Temporal dynamics of faculty hiring in mathematics

The study investigates how mathematics Ph.D. graduates transition to doctoral-granting (DG) faculty positions and how this process has evolved over seven decades. Motivated by evidence that faculty hiring networks are hierarchical and can perpetuate inequities, the authors seek a detailed, historical picture specific to mathematics. They examine individual-level factors associated with successfully becoming DG faculty (the graduate-to-faculty transition, GFT) and departmental-level dynamics of prestige using network centrality. The goals are to quantify temporal trends in the ease of obtaining DG faculty roles, assess academic and demographic correlates (including prestige and inferred gender), and track department-level prestige changes over time.

Prior work across multiple fields shows hierarchical faculty hiring networks in which doctoral program prestige strongly predicts placement and where gender disparities can persist (Clauset et al., 2015). Mechanistic models suggest hiring hierarchies arise from faculty production and local homophily (Lee et al., 2021). Large-scale analyses across U.S. academia document hierarchy, elevated attrition among certain groups, and changes in gender composition largely driven by retirements (Wapman et al., 2022). Survey-based studies highlight associations between job offers and factors like application volume, awards, citations, high-profile publications, and postdoctoral fellowships, and negative associations with time on market and dual industry–academic searches (Fernandes et al., 2020). Earlier mathematics-specific work using the Mathematics Genealogy Project (MGP) linked hub/authority centrality with external rankings (Myers et al., 2011). Despite these contributions, a longitudinal, mathematics-focused account of hiring dynamics and the GFT over many decades remained limited; this study addresses that gap.

Data sources and scope: The authors compiled 150 Ph.D.-granting mathematics departments from the union of U.S. News rankings (1998, 2010, 2018). From the Mathematics Genealogy Project (MGP; collected Oct 4, 2022), they retrieved 121,521 graduate records (150 schools), including name, Ph.D. year, and profile link. After excluding 466 records without a year, 121,055 records remained (years 1792–2022; median 1997; mean ~1993).

Inferring DG faculty status and institution: A graduate was inferred to be DG faculty if their MGP profile listed any Ph.D. students. The primary DG faculty institution was assigned as the mode of the Ph.D.-granting institutions of those students (ties broken by earliest). This approach cannot identify non-Ph.D.-granting faculty, DG faculty without listed students, or missing MGP entries. They identified 24,928 DG faculty; restricting to the 150 U.S. News schools yielded 19,372.

Advisor and gender inference: When available, the advisor’s Ph.D. institution and total number of students advised (from MGP) were recorded. First names were processed with genderize.io to infer binary gender and a probability. To reduce bias and exclusion (particularly for East/South Asian names), they selected a probability threshold p* = 0.6 based on aggregate internal consistency criteria. Inferred counts: 93,882 men (77.2%), 22,410 women (18.4%), and 5,229 (4.3%) without sufficient probability for inference.

Graduate-to-faculty transition (GFT): The annual GFT rate is defined as the fraction of graduates in a year who later appear as DG faculty (via advising), computed across 1900–2019. A subset analysis considered “well-placing” schools that, for every year 1950–2015, graduated at least one Ph.D. who later advised a student in one of the 150 departments (10 schools: Harvard, MIT, Princeton, Stanford, University of Chicago, UNC–Chapel Hill, UC Berkeley, University of Michigan, University of Pennsylvania, University of Wisconsin–Madison).

Network construction and centrality: For departmental analysis, directed weighted edges represent hiring flows from a DG faculty department to the Ph.D.-granting department of that faculty member. Hub and authority centralities (Kleinberg) were computed as the leading right/left singular vectors of the adjacency matrix (scaled to sum to 1). Temporal dynamics were analyzed with 10-year rolling windows from 1950–2019. A subset of 106 departments that had nonzero centrality in every rolling period was used for temporal comparisons.

Logistic regression model: Outcome: whether an individual became DG faculty at one of the 150 schools. Explanatory variables: Ph.D. year; inferred gender (woman indicator); interaction (year × woman); target’s Ph.D. authority score (10-year window up to but excluding Ph.D. year); advisor’s Ph.D. hub score (same window); advisor’s number of Ph.D. students (same window). Due to correlations among network measures, only target authority and advisor hub were included (lowest inter-correlation). Data filtering: Ph.D. years 1950–2015; advisor’s Ph.D. institution among the 150 schools; records with gender inference retained; records with computable prestige scores retained. This yielded N = 81,691; observed positive outcome frequency = 0.16. Model fitted via logistic regression (glm in R). A likelihood ratio test versus a null model gave p < 0.001. Coefficient estimates are reported in Table 1.

• The number of mathematics Ph.D.s awarded has grown substantially since 1900, while the number of graduates who later become DG faculty plateaued after ~1970, widening the disparity.
• The GFT rate has decayed nonlinearly over time, approaching its lowest levels in the last 30 years; recent years are also affected by lag to first advisee.
• Even among “well-placing” departments (10 identified), the minimum, median, and maximum annual GFT rates all decline from 1950 to 2015.
• Departmental prestige and GFT: Across 1950–2019, the log of GFT rate correlates approximately linearly with the log of the authority score of the Ph.D.-granting department (least-squares on log–log axes, r² = 0.7). Example outlier: San Diego State University, due to very small n (2 graduates, 1 DG faculty).
• Upward mobility fraction: Among those who become DG faculty at one of the 150 schools, the fraction moving to a department with higher authority than their Ph.D. department remains relatively stable at ~15–25% from 1950–2019.
• Logistic regression (N = 81,691; positive rate 0.16): • Year: negative coefficient (Estimate −0.0377, p < 0.001) → decreased probability of DG placement over time. • Inferred gender woman: negative (−13.9, p < 0.001) → women have lower odds than men, on average. • Year × woman: positive (0.00688, p < 0.001) → gender disadvantage narrows over time. • Target’s Ph.D. authority: positive (1.37, p < 0.001) → higher prestige associated with higher placement probability. • Advisor’s Ph.D. hub: not significant (0.0714, p = n.s.). • Students advised by advisor: negative (−0.0479, p < 0.001).
• Centrality concentration (106 departments, 10-year windows 1950–2019): 5–7 departments hold 50% of authority centrality; 11–19 departments hold 50% of hub centrality. Roughly one-third of departments hold 90% of authority and about two-thirds hold 90% of hub centrality.
• Elite departments (14: Caltech, Carnegie Mellon, Columbia, Cornell, Harvard, MIT, Princeton, Stanford, University of Chicago, UC Berkeley, University of Michigan, University of Washington, University of Wisconsin–Madison, Yale) consistently hold ~72% of authority centrality and ~43% of hub centrality over 1950–2019.
• Trajectories within elites: Carnegie Mellon increased both hub and authority centrality consistently from 1950–2019; MIT and Yale declined in both. These trends align with temporal patterns in averaged DG faculty hires and averaged graduate outputs who later become DG faculty.

The findings demonstrate that transitioning from mathematics Ph.D. to DG faculty has become more difficult over time, even for historically strong placement departments. This addresses the central question by quantifying the GFT decline and linking it to both temporal and institutional factors. Prestige, captured via authority centrality of the Ph.D.-granting department, strongly associates with higher placement probability, reinforcing the hierarchical nature of hiring networks. Gender disparities persist, with inferred women experiencing lower placement odds; the positive interaction with time suggests gradual improvement but not parity. Department-level analysis shows that network prestige is highly concentrated and relatively stable at the group level: a small elite commands most authority and a large share of hub centrality across decades. Nonetheless, individual departments can move substantially—Carnegie Mellon’s sustained gains indicate that institutional prestige is not entirely fixed and may be influenced by strategic hiring and successful graduate placement. Together, these results deepen understanding of the mechanisms and temporal dynamics underlying mathematics faculty hiring, highlighting structural constraints and areas where change is possible.

This study provides a seven-decade, mathematics-focused analysis of faculty hiring dynamics using MGP. Main contributions: (1) documentation of a long-term decline in the graduate-to-faculty transition rate, (2) identification of academic and demographic associations with placement—particularly the strong role of Ph.D. department prestige and ongoing gender disparities, and (3) characterization of temporal departmental prestige dynamics, revealing persistent concentration among an elite group but also meaningful shifts (e.g., Carnegie Mellon’s rise). Future directions include integrating richer individual-level covariates (applications, awards, publications, postdoctoral training, time on market), collecting self-identified, non-binary gender and other demographics, expanding beyond the 150 departments and outside mathematics, and employing more sophisticated temporal/multilayer centrality frameworks to probe localization and coupling effects. Ethnographic or qualitative work could illuminate mechanisms behind the negative association with advisor student load and institutional cultural factors that drive departmental prestige changes.

• Data source constraints: DG faculty status inferred from presence of advisees in MGP; misses DG faculty without listed students and those absent from MGP, and cannot capture non-Ph.D.-granting faculty roles.
• Sampling frame: Focus on 150 U.S. News-ranked mathematics departments; for logistic modeling, DG placements outside these 150 were coded as non-events, potentially understating overall placements.
• Temporal censoring/lag: Recent graduates (post-2010) may not yet have had advisees, depressing recent GFT estimates.
• Gender inference: Based on names via genderize.io with a binary outcome and p* = 0.6 threshold; not equivalent to self-identified gender and may introduce bias, particularly across cultures.
• Missing covariates: No data on applications, awards, citations, high-profile publications, postdoctoral fellowships, time on market, or job-search strategies; these factors are known to associate with hiring outcomes.
• Advisor/institution prestige measures: Hub/authority scores computed from the same network can be correlated; model includes a subset to aid interpretability but may omit relevant signal.
• Network methodology: Eigenvector-based centralities can localize, concentrating centrality in few nodes. Temporal analysis via rolling 10-year windows is straightforward but does not exploit more advanced temporal coupling models; choice of window and method may affect estimates.
• Geographic coverage: Advisor institutions outside the 150 were largely excluded in modeling, and many excluded advisors appear to be non-U.S. institutions, limiting generalizability.
• Potential measurement error: Assigning DG institution by mode of students’ Ph.D. locations may misclassify multi-institution advising or joint appointments.