Elitism in mathematics and inequality

Mathematics, often perceived as objective and egalitarian, exhibits significant inequalities in recognition. This study examines the Fields Medal, a prestigious award in mathematics, as a case study of how prize-giving can either perpetuate existing elites or reshape their definition. While the medal's original intention was to elevate underrepresented mathematicians, concerns have arisen about its tendency to reward those already within established elite circles. Previous research has focused on citational practices, but a comprehensive understanding of the structural barriers to access remains elusive. This research addresses this gap by analyzing the flow of elite mathematicians across national and linguistic-ethnic lines, leveraging both network science and natural language processing techniques.

Existing literature on elitism in science explores various aspects of bias, including the Matthew Effect (over-representation of top scholars), the Matilda Effect (under-representation of women), and the self-reinforcing nature of elite networks. Studies have utilized citational analysis and network science to examine collaboration patterns, hiring practices, and departmental prestige in mathematics. While prior work has investigated mentorship's role in achieving awards like the Fields Medal and Wolf Prize, the relationship between mentorship, prize-giving, and lingo-ethnic identity has not been thoroughly examined due to limitations in data availability and analytic techniques. This study addresses this gap by integrating network analysis with natural language processing (NLP) to analyze lingo-ethnic identities within the mathematical genealogy.

The study utilizes data from the Mathematics Genealogy Project (MGP), containing information on over 240,000 mathematicians and their advisor-advisee relationships. An "elite circle" was constructed by identifying Fields Medalists and computing the shortest paths connecting them. This resulted in a fully connected subgraph representing the minimal network encompassing all medalists. Lingo-ethnic identity, absent from the MGP, was inferred using the ethnicolr package, an LSTM neural network trained on Wikipedia and census data. This classifier, while imperfect, allows for the investigation of identity's role in the flow of elite mathematicians. The study then uses network analysis to examine the flow of mathematicians between countries and lingo-ethnic categories. Ternary diagrams were created to visually represent the in-flow, out-flow, and self-flow of mathematicians within these meso-groups. The power ratio was calculated to quantify the likelihood of winning a Fields Medal for different lingo-ethnic groups within specific institutions.

The analysis reveals historical patterns of elite migration influenced by major events such as World War II and the Cold War. The study demonstrates the Fields Medal's contribution to the integration of Japanese mathematicians into the global elite after WWII. However, persistent inequalities remain. While pluralism (proportion of non-dominant ethnic groups) has increased in major countries like the US and Germany, Arabic, African, and East Asian identities are significantly underrepresented at the elite level. The analysis of meso-level networks shows that while self-reinforcing behavior exists among elite mathematicians, it has also been used to elevate mathematicians from previously marginalized nationalities. The study also reveals that the United States, while exporting many mathematicians, imports a disproportionate number of elite-level mathematicians. Examination of lingo-ethnic identities show that those with European names have high self-reinforcing behavior at the elite level, while Asian, African, and Arabic names demonstrate significantly less self-flow, dispelling the assumption that minority groups cluster together due to homophily. A genealogical analysis of Fields Medalists reveals a high concentration of medalists stemming from a small number of connected components, suggesting a significant degree of concentration within established lineages.

The findings highlight the complex interplay between historical events, institutional structures, and identity in shaping the elite in mathematics. While the Fields Medal has played a role in promoting diversity in some instances, systemic biases persist, limiting access for mathematicians from certain linguistic-ethnic backgrounds. The continued underrepresentation raises concerns about the equitable distribution of resources and opportunities within the field. The significant concentration of Fields Medalists within a few connected genealogical components reinforces the importance of addressing the self-reinforcing nature of elite networks. The results demonstrate that concerted efforts, such as prize-giving, can shape the definition of elite status but that sustained effort is needed to foster greater inclusivity.

This study demonstrates that academic genealogical analysis, combined with NLP techniques, provides a valuable methodology for examining equity and bias in academic fields. The findings highlight the persistent challenges in promoting diversity and inclusion in mathematics. Further research could explore other factors contributing to inequality, such as implicit bias in evaluation processes and access to resources. Efforts to diversify the field should focus on dismantling existing structural barriers and creating more inclusive environments for mathematicians from underrepresented groups.

The study's reliance on inferred lingo-ethnic identities using an imperfect classifier introduces a degree of uncertainty. The accuracy of the ethnicolr package, while significant, is not perfect, and misclassifications could affect the results. Additionally, the MGP dataset, while extensive, may itself reflect existing biases, potentially underrepresenting mathematicians from certain regions or backgrounds. The definition of "elite" used in this study is limited to those connected to Fields Medalists, potentially neglecting other important indicators of academic success.