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Elitism in Mathematics and Inequality ✉ Ho-Chun Herbert Chang1,2,4 & Feng Fu 2,3,4

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Elitism in Mathematics and Inequality ✉ Ho-Chun Herbert Chang1,2,4 & Feng Fu 2,3,4 ARTICLE https://doi.org/10.1057/s41599-020-00680-y OPEN Elitism in mathematics and inequality ✉ Ho-Chun Herbert Chang1,2,4 & Feng Fu 2,3,4 The Fields Medal, often referred as the Nobel Prize of mathematics, is awarded to no more than four mathematicians under the age of 40, every 4 years. In recent years, its conferral has come under scrutiny of math historians, for rewarding the existing elite rather than its original goal of elevating under-represented mathematicians. Prior studies of elitism focus on cita- tional practices while a characterization of the structural forces that prevent access remain 1234567890():,; unclear. Here we show the flow of elite mathematicians between countries and lingo-ethnic identity, using network analysis and natural language processing on 240,000 mathemati- cians and their advisor–advisee relationships. We present quantitative evidence of how the Fields Medal helped integrate Japan after WWII, through analysis of the elite circle formed around Fields Medalists. We show increases in pluralism among major countries, though Arabic, African, and East Asian identities remain under-represented at the elite level. Our results demonstrate concerted efforts by academic committees, such as prize giving, can either reinforce the existing elite or reshape its definition. We anticipate our methodology of academic genealogical analysis can serve as a useful diagnostic for equity and systemic bias within academic fields. 1 Annenberg School for Communication and Journalism, University of Southern California, Los Angeles, CA, USA. 2 Department of Mathematics, Dartmouth College, Hanover, NH, USA. 3 Department of Biomedical Data Science, Geisel School of Medicine, Dartmouth College, Hanover, NH, USA. 4These authors ✉ contributed equally: Ho-Chun Herbert Chang, Feng Fu. email: [email protected] HUMANITIES AND SOCIAL SCIENCES COMMUNICATIONS | (2021) 8:7 | https://doi.org/10.1057/s41599-020-00680-y 1 ARTICLE HUMANITIES AND SOCIAL SCIENCES COMMUNICATIONS | https://doi.org/10.1057/s41599-020-00680-y Introduction lthough mathematics is often framed as objective and mentorship on protégé performance, but focuses on metrics of Aegalitarian, recognition of its elite is not equally conferred. academic success like publication record. Recent attention has been given to the Fields Medal, one For prize-giving, Ma and Uzzi study how networks of different of the most prestigious awards in math, and its elite community. prize winners push the boundaries of science (Ma and Uzzi, When the award was first conceived in 1930, it was in part 2018), and show a correlation between network structure and designed to elevate underrepresented mathematicians (Barany, multiple prize-winning individuals. A similar study of self- 2018). The award was intentionally given to individuals that reinforcing behavior has been conducted for the Nobel Prize would otherwise not receive any recognition, rather than the best (Wagner et al., 2015), motivated similarly as Zuckerman’s work young mathematician. Although prizes can be seen as sources of but using contemporary network approaches. However, in both elitism, the criteria for an award helps shape the definition of cases, collaboration (co-author) networks have been the focus, what elite means. The Fields Medal presents a case-study of a and ethnicity and gender identity has been unexplored. prize based on an expansive and equitable vision of scientific A birds-eye view between mentorship, prize-giving, and eth- community. This study thus examines whether the Fields Medal nicity is thus desired, and the lack of metadata in these genea- succeeded, and if not, how it deviates from its original goal. logies has limited the scope of investigation. However, as natural The production of science is a social and systemic endeavor, language processing (NLP) techniques have advanced, network whose process has been analyzed across many dimensions science combined with lingo-ethnic classifiers may provide novel, (Merton, 1973). When observing the growth of publications albeit imperfect, insight towards how linguo-ethnic identity within physics, Price observed the informal affiliation of scientists mediates the historical production of science. with common interests across distant colleges. Invisible colleges,as In Zuckerman’s work, she does not indite the “accumulation of he called it, produced an elite who welded great respect within a advantage” and work of Nobelists. Rather, she asks if limited discipline, and through this hierarchy generated bias of two pri- access to elite status demonstrates a fundamental restriction to mary types: citational and relational (de Solla Price, 1965). the democratic production of science. It is with a similar moti- Bias has been characterized in a few different ways. The vation we approach our study. In this paper, we analyze the flow Matthew Effect, addresses the over-representation of “top scho- of elite mathematicians between nations and lingo-ethnic cate- lars” regardless of research similarity. The Matilda Effect refers to gories, using social network analysis (SNA) and neural-based the systematic under-representation of female scientists (Rossiter, NLP. Like Gargiulo et al., analysis was performed on the 1993). Most of these studies come out of sociology, and the work Mathematics Genealogy Project (MGP), featuring more than on prize giving and elitism is best exemplified by Harriet Zuck- 240,000 mathematicians, where we defined an elite circle formed erman. In Zuckerman’s seminal Scientific elite: Nobel laureates in around Fields Medalists. In the methods, we specify the details of the United States, Zuckerman uses a database of 60,000 academics our network construction, the classifiers used to enrich the to illustrate the self-reinforcing attributes of America’s elite sci- database, and the critical measures we use to analyze our results. entists (Zuckerman, 1977). Indeed, she provides fundamental Our analysis then demonstrates that while self-reinforcing notion of “accumulation of advantage” to describe how relative behavior among the elites were present (congruous with the advantage is retained. In particular, she shows the Nobelists existing literature), it had also been used to elevate mathemati- began their careers with the advantages of family support, a cians of marginalized nationalities. The Fields Medal was part of a privileged education, early access to scientific equipment. larger effort to integrate Japan after WWII. This is consistent with These sociological studies paved the way to our understanding Parshall’s analysis of the Fields Medal, as part of a greater push to of how identity—gender, language, and ethnicity—mediated the mend international relations, such as integrating Germany after production of science. With the advent of the internet, digitiza- World War II (Parshall, 2009). While we show increases in tion, and public data, the sociological approach has been aug- pluralism among major countries, Arabic, African, and East mented with network science. Within mathematics alone, several Asian identities remain under-represented at the elite level. studies on elitism have been conducted. Methods draw pre- We conclude by discussing how concerted efforts by academic dominantly from the complex network perspective (Zeng et al., committees, such as prize giving, can either reinforce the existing 2017), leveraging network repositories such as citational net- elite or reshape its definition. A return to its roots, as Barany works. For instance, Ding finds collaboration between top sci- advocates, may provide just that. We anticipate our methodology entists have increased from the 1990s onward. Beyond of academic genealogical analysis can serve as a useful diagnostic scholarship, studies have also considered hiring practices (Clauset for equity and systemic bias within academic fields. et al., 2015) and departmental prestige (Myers et al., 2011). We now take a closer look at mentorship and prize giving. Prior work has investigated the relationship between scientific Methods mentorship and winning the Fields Medal or Wolf Prize. Rossi Graph construction. The graph was constructed using the et al. studied the role of advisor–advisee relationships (Rossi et al., Mathematics Genealogy database (North Dakota State University, 2017) and proposed the genealogy index, adapted from the h- 2014). Nodes are mathematicians, and directed edges represent index which was initially developed by Hirsch (2005). While this advisor–advisee relationships. The dataset contained information showed the propagating effects of strong mentorship, its rela- (listed in order of completeness) on the academic, tionship to prize giving is tenuous. Gargiulo et al. studied the advisor–advisee links, school, Ph.D. graduation year, country, and entire, connected giant component of the mathematical genealogy dissertation title and topic. The IDs of Fields Medalists were project (MGP), one of the most complete advisor–advisee data- identified, and then the shortest path was computed in a pairwise bases maintained today. They further enriched the data using fashion. data mining techniques (Gargiulo et al., 2016). Their work The subgroup of elites was thus created by taking the union of focused on integrating math history with temporal network shortest paths between Fields Medalists. Our elite group is fully analysis, and provides a descriptive analysis of how fields in math connected and denotes a minimal graph that connects all the evolved based on country, discipline, and the structure of aca-
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