the 1950s–‘70s, concentrated on their own disciplines, circa the 1970s, and subsequently slightly diverged to other one to two disciplines, as reflected in the up-down-up-shaped curve of the 1 − Gini coefficient and information entropy values. This is related to the gradual fragmentation of these 2 fields into many small specialties since the 1950s, additionally reflecting the lack of major paradigm shifts in physics and chemistry since the middle of the last century (Gingras & Wallace, 2010). Meanwhile, as the disciplines mature, their concepts, theories, tools, and methods are diffused to other disciplines. The most obvious example is the wide emergence of biochemistry and biophysics.

Conversely, Physiology or Medicine showed a dynamic shift from decentralization to centralization in terms of the balance degree of integrated disciplines. Physiology or medicine has made breakthroughs in theories and experiments, benefiting from the dissemination of physics and chemistry knowledge, thereby entering a period of rapid specialized development since the 1950s. The most frequent interdisciplinary relationship in this field prominently changed from physiology–neuroscience to BMB–cell biology, highlighting a paradigm shift in this field. Biochemistry and molecular biology have gradually become the focus of the field. However, such major changes are not observed in the two disciplines of chemistry or physics, as there are no obviously important long-distance discipline knowledge integration or changes in interdisciplinary relations.

Furthermore, Physics presents the lowest variety, the lowest balance, and the lowest disparity, while Physiology or Medical shows the highest diversity, the highest balance, and the highest disparity. The magnitudes of various indicators in Chemistry are slightly less than those in Physiology or Medical. These findings indicate that scientific fields with similar comprehensive interdisciplinary indicators may vary remarkably in distinct characteristics of diversity, especially in long-term development trends. Hence, this study expands Zhang et al. (2019) findings by demonstrating the need to analyse the three aspects of diversity separately to precisely understand the characteristics of interdisciplinarity. By distinguishing the three aspects of diversity in three fields over a long time, we are able to identify the different development trends across the three fields, thus providing new evidence on the dynamics between balance and scientific breakthroughs across a long time period. It deepens the understanding of the relationship between distinct and comprehensive interdisciplinary characteristics and the quality of scientific research. Hence, this study completes studies by Wang et al. (2015), Yegros-Yegros et al. (2015), and Zhang et al. (2021).

(3) Nobel-winning research presents a trend of a greater degree of knowledge interconnection, and the migration of combined research methods, tools, and basic disciplines contributes to the increasingly intense structure of knowledge combination. This can be seen from the increasing coherence of disciplinary networks as well as the prominent bridging roles of basic disciplines, engineering, and instrumentation disciplines in the network of knowledge integration.

Bridging disciplines, which facilitate knowledge exchange, have shifted in disciplinary networks across the three time periods. Chemistry and physiology or medicine have experienced a more prominent shift, while physics has remained relatively stable. Bridging disciplines in chemistry have shifted from physics, BMB, and chemistry to BMB dominance, while those in physics have shifted from the absolute centre of physics to the dual centre of physics and engineering, although the relationship between physics and other subjects is predominant. Bridging disciplines in physiology or medicine have gradually shifted from microbiology, immunology, and physiology to BMB, cell biology, neuroscience and neurology, and genes and genetics.

These changes indicate that disciplines with strong fundamental research content and high universality of research tools/methods influence knowledge communication among all three disciplines, suggesting that a sound accumulation of basic knowledge, such as physics, chemistry, and BMB, is the foundation of high-quality interdisciplinary research.

Unlike most extant research on interdisciplinarity, this study addresses the feature of knowledge combination in a network and the interconnection of knowledge as an important perspective to understand the interdisciplinary nature, in addition to diversity analysis (Rafols & Meyer, 2010; Rafols et al., 2012; Zwanenburg et al., 2022). By combining the bibliometrics and SNA approaches to better capture the large-scale breadth of the knowledge base of scientific breakthroughs and the novelty of their knowledge integration, we reveal that the interdisciplinary nature of scientific breakthroughs features a trend of increasing diversity and coherence concurrently, resulting from deep and novel integration of multi-/interdisciplinary knowledge, albeit to a different degree across the three fields. This completes the understanding of the interdisciplinary characteristics of scientific breakthroughs (Chen et al., 2021a; Li et al., 2022; Zhang et al., 2019).

4.2 Policy implications

These research findings have two relevant policy implications. Firstly, policy-makers should consider the characteristics and dynamics of interdisciplinary knowledge integration in different disciplines and development stages when promoting high-quality scientific research. The necessity and feasibility of coordinated development among disciplines could be evaluated before issuing such policies.

Secondly, policy aimed at promoting interdisciplinary research should address the role of basic disciplines, engineering disciplines, and tool disciplines in bridging the integration of knowledge among disciplines. Knowledge among various disciplines of science is connected in a more extensive and closer pattern, although a deep disciplinary research foundation is the premise of successful interdisciplinary research. A stronger foundation in these disciplines is more conducive to driving the development of interdisciplinary research and making scientific breakthroughs.

4.3 Limitations and future research

Our results should be viewed in light of the following three limitations, which also provide avenues for future research. First, the sample publication data are limited to the WoS. More data sources, such as Scopus, PubMed, Google Scholar, etc., could be incorporated into studies in the future. Second, we rely on SCs as the discipline classification, which is classified at the journal level rather than at the article level. Although this is the most common and dominant classification method in the literature, the disciplines of articles and journals are not fully identical. Third, the findings about the comparison of Nobel achievements with general publications are based on a comparison with the research findings by Porter and Rafols (2009) and Larivière et al. (2010). The research fields of their data do not completely overlap with those of the sample data in this study. Such differences should be considered when understanding the comparison arguments. More comparable datasets could be constructed and estimated in future studies and research efforts. Additionally, a non-parametric matching approach could be used to conduct such an analysis (Li et al., 2022).