Temporal dynamics of faculty hiring in mathematics

University faculty hiring networks are known to be hierarchical and to exacerbate various types of inequity. Still, a detailed, historical understanding of hiring dynamics lacks in many academic fields. We focus on the field of mathematics, analyzing over 120,000 records from 150 institutions over seven decades to elucidate the temporal dynamics of hiring doctoral-granting (DG) faculty at the individual and departmental levels. We demonstrate that the disparity between the number of mathematics Ph.D.s awarded and the number of DG faculty positions filled has grown over time. Even institutions with the best records of DG faculty placement have experienced a temporal decline in the probability of their graduates obtaining a DG faculty position. By quantifying the mathematical prestige of each department with a network statistic, authority centrality, we find an approximately linear relationship between the log of the prestige of one's Ph.D. institution and the log of the probability of obtaining a faculty position. Moreover, we observe associations suggesting that the probability of DG faculty placement has decreased over time and is smaller for women than for men. On the departmental level, a group of 14 elite departments dominated the authority centrality of the entire network between 1950 and 2019. Strikingly, one department within this elite group increased its centrality scores consistently, which hints at the possibility for a department to improve its prestige. This analysis highlights the challenges of transitioning from Ph.D. holder to faculty member in mathematics.