Temporal dynamics of faculty hiring in mathematics

The United States awards approximately two thousand mathematics Ph.D.s annually, yet only about 300 tenure-track positions in doctoral-granting mathematics departments are available each year. A significant portion of these positions are filled by individuals who are not new Ph.D. graduates. The hiring process is often opaque and competitive, with success potentially influenced by factors beyond research productivity and academic credentials, including demographics such as gender. Prior research has highlighted the hierarchical structure of faculty hiring networks and the presence of biases. This study aims to provide a comprehensive, historical understanding of mathematics faculty hiring dynamics at both the individual and departmental levels over the past 70 years, focusing on the transition from Ph.D. holder to faculty member (Graduate-to-Faculty Transition, or GFT). The study leverages the Mathematics Genealogy Project (MGP) database, a rich resource containing graduate advisor-advisee relationships, to analyze over 120,000 records from 150 US mathematics departments. The study will investigate factors influencing individual success in the GFT and explore the temporal dynamics of departmental prestige using network analysis methods, specifically hub and authority centrality.

Existing research on faculty hiring utilizes network science approaches to analyze hiring patterns across various fields. Studies have revealed hierarchical structures in faculty hiring networks and shown that doctoral program prestige is a strong predictor of faculty placement. Bias towards men over women, particularly in fields like business and computer science, has also been documented. Other research explored the influence of socioeconomic status on faculty position acquisition, finding that faculty members often come from wealthier backgrounds. While previous studies have examined faculty hiring across various fields and time periods, a detailed, longitudinal analysis of mathematics faculty hiring remains lacking. This study aims to address this gap by providing a comprehensive analysis spanning seven decades.

The study collected data from the Mathematics Genealogy Project (MGP) on October 4, 2022, focusing on 150 US Ph.D.-granting mathematics departments identified from US News Graduate Schools Top Mathematics Programs rankings (combining rankings from 1998, 2010, and 2018). The data included over 121,000 records of Ph.D. graduates, their graduation years, and advisor information. To infer whether an individual became a doctoral-granting (DG) faculty member, the researchers checked if they advised Ph.D. students listed in the MGP. The gender of individuals was inferred using the genderize.io algorithm, acknowledging the limitations of this approach, particularly regarding the binary nature of the gender classification and potential biases in the underlying data. A threshold of p ≥ 0.6 was used to reduce the impact of potential bias in the inferred gender data. The study then computed the Graduate-to-Faculty Transition (GFT) rate, representing the probability of a mathematics Ph.D. holder becoming a DG faculty member. Network analysis methods were employed to quantify departmental prestige using hub and authority centrality scores, based on the approach described in Myers et al. (2011). A logistic regression model was constructed to identify factors associated with obtaining a DG faculty position, incorporating variables such as year of Ph.D. receipt, inferred gender, prestige measures of the Ph.D. granting institution and advisor's Ph.D. granting institution, and the number of Ph.D. students advised by the advisor. The analysis included several data filtering steps to ensure consistency and to account for missing data. The temporal dynamics of departmental centrality were analyzed using a rolling 10-year window.

The study revealed a growing disparity between the number of mathematics Ph.D. graduates and the number of DG faculty positions filled, particularly after 1970. The GFT rate showed a nonlinear decay over time, indicating that it is becoming increasingly difficult to obtain a DG faculty position. This trend was observed even for historically successful departments. A strong positive correlation was found between the log of the GFT rate and the log of the authority score of the graduate training institution, suggesting a strong link between Ph.D. institution prestige and career success. The logistic regression model confirmed the association between time and reduced probability of obtaining a DG faculty position. Being an inferred woman was also associated with a decreased probability, although this disadvantage appeared to lessen over time. The prestige of the Ph.D. granting institution (measured by authority score) positively influenced the probability of obtaining a faculty position. A surprisingly negative association between the number of students advised by the advisor and the probability of faculty placement was also observed. Network analysis showed that a small group of 14 elite departments consistently held a large portion of the network centrality (approximately 70% of authority centrality and 43% of hub centrality). However, the centrality scores of individual departments within this elite group varied over time. Notably, the Carnegie Mellon University Department of Mathematics consistently increased its centrality scores, while the Massachusetts Institute of Technology and Yale University Departments of Mathematics experienced a decline. The temporal dynamics of graduate production and faculty hiring at these institutions were correlated with their centrality changes.

The findings highlight the increasing competitiveness of the academic job market in mathematics, emphasizing the challenges faced by Ph.D. graduates in securing faculty positions. The strong influence of Ph.D. institution prestige underscores the need to address inequities in access to high-quality graduate education. The gender disparity observed in the hiring probabilities necessitates further investigation into potential systemic biases. The consistent dominance of a small group of elite departments raises concerns about potential concentration of power and resources within the field. The observation of one department's significant increase in centrality, however, suggests that institutional strategies can influence prestige and hiring success. The negative association between the number of students advised by the advisor and faculty placement warrants further exploration. The results provide important insights for individuals pursuing academic careers in mathematics, policy makers aiming to promote diversity and equity in academia, and institutions seeking to enhance their prestige and hiring success.

This study offers a comprehensive, longitudinal analysis of faculty hiring in mathematics, revealing significant trends and disparities. The declining GFT rate, the influence of institutional prestige, and the persistent gender gap highlight challenges in the field. The observation that departmental prestige is not static, however, offers a degree of optimism. Future research should investigate the specific factors driving changes in departmental prestige and the underlying mechanisms contributing to the observed gender gap. More granular data on job applications, citations, and career trajectories would enhance the understanding of individual career paths.

This study has several limitations. First, the reliance on inferred gender from the genderize.io algorithm limits the accuracy of gender analysis, especially considering the binary gender classification. The study lacked information on several factors previously shown to be associated with academic job offers (e.g., number of job applications, awards, citations, postdoctoral experience). It only focused on the transition to DG faculty positions in mathematics, excluding faculty members in non-DG departments or those not listed in the MGP. The chosen centrality metrics, while interpretable, can be affected by localization, a phenomenon where centrality is concentrated in a few nodes. The relatively simple approach to measuring temporal centrality could be enhanced using more sophisticated methods developed for temporal networks. The study's reliance on the MGP dataset introduces limitations related to data completeness and potential biases in the reporting of advisor-advisee relationships.