Scientific prizes and the extraordinary growth of scientific topics

Fast growing scientific topics have famously been key harbingers of the new frontiers of science, yet, large-scale analyses of their genesis and impact are rare. We investigated one possible factor connected with a topic’s extraordinary growth: scientific prizes. Our longitudinal analysis of nearly all recognized prizes worldwide and over 11,000 scientific topics from 19 disciplines indicates that topics associated with a scientific prize experience extraordinary growth in productivity, impact, and new entrants. Relative to matched non-prizewinning topics, prizewinning topics produce 40% more papers and 33% more citations, retain 55% more scientists, and gain 37 and 47% more new entrants and star scientists, respectively, in the first five-to-ten years after the prize. Funding do not account for a prizewinning topic’s growth. Rather, growth is positively related to the degree to which the prize is discipline-specific, conferred for recent research, or has prize money. These findings reveal new dynamics behind scientific innovation and investment.


Introduction
The extraordinary growth of a scientific topic occurs when there is a period of unexpected and abnormally large growth in a topic's impact or size [1][2][3] . Classical studies of extraordinary growth focus on the specifics of illustrative cases, such as the Copernican revolution and its associated changes in astronomical topics' productivity and impact on scientific thinking 1,4 . Newly-available, large-scale data on nearly all scientific topics enables the study of periods of extraordinary growth from a statistical perspective. Here we investigate generalizable factors associated with the onset and magnitude of the extraordinary growth of scientific topics using a large and diverse sample of scientific topics 2,5-7 .
We investigated the statistical dynamics around a possible correlate of the onset of a scientific topic's extraordinary growth: a topic's association with a scientific prize 8,9 . Scientific prizes were originally restricted to certain scientific disciplines and topics, but they have proliferated and are now awarded in nearly all disciplines 3,9 . Prize research has primarily studied how awards change prizewinners' careers [10][11][12][13][14][15][16] by recognizing 17,18 , celebrating 9,18,19 , and changing perceptions of a scholar's work 2,20,21 . For example, case studies of Howard Hughes Medical Investigators and John Bates Clark and Fields medalists have shown that prizewinners' papers published before their prize is conferred gain citations significantly faster than expected [10][11][12]14,15,22 after the prize and that winning one prize increases the probability of the same scholar winning future prizes 9 .
It is uncertain whether the link between prizes and unexpected growth for a single prizewinner's work extends to changes in the growth of an entire topic, and current theoretical arguments and empirical work are nascent. On the one hand, scholars have argued that the increased interest in a prizewinning scientist's work may likewise increase interest in the topic associated with a prize 11,23,24 . On the other hand, scholars have claimed that prizes signal that the best work associated with a topic has been done, which would lessen rather than an expand interest in a topic 11,25 . An impression reinforced by the fact that prizewinners tend to move onto new topics after winning a prize 10,12 and the papers by matched contenders for the prize are concommitently cited less than expected 11,12 .
As a first step toward understanding the possible links between prizes and a topic's extraordinary growth, we investigated whether prizes are statistically associated with the onset of a period of abnormal growth in a topic's productivity, impact, and the migration of scientists into and out of the topic. Our analysis uses new data on hundreds of recognized scientific prizes worldwide 9 and longitudinal data on over 10 thousand scientific topics.
From various sources, we collected data on 405 scientific prizes conferred 2,900 times between 1970 and 2007 with respect to 11,539 scientific topics in 19 disciplines. Scientific prize data was collected from Wikipedia pages on prizes and scientists. The prizes in our sample include awards like the Wolf Prize and Turing Prize, as well as hundreds of other prizes recognized on Wikipedia's "scientific prizes" page 9,16 . To validate the Wikipedia data, we manually crosschecked it with prize-related data on dedicated webpages and in print media. Fig. 1a illustrates how prizes and topics are linked. Prizes were linked to topics by associating the prizewinning scientist with the topics to which they are considered to have made meaningful contributions, also known as their "known-for" topics. We defined known-for topics empirically and via crowdsourcing. Empirically, known-for topics are the topics on which a scientist has published 10 or more total papers. We cross-validated this operationalization using Wikipedia's "Known-For" dataset, which lists a scientist's known-for topics based on the crowdsourced opinions of scientists and Wikipedia users (see Methods section for details). Consistent with our 10-paper threshold, we found that a scholar's Wikipedia "Known-For" topics were those topics scholars had 10 papers on average (See Supplementary Fig. S1 for alternative thresholds and robustness checks).
Scientific topic data comes from Microsoft Academic Graph (MAG). MAG covers over 172 million publications by 209 million authors in 48,000 journals from 1800 to 2017. It uses crowdsourcing, AI, and NLP to generate meaningful and plausible classifications of scientific topics in ways that integrate human expert observations and empirical replicability. MAG defines the universe of scientific topics using Wikipedia article pages that are classified as being on "scientific topics"; these pages are created and updated by scientists and users through crowdsourcing. MAG then uses NLP and AI to assign research publications to topics by associating a paper's text (not just keywords) with the linguistic content of Wikipedia's scientific topics pages 26 . As a validity check, MAG uses statistical sampling to verify the face validity of the classification of papers to topics 27,28 (see SI. Sec.1 for details).
To test whether a prizewinning topic's growth after the prize is awarded is significantly greater than expected, i.e., "extraordinary," we used a difference-in-differences (DID) regression design. DID regression tests for the effects of randomly assigned treatments as well as non-causal tests of statistical significance, in which one group experiences an event that the other group does not experience [11][12][13]29 . Following prior prize research [11][12][13] , we used DID to test for non-causal statistical relationships between prizewinning and a topic's extraordinary growth. Also, following the literature, we combined DID with Dynamic Optical Matching (DOM) [30][31][32][33] . DOM is a longitudinal case control matching procedure that identifies a matched group of non-prizewinning topics. (The Method section reports measurement details and the formal regression equation.) Using DOM [30][31][32][33] , we identified five non-prizewinning topics that had growth patterns statistically equivalent to prizewinning topics before the prize year on six growth criteria. Three  26,[34][35][36][37][38] . To ensure that prizewinning topics and their matched topics have yearly parallel growth before the prize year, prizewinning and matched topics had to be from the same discipline and had to have statistically indistinguishable growth patterns on all six measures, each year, for 10 years before the prize 39,40 .
"Productivity" measures a topic's yearly number of publications and relates to a topic's output, resources, and publication norms 41 . "Citations" measures a topic's yearly number of citations and captures a topic's impact 42 . Citation growth was measured on an absolute and per capita basis. "Impact of Topic's Leading Scientists" measures the mean total citations of the upper 5% of scientists working on a topic and captures the impact of a topic's intellectual leaders. To measure a topic's size 36 , we created the variable "#Incumbents," which measures a topic's yearly number of continuing scientists, and the variable "#Entrants," which measures the yearly number of scientists who publish for the first time on a topic. "#Disciplinary Stars" measures the number of scientists working on a topic that are among the 5% most cited scientists in the topic's discipline 43 . The last three variables ensure that matched topics and prizewinning topics have equivalently eminent scientists and likely prizewinners 12,44 . Supplementary Fig. S4  To test for a statistical relationship between prizes and extraordinary growth, we compared the post-prize growth in prizewinning topics at time t against the average growth rate of the matched topics at time t. We refer to this difference in growth as Δ , formally expressed as: is the prizewinning topic's growth at time and ̃ is the same quantity based on the average growth of the matched topic group (see Fig. 1b for an illustration). Time 's range is -10 to +10.
A Δ = 0.0 indicates no difference in the growth of the prizewinning and matched groups. Time t represents actual time in years (i.e., no rescaling). Extraordinary growth occurs when Δ is statistically and significantly different from zero. We analyze the growth dynamics associated with a topic's first prize and consider a prize to be correlated with the onset of extraordinary growth if growth starts shortly after the prize year. The SI reports confirmatory robustness checks for alternative measures of Δ ( Supplementary Fig. S2).

Results
Prizewinning is strongly and positively related to and extraordinary growth. Relative to matched topics, prizewinning topics have unexpected and significant increases in growth on all six measures of growth. In comparing the overall impact of prizewinning topics to matched topics, we observe large and consistent growth differences. Prizewinning topics display strong post-prize extraordinary growth in productivity and citation impact. At 10 years after the prize, prizewinning topics are 39.8% more productive in terms of the number of publications ( Δ 10 = 0.3351 , 10 − 1 = 0.3981) than matched topics (Fig. 2a). Figure 2b and 2c show changes in citation impact.
Prizewinning topics have 32.6% more yearly citations (Δ 10 =0.2825, 10 − 1 = 0. 3264) and experience a 7.75% average increase in per capita citations per paper at year 10 over matched topics ( Supplementary Fig. S3), indicating that the increase in citation impact holds on a per scientist basis as well. Lastly, the citation impact of leading scientists within the topic is 25% greater than the impact of leading scientists working on non-prizewinning matched topics (Δ 10 = 0.2232, 10 − 1 = 0.2500, Fig 2c).
The migration of scientists into and out of a topic is an indicator of a topic's research attractiveness. Prizewinning topics retain significantly more incumbents (Fig. 2d). After the prize year, incumbent scientists continue to routinely publish on that topic at a rate that is 54.8% (Δ 10 = 0.4366, Δ 10 − 1 = 0.5475) higher than incumbent scientists publishing in matched topics.
New entrants enter prizewinning topics in abnormally high numbers. Prizewinning topics gain over 36.7% more new entrants on average than do matched topics (Δ 10 = 0.3129, 10 − 1 = 0.3673, Fig. 2e). About half of new entrants (46.3%) are rookie scientists who make their first publication on the prizewinning topic. This indicates that prizewinning topics attract young scholars who often make longer-term research commitments 45 .
Star scientists are at the other end of their career stage relative to rookie scientists. Star scientists are the 5% most highly-cited scholars in their discipline (physics, chemistry, sociology, etc.) 46 . Star scientists move into prizewinning topics in larger numbers than into matched topics.
Finally, we tested whether extraordinary growth is associated with a topic's paradigmatic diversification, a relationship hypothesized in the literature 1 . We created a master list of the topics that new entrants into prizewinning and matched topic groups had published before the prize year.
We used Shannon Entropy to quantify the topic diversity of the lists (see SI). The findings suggest that extraordinary growth positively correlates with paradigmatic diversification. As the Δ 10 of topics increase, the paradigmatic diversification of the prizewinning topic grows systematically greater than the paradigmatic diversification of the matched topic group. For example, for topics with a Δ 10 value of 1.5, the prizewinning topic group's paradigmatic diversity is 11.6% greater than the matched topic group (see Supplementary Fig. S7 for all change comparisons).

Funding and Extraordinary Growth
Does funding explain the results? Funding can provide resources that may affect a topic's growth and impact 47 . Also, funding agencies explicitly ration their funds to the most promising research topics 48,49 , which implies that topics that receive grants are seen by funders as having special growth potential. To examine whether funding differences between prizewinning and matched topics explain the extraordinary growth of prizewinning topics, we collected funding data on the subset of our data for which it is available. The NIH publishes funding data in the form of a public list of all papers funded by a specific grant. Using this list, we found that a subsample of 2,853 out of the 11,539 prizewinning topics in our full sample received NIH funding from 1985 to 2005.
For the sample of 2,853 topics, we used DOM to create a new matched group of five nonprizewinning topics for each prizewinning topic, just as we did in the main analysis to ensure that the prizewinning and matched topic groups were balanced and met the parallel trends criteria. In this subsample, we used the same six matching criteria as in the main sample. Seventy-six percent of the matched topics turned out to also be NIH grant recipients, which makes sense, since funding should correlate with our six matching criteria.
To further validate the preceding analysis, we conducted a second analysis with a different subsample. In the second subsample, we matched prizewinning NIH funded topics based on the six criteria used in the main analysis plus a seventh criteria: the matched topics had to have received NIH funding. The results replicate the funding analysis shown above and the main findings, further demonstrating that funding differences do not explain the extraordinary growth of prizewinning topics (please see Supplementary Information, Supplementary Fig. S8, Tab. S13).
Based on the above findings, we concluded that research funding appears to be uncorrelated with a topic's extraordinary growth, at least within this subsample of NIH projects.
First, prizewinning topics have equivalent or slightly less NIH funding before the prize than matched topics (Fig. 3a-c). Second, the level of NIH funding of prizewinning topics is the same before and after prize year (Fig. 3d). Third, consistent with the main results, after accounting for funding levels of prizewinning and matched topics, we find that the onset of the extraordinary growth of prizewinning topics begins the first year after the prize year ( Fig. 3e-j).

Topic-by-Topic Generalizability and Placebo Tests
Our main findings compare differences in post-prize growth for prizewinning and matched topic groups. Here, we examined the growth of each prizewinning topics (N = 11,539) and their five matched topics separately. After the prize, 60% of the prizewinning topics show growth larger than that of their specific five matched topics (binomial test, all p-values<0.001). This finding indicates that the results are not driven by outlier topics and are generalizable (See Supplementary Tab. S1). The binomial tests were reinforced by placebo tests 40,50,51 . The placebo test examines whether the matched topics showed abnormal growth following the prize year of the prizewinning topic (even if they grew slower than prizewinning topics). Supplementary Fig. S5 shows that matched topics have no coincidental extraordinary growth (all p-values>0.05), reinforcing our main finding-prizewinning is associated with the onset of a topic's sustained period of unexpected and extraordinary growth.
Prize Characteristics and the Post-Prize Magnitude of Extraordinary Growth A prize's characteristics and a topic's growth dynamics may be interrelated. 9,24 For example, prizes have been explicitly established for specific fields or with money to send "a symbolic message to the general public that perhaps science and scientists really mattered 24 ". We researched three features of prizes that appear broadly in prize data: money, discipline-specificity, and research recency 18,19 .
Moneyed prizes provide symbolic cultural value and dedicate valuable resources to a topic 19,25 . For example, the 2012 Fundamental Physics Prize, 2013 Tang Prize in Chinese Studies, and the Breakthrough Prize in the Life Science are monied prizes created to communicate to scientists and the public that "the best minds should make at least as much as any trader on Wall Street" and that science aims to "contribute to world development 52 ." Nevertheless, the impact of monetary prizes is unknown. On the one hand, prize money might raise perceptions of a topic's importance, and on the other hand, extrinsic rewards can reduce intrinsic motivation or make little topic-wide difference if money goes to a single individual, not to science 52 . We operationalized prize money as a binarymoney vs. no money variable (45% of prizes were coded as monied).
We also created a three-category money variable defined as (a) no money, (b) money below the median, and (c) money above the median (see Supplementary Tab. S11), which confirmed the simpler binary variable reported below.
Discipline-specific prizes often have greater perceived within-discipline status than do general prizes. For instance, the Fields Medal in math is generally viewed as more prestigious than the general-science National Medal of Science Prize 18,19 . The discipline-specific variable takes on the value of one if at least 85% of all the winners of the prize come from the same discipline; zero otherwise (78% of prizes were coded as field-specific).
Though prizes can be given for recent or past research, most are generally awarded for contemporary work, not longstanding research; otherwise, many prizes would exclude younger scholars 53 . For example, the MacArthur Prize website acknowledges that the fellowship "…is not a reward for past accomplishment, but rather an investment in a person's originality, insight, and potential." To code a prize for its association with recent or past research, we counted the interevent time in years between a prize year and the first year a prizewinner worked on the prizewinning topic. We then created a distribution of inter-event times across all prizes.
To examine the link between prize characteristics and magnitude of extraordinary growth, we regressed the Δ 10 of our six growth variables on money, discipline-specificity, and recency,  predict an increase in Δ 10 of 1.9% or 5.3% in citation growth, respectively. These findings indicate that prizes are associated with extraordinary growth in a topic and that the magnitude of extraordinary growth is strongly predicted by a prize's features. Supplementary Tables S2-S10 report all regression-detailed estimates, robustness checks, and other fit statistics 54 .

Discussion
The rapid, unexpected growth of scientific topics have long held a reputation in science because of their connection to unexpected shifts in research efforts, technology developments, and individual scientific careers. Yet, most work has focused on intricate analyses of specific cases rather than on the statistical dynamics of extraordinarly growth. We conducted a large-scale, science-wide analysis of one factor that may be associated with the onset and magnitude of growth: scientific prizes. We found that scientific prizes predict unexpectedly large changes in the growth of a research topic.
Relative to matched, non-prizewinning topics with equivalent historical growth, disciplinary status, and demography, prizewinning topics are significantly more productive, higher impact, and attractive to incumbent, rookie, and star scientists. At five-to-10 years after the prize year, prizewinning topics are over 30% more productive and are associated with significantly higher citation impact on average on a per capita basis. Also, we found that prize characteristics predict the magnitude of a topic's unexpected and extraordinary growth. The magnitude of growth is greatest when the topic of research associated with the prize is recent, the prize is a disciplinespecific rather than general science award, and the award is monied. Surprisingly, we found no evidence that funding is related to the extraordinary growth of prizewinning topics. These findings have implications for the study of the mechanisms behind the extraordinary growth of prizewinning scientific topics.

Possible Mechanisms Behind the Extraordinary Growth of Scientific Topics
While our work is among the first to look at how prizewinning relates to the growth of ideas rather than the careers of individual scientists, the mechanisms by which prizewinning plays a role in the abnormal growth of topics remains an important avenue of future research. We focused on the statistical links between prizes and the onset of extraordinary growth, which can provide a basis for examining mechanisms. Our findings relate to what Thomas Kuhn called the "essential tension between tradition and innovation" 1,3,55 . Kuhn argued that conservative investment and risk-taking are interconnected in scientific advances. Consistent with Kuhn, we found that prizewinning topics retain a base of incumbents who perhaps reinvest in the topic with a conservative orientation that takes current ideas further, while at the same time the new entrants attracted to prizewinning topics bring with them new viewpoints that promote a risk-taking orientation for experimentation.
The new points of view that entrants bring to the prizewinning topic may also be connected to Kuhn's notion of paradigm shifts. Paradigm shifts have been identified in a few detailed case studies and focus on a topic's revolutionary growth in size and impact. For example, Kuhn references work on the Copernican revolution that indicated that the earth-centric view of the solar system was replaced with sun-centric view of the solar system over a more than 100-year period.
Our work suggests that a possible early source of a paradigm shift maybe the onset of a topic's unexpected growth, which involves an influx of new scientists whose research expertise and diverse demographics provide the potential building blocks of new paradigms, a notion compatible with the teams, social network, and organizational literatures that have shown that new entrants with diverse backgrounds can transform thinking and stimulate innovation [56][57][58][59][60][61] .
Our findings also relate to Zuckerman's prizes-as-signals argument 62 . In this theoretical argument, Zuckerman argued that prizes may act as signals to scientists that a prizewinning topic offers comparatively strong prospects for professional growth, or conversely, prizes signal the end of a period of growth by suggesting that a topic's potential opportunities for professional recognition have run their course, leading scientists to move away from the prizewinning topic 25 .
Examining our findings in light of these crisscrossing arguments suggests conditional support for the claim that a prizewinning topic's intellectual and professional attractiveness become more rather than less positive after the prize's conferment. First, we found that the prize characteristics of money, disciplinary-specialization, and recency are positively related to the onset and magnitude of extraordinary growth. Second, we found that rookie and star scientists begin working on prizewinning topics in unexpectedly high numbers after the prize's award.
Nevertheless, a firm conclusion may have to wait for new data or emerging natural experiments that could shed more definitive light on these causal arguments and their contingencies.
Funding stands out as a possible driver of the growth of topics because funding decisions intentionally involve peer and expert reviews designed to steer researchers and resources to topics predicted to be promising research areas 47

Future Prize Research
A central question in the scientific prize literature since its inception has been whether prizes "select" the highest quality research 9,62 . To date, the answer to this question has remained beyond the reach of empirical work, including in this work, as the answer depends on many factors such as the multiple ways in which an idea's quality can be defined and measured. What has been determined is that prizes are awarded on average to worthy work. For example, the official statement by the International Congress of Mathematicians, which include the Field's Medal, noted that on average prizes are not intended to select the best work, just work that is worthy: "We must bear in mind how clearly hindsight shows that past recipients of the Field's medal were only a selection from a much larger group of mathematicians whose impact on mathematics was at least as great as that of the chosen" (ICM 1994). 12 If one accepts the ICM's approach to prizes, newly identified linkages among prizewinners and prizes raise related questions about prizes and meritocracy.  found that the number of prizes worldwide have proliferated, which presumably offers more opportunity to celebrate scientists and ideas 9 . However, as prizes have proliferated, prizes have become increasingly concentrated within a relatively small network of elite scientists and their mentees.
Further, the most successful mentees study topics that differ from their mentor's topics of study, suggesting that skills associated with conducting prizewinning work can be mentored and applied to new research areas 16 . Future research may therefore examine ways in which prizewinning tacit knowledge and research skills can be diffused more broadly across scientists and topics, and how vacancy chains within the prize network may open and close.
Another area of prize meritocracy focuses on representation. New research indicates that women are winning prizes more inline with their participation rates in science but continue to be but statistically less likely to win research prizes than their male peers 18 . Focusing on research areas where women's participation is large and there are many prizes, such as biomedicine, women are winning prizes a rates closer to their representation in the field but the prizes they win have lower prestige and less money than the prizes won by their male counterparts 18 . Those trends coupled with the finding that a prize's prestige and money predict the magnitude of extraordinary growth a prize can have on a topic suggests that future research should investigate how prize committee nomation and decision procedures are linked to diversity, a process already taking place among some prize committees 66 .
Relatedly, the question of prize meritocracy in science depends on the availability of data that can connect scientists, topics of study, and impact. Here we used the relatively new Microsoft Academic Graph (MAG) data, which uses expert human opinion and algorthims to identify differences in ideas and topics. The relatively new benefits of the MAG data is that it has explicit reproducbile procedures that can be evaluated for bias. Nevertheless, science is an ever changing entity.
Year to year, new fields emerge and the semantic meaning of terms change over time and at different rates across different communities of practice, which means MAG provides a defensible snapshot of scientific topics, but not necessarily an immutable one.
In this way, our work contributes to knowledge about changes in scientific thinking, the mobility of scientists between topics, and investment funding that together broaden understanding of how the frontiers of science develop.

Methods
Difference-in-Difference Regression event, we combine difference-in-difference regression with matching. This approach has been used frequently in studies of prizes and in other areas where observation data is not randomly assigned and where experimental random assignment may be impossible due to factors such as harm to subjects 12,22,29 . Borjas and Doran 12 studied how Field Medal prizewinners' career change relative to non-prizewinners. In their case, like ours, prizes were not assumed to be randomly assigned to topic. Hence, they used matching, where matching is done between the prizewinner and a set of "contenders" non-prizewinners whose historical scholarly performance would have made them contenders for the prize. To justify matches between prizewinners and non- shows that past recipients of the Fields Medal were only a selection from a much larger group of mathematicians whose impact on mathematics was at least as great as that of the chosen" (ICM 1994) 12 . The arbitrariness in the number, timing, and field distribution of Fields Medal recipients means that a similarly great group of "contenders" should exist that can be contrasted with the winners in a difference-in-differences strategy to determine how winning the medal influences productivity and research choices." Similarly, the DID regression used in our analysis is specified as follows: where , is one of our six outcome variables for topic at time . is a dummy variable quantifying whether the topic is a prizewinning topic or a non-prizewinning topic from a matched group. is a dummy variable measuring whether time is before or after the prizewinning event 68 . If the topic belongs to the matched group, the prizewinning year of the related prizewinning topic will be used as the reference point. , is an error term. Regression is specified with fixed effects for discipline and prize year and robust standard errors. The parallel trend assumption (PTA) is essential for DID analysis. We met the PTA criteria by matching prizewinning and non-prizewinning topics on six separate growth indices that uses a procedure that ensures that the pre-prize growth indices of the prizewinning and matched group parallel each other (Fig. 2). Moreover, our analysis meets the PTA criteria of "indistinguishability." "Indistinguishability" is a stronger version of the PTA criteria. PTA requires growth is constant. We also ensure that the selected known-for topic has been studied by the prizewinner before the associated prizewinning event. Since we want to study the relationship between prizewinning and topic's growth pattern, we need 10 years of data prior to the prizewinning event to perform the matching method, and 10 years after prizewinning to allow different statistical analyses of the growth pattern. Hence, we measure the growth pattern of topics from 1960 to 2017.
First, we selected a matched topic candidate pool 32 . To achieve this, for each prizewinning topic , we selected up to 40 close-distance topics in terms of a distance measure ( , ) from the same discipline, generating a peer non-prizewinning candidate pool. For 95% of the prizewinning topics, a proper non-prizewinning candidate pool was identified (11,539/12,041= 95.8%). To achieve matching, we defined a distance measure , to quantify the closeness between the prizewinning topic and a non-prizewinning topic 29,70 : Second, to ensure the balance between the matched and prizewinning topics for the entire system, we select 5 matching topics from the candidate pool to be the topic's peer group. In this process, we (1)         show the raw data relationship between a prize's characteristics and the estimated magnitude of Δ 10 on 6 growth measures (*** p <0.001; ** p <0.01; and * p <0.05). The color dots with error bars represent the mean value and 95% CI, the center line of the black box plot is the median, box limits correspond to the data's first and third quartiles, and violin shades represent the data's distribution. Two-sided t-test are used in these analyses. The p-value for (a) ranges from 2.70 * 10 −180 to 5.30 * 10 −67 , for (c) ranges from 1.60 * 10 −25 to 9.06 * 10 −9 , and for (b) p-value ranges from 0.0017 to 0.013 except for lead scientist impact (p-value =0.374). Sample sizes for topics associated with prizes with recency, money and discipline specific are n=5,672 (46.73%), n=6,102 (50.27%) and n=8,812 (72.59%) respectively. (d)-(f) show the standardized coefficient from a regression of Δ 10 on all three prize characteristics, indicating the significant and substantive association between prize characteristics and the magnitude of the expected level of extraordinary growth in a topic after it is associated with a prize. Control variables are lagged Δ at t = -1, -2, -3, discipline, year, prize visibility and reputation, and prizewinner status. Error bars demonstrate 95% CI. Please see Supplementary Tab. S2-S10 for details of regression analyses and further robustness checks. Mechanics, Algebra, etc.), which are nested with 19 disciplines (e.g., Physics, Mathematics, etc.).

Scientific Prizes and the Extraordinary Growth of Scientific Topics
Because the algorithm that assigns a paper to topics based on a paper's complete text and in relation to other texts, a paper's assigned topics are not synonymous with author-defined "keywords." For example, the paper, "The human disease network 4 ," has the keywords biological networks, complex networks, human genetics, systems biology, and diseasome and classified firstly in the topics: Human Ineractome and then network medicine.
The above process generated a list of research topics for each publication of every prizewinner.
To avoid misclassification errors of topic-labeling in MAG and to make sure that the listed topics are a meaningful part of a scientist's reputation, we considered a topic to be associated with a scientist prizewinner only if the scientist published at least = 10 papers on the topic. We validated this criterion using Wikipedia's "known for" dataset, which crowdsources scientist opinions about the topics that other scientists are known for. The known for data has 3,427 "known-for" topics for our prizewinners.  Fig. S1).

NIH Grants:
We collected NIH grant data from 1985 to 2015 that estimated the amount of funding a topic received before and after the prize year. Grants were linked to different research topics through the NIH publication list associated with each grant. By counting the number of NIH grant links, we obtained an estimated "NIH grant mention" for each topic. Because the total number of NIH grants change year-by-year ( ( )) and, by definition, the NIH mention will change with this number, we adjusted the NIH mention by normalizing it with the total number of NIH grants ( ( )) where ( ) is the total number of NIH grants for year , and < ( ) > calculates the average total number of NIH grants for different years. We find the adjusted NIH mention for the prizewinning topic is flat before and after the prizewinning event, indicating the funding has no measurable influence on the post-prize growth.

Quantifying Growth Patterns of Research Topics
To study whether a growth pattern before and after a topic is associated with a topic's prizewinning event, we find five topics in the same discipline that had growth patterns that were statistically indistinguishable from the prizewinning topics for ten years before the prize year.
To quantify the comparative growth of the prizewinning relative to the peer topics, we defined ! over time : which measures the differences in the logarithm of the quantities and provides an appropriate method for establishing percentages changes in a quantity (prizewinning topic's growth, ! ) relative to a baseline (geometric mean of the peer topics growth, ! F ) since quantities such as citations may have fat-tail distributions 5,6 . As it is well known, the absolute differences perform better for quantities with a narrow Gaussian like distribution, which can be achieved by taking the logarithm of the six quantities, leading to our logarithm difference measure.
Robustness Check: To make sure our results are not methodology-dependent, we also test our results with standard ratio difference measure 7,8 ( Supplementary Fig.S2 a-f), which show growth patterns similar to the ones we present in the main text. A further placebo test also corroborates our main findings ( Supplementary Fig.S2 g-l). Specifically, for each of the prizewinning topic, we selected one non-prizewinning topic from its peer topic candidate pool as a "pretend winning topic", repeating the analysis in Supplementary Fig.2 a-f, finding that there is no difference in the expected growth for pretend topic before and after the prizewinning event, supporting our main conclusions.

Dynamic Optimal Matching Method
To select the peer non-prizewinning topics, we use a Dynamic Optimal Matching method, which applies the Optimal Matching Method 9-11 to a time-series data to simultaneously maximize the closeness and balance characteristics of accurate matching [10][11][12][13] . We focus on prizewinning between 1970 and 2007, resulting in a sample of 12,041 prizewinning and peer non-prizewinning topics. 11,539 topics (> 95%) could be statistically matched to peer topics using DOM. If a topic has multiple prizes over its lifetime, we match for the first prizewinning.
First, we select a peer topic candidate pool 9 . To achieve this, for each prizewinning topic , we selected up to 40 close-distance topics in terms of a distance measure ( ",$ ) from the same discipline, generating a peer candidate pool. For 95% of the prizewinning topics, a proper peer candidate pool was identified (11,539/12,041= 95.8%). To achieve matching, we defined a distance measure ",$ to quantify the closeness between the prizewinning topic and a nonprizewinning topic 7,8 : , where ",% indicates the quantity for the topic in terms of one of the =6 matched categories (i.e. Productivity, Citations, Lead Scientist impact, #incumbents, #Entrants and #Disciplinary Stars). measures number of years prior to the prizewinning year. * represents the prizewinning year for topic , and + = 10, indicates we traced the growth pattern for topics in an 11-year duration, which includes 10 years prior to the prizewinning year.
Second, to ensure the balance between the peer and prizewinning topics for the entire system, we select 5 matching topics from the candidate pool to be the topic's peer group. In this process, we (1) minimize the distances between the peer and prizewinning topics in terms of ",$ , and (2) make sure the distribution of the peer and prizewinning topics are acceptably and simultaneously close for all 66 covariates.
Specifically, we make sure the differences between the prizewinning and peer topic groups are small enough for each matching category n, and for any time before the prizewinning event (−10 ≤ ≤ 0), where the differences between the prizewinning topic and its expected growth at time and category are quantified by Δ ",% ( ) = Elog ",% ( ) − log M ",% ( )G . The expected growth is obtained by averaging the trajectory of the matched topics.
This problem is a classical optimization problem, which could be solved with typical Mixed Integer Programming (MIP) methods 9,13 . We found the best-optimized matching possible where (1) the distance between the prizewinning topics and the peer topics is minimized; at the same time, (2) the difference between the peer and prizewinning groups is not statistically significant for any ∈ [−10,0] and ∈ [1,6]. Mathematically, we have: "'* − 0R < 1.96 * (Δ ",% ( )). ∀ 1 ≤ ≤ 6, −10 ≤ ≤ 0 Here (Δ ",% ( )) measures the standard error of the Δ ",% ( ) for the prizewinning topics at time and in category , and captures number of prizewinning topics. To prevent bias by topics with a large Δ ",% ( ) in the MIP process, we also monitored the topic-by-topic growth of each individual topic. Specifically, for any (−10 ≤ ≤ 0), we compare the growth pattern of each prizewinning topic and all of its peer topics (11,539*5=57,695 pairs). For each of the 66 covariances, we ensure each prizewinning topic had equal probability to grow faster or slower than any of its peer topics. Supplementary Fig. S4 shows the binomial tests validating our method, demonstrating that all p-value is larger than 0.2. This method not only guarantees closeness between the peer and prizewinning topics but also unsure good balancing between and within topic groups.
To further validate our DOM method, we also run an additional "placebo" tests that pretend that each peer topic is a prizewinning topic with the purpose of testing whether the peer topics also showed abnormal growth following the prize year of the prizewinning topic ( Supplementary Fig.   S5). Specifically, for each of the prizewinning topic, we selected a non-prizewinning topic from its matching candidates as a "pretend winning topic", matched it with 5 peer topics, repeating the whole analysis in Fig. 2, finding that peer topics have no coincidental extraordinary growth (all p-values>0.05), reinforcing our main finding prizewinning is associated with and a topic's onset of a sustained period of extraordinary.
To account for possible correlations among different variables, we also repeat the analysis by adopting Mahalanobis distance to quantify the closeness of the topics. Specifically, we present the pre-prize growth patterns of a topic as a 66-element (6 categories * 11 years) vector / [ [[⃗, quantifying the logarithm growth of the topic in the 11-years period before the prizewinning event in terms of the six measures. We can calculate the Mahalanobis distance between the prizewinning topic and a non-prizewinning topic : where is the covariance matrix. By adopting this distance measure in our matching procedure, we repeat the main analysis, finding consistent results ( Supplementary Fig. S6).

Paradigmatic Diversification
Prizewinning topics become paradigmatically diverse than matched peer topics.
Paradigmatic diversification refers to the heterogeneity of concepts scientists use to study a topic 14,15 . To measure paradigmatic diversification, we created a master list of all the topics new entrants in prizewinning or peer topics had published on before becoming a new entrant. Topics in the master list were defined as different from one another if topics were associated with different disciplines (N=19 disciplines). The topic diversity of the master list was then measured using Shannon Entropy as: where represents a discipline, and $ measures the probability that a topic in the list belongs to discipline . We observe that paradigmatic diversity's distribution at Δ *+ ≥ 0 for prizewinning topics is significantly more diverse than peer topics (K-S test, Δ *+ ≥ 0 group, < 0.0001). Supplementary Fig. S7 shows that when Δ *+ equals zero (i.e., no growth differences), prizewinning and peer topics have no significant difference in paradigmatic diversification. However, as Δ *+ grows, relative paradigmatic diversification increases significantly (slope = 0.109 , < 0.0001 ). For example, when Δ *+ equals to 1.5, paradigmatic diversity is 11.6% greater for prizewinning topics than it is for peer topics.

Prize Characteristics Predict Magnitude of Extraordinary Growth
To examine the results' sensitivity to confounds, we regressed the Δ *+ of our six growth variables on money, discipline-specific, and recency along with control variables. Control variables include lagged values of each growth trend at times t-1, t-2, and t-3 years to account for autoregressive effects of Δ *+ . A disciplinary fixed effect variable controls for stable disciplinary differences such as prestige, theoretical vs bench science disciplines, and level of paradigm topic from the matching candidate pool as a "fake prizewinning topic". We repeat the DOM matching process for this faked topic, and search for the five peers for it. We perform the same analysis as we did for the prizewinning topic, finding that for these faked topics, there is no significant difference before and after the prizewinning event, validating our DOM method. We rematch each prizewinning topic with this new distance measure, repeating the main analysis, finding consistent growth patterns. Of the 2,853 NIH funded prizewinning topics, 2,569 prizewinning topics were matched with five non-prizewinning, NIH funded peer topics using DOM. This procedure ensures that 100% of the peer topics are also NIH funded topics and the subsample is balanced and meets the parallel trend requirement. By repeating this matching process in this NIH funded topic pool, we find prizewinning topics grow relatively larger than peer topics after the prize year, in consistent with the main results reported in the main manuscript.  Supplementary Table S1. Binomial tests for extraordinary growths after prizewinning events. For each of our 11,539 prizewinning topics and their peer topics, we calculate the fraction of pairs where the prizewinning topic grows faster than the peer topic, we find around 60% of the prizewinning topics are likelier to growth faster than their specific peer topics (binomial test, all p values<0.001), indicating that the link between prizewinning and extraordinary growth generalizes on the topic-by-topic level. As a comparison, the same analysis has been performed for the data 10 years before the prize, we find the fraction of topics with a positive growth is no significant different with 0.5 (two-tailed binomial test, all p values> 0.2, specific p-value see Fig.  S4), indicating the difference between the prizewinning topics and the peer topics are well balanced before the prizewinning year, further validating our DOM method. Supplementary Tab S13: DID analysis of a prizewinning topic's comparative post-prizewinning growth on six measures for topics that received NIH funding (both prizewinning and peer topics). This table reported a new analysis where both the prizewinning and peer topics are NIH funded topics. Of the 2,853 NIH funded prizewinning topics, 2,569 prizewinning topics were matched with five nonprizewinning, NIH funded peer topics using DOM. This procedure ensures that 100% of the peer topics are also NIH funded topics and the subsample is balanced and meets the parallel trend requirement. By repeating the matching process in this NIH funded topic pool, we find the results are consistent. OLS regression are used in these analyses.