PhD Mentorship and
Gender Representation in
Academic Mathematics

CU Boulder Applied Math Seminar
April 16th, 2026

Phil Chodrow
Department of Computer Science
Middlebury College

Hi everyone! I’m Phil Chodrow

New-ish professor of CS at Middlebury College, a small liberal arts college in Vermont.

Students/postdocs: ask me about #LiberalArtsLife if you’re curious.

PhD: Operations Research at MIT

Postdoc: Math at UCLA (with Mason Porter)

I work on…

• Higher-order networks, hypergraphs
• Math models of social systems
• Misc. data science

I teach…

• Machine learning
• Network science
• Discrete math

Also: aikido, hiking, cycling, tea, chess, gardening, books (scifi, fantasy, history)

Yes, it really does look like this 😁😁😁

Gender Representation in Academic Math

Data from the 2020 AMS Departmental Profile 🤦🏻‍♂️

*Actually this one is from 2017-2018 (Report on New Doctorates) 🤦🏻‍♂️🤦🏻‍♂️🤦🏻‍♂️

Much Work (Including From Here!)

Focus For Today

Questions for today

What mechanisms drive (lack of) gender representation in academic mathematics?

What could the effects of interventions be on gender representation in math?

The Team

	Heather Brooks Harvey Mudd		Harlin Lee UNC Chapel Hill
	Mason Porter UCLA		Juan G. Restrepo CU Boulder
	Anna Haensch Tufts		Phil Chodrow Middlebury

Our Data

Our Data

Our Data

Ben Brill, UCLA ’22

Total of 116,306 advisor-student pairs in the US since 1950, representing 21,781 distinct advisors.  We observe or estimate math subfields for 94% of these pairs (predictions based on thesis titles).  We estimate gender for 95% of PhD students and 97% of advisors. 

Data issues…

Misgendering

Incorrect MSCs inferred

More missing recent advisors –> undercounting female advisors

Various shenanigans

Some Hypotheses

Mentorship

Female advisors are more effective in attracting or retaining female graduate students.

Belonging

Greater representation in the grad student community attracts women to programs and subfields.

Attrition

Addressing disparities in career attrition for female faculty would help to close the gender gap.

Two-prong modeling strategy

Advisor production

Model the number of graduate students produced by a given advisor.

Technique: maximum likelihood estimation in a bespoke stochastic model.

Student gender

Model the gender of students produced by a given advisor.

Technique: logistic regression.

Generative model of advisor production

Assumptions:

• Startup depends on subfield.
• Career length depends on gender.
• # students per year depends on subfield and gender.

Latent variable model

We model an observed sequence of students \(\color{#086788}{\mathbf{S}} = (\color{#086788}{S}_1, \color{#086788}{S}_2, \ldots, \color{#086788}{S}_T)\) produced by an advisor as a function of an unobserved advisor career \(\color{#07A0C3}{C}\) specified by the startup period length and retirement year.

\[ \begin{aligned} p(\color{#086788}{\mathbf{S}};\color{#F25C54}{\boldsymbol{\theta}}) &= \sum_{\color{#07A0C3}{C}\in\mathcal{C}} p(\color{#086788}{\mathbf{S}}|\color{#07A0C3}{C};\color{#F25C54}{\boldsymbol{\theta}})p(\color{#07A0C3}{C};\color{#F25C54}{\boldsymbol{\theta}}) \end{aligned} \]

We learn \(\color{#F25C54}{\boldsymbol{\theta}}\) using a hybrid expectation-maximization algorithm: some parameters can be estimated efficiently via EM, while others must be estimated by direct gradient methods.

Men have estimated careers ~4 years longer (on average)

Attrition

Addressing disparities in career attrition for female faculty would help to close the gender gap.

Qualitative match to Barrett-Walker et al. (2023).

Longer careers \(\times\) more students per year = more students per career

We hypothesize that greater student production per year by male advisors reflects unequal access to research resources; cf. Zhang et al. (2022)

Logistic model for advisee gender

Estimate the odds that the next student produced by an advsior is female based on subfield, advisor gender, and representation of women in advisor group and subfield.

\[ \begin{aligned} \log (\text{odds F}) = & \beta_0 \;+ \\ & \rho \times (\text{advisor is F}) \;+ \\ & \gamma \times (\text{proportion F advisees in group}) \;+ \\ & \eta \times (\text{proportion F in subfield}) &\quad \phantom{\eta = -3.27 \; (0.12)}\\ \end{aligned} \]

We tried a lot of other models with other features (e.g. decade, nonlinear transformations, etc) but this one was near-best (and simplest) in cross-validation among those without an explicit term for the topic of the subfield.

Logistic model for advisee gender

Estimate the odds that the next student produced by an advisor is female based on subfield, advisor gender, and representation of women in advisor group and subfield.

\[ \begin{aligned} \log (\text{odds F}) = & \beta_0 \;+ &\quad \beta_0 &= -2.14 \; (0.04)\\ & \rho \times (\text{advisor is F}) \;+ &\quad\rho &= \phantom{-}0.42 \;(0.02)\\ & \gamma \times (\text{proportion F advisees in group}) \;+ &\quad \gamma &= \phantom{-}1.16\; (0.06)\\ & \eta \times (\text{proportion F in subfield}) &\quad \eta &= \phantom{-}3.27 \; (0.12)\\ \end{aligned} \]

Mentorship Female advisors are more effective in attracting or retaining female graduate students.

Belonging Greater representation in the grad student community attracts women to programs and subfields.

Homophily effects: advisor-student and student-student

Both the gender of a students’ specific advisor and the overall proportion of female advisors in the subfield’s population contribute to the likelihood that the student is female.

High uncertainty in the model predictions for large \(p_F\) reflects the fact that we have very little data in that region.

Interlude: The Cool Math Story I Wanted To Tell You

If \(p^*\) is the stationary proportion of graduates in the subfield, then \(p^*\) approximately satisfies \[ \begin{aligned} p^* = \color{#ffaf03}{w_f}\color{#ffaf03}{\sigma_f}(p^*) + \color{#5b427c}{w_m} \color{#5b427c}{\sigma_m}(p^*) \end{aligned} \]

\(\sigma_g(p^*)\): prob. next student of an advisor of gender \(g\) is female.

\(w_g\): proportion of students in subfield advised by advisors of gender \(g\) (estimated from advisor production model).

Mean-field assumption: advisor groups have same demographics as advisor’s subfield.

Instead: What might we expect near-to-medium term?

100 simulations initialized with 1,000 active advisors who received PhDs over period 1980-2000, 20% female.

Modeling Interventions on Attrition and Student Production

Attrition Hypothesis

Addressing disparities in career attrition for female faculty would help to close the gender gap.

Approach

Equalize career length and student production parameters over a 10-year intervention period.

Intervention: 2025-2035

• Faculty only: Female faculty during the intervention period gradually change career and production parameters to match those of their male colleagues.
• Students only: Starting in the intervention period and continuing thereafter, graduating female students adopt the same career and production parameters as their male counterparts.
• Both: Both.

Modeling Interventions on Medium Timescales

No Intervention

Faculty Intervention

Parameters are equalized over a 10-year period for active advisors during that period.

Student Intervention

Parameters are equalized for students graduating during the intervention period and thereafter.

Both

Parameters are equalized for both active faculty and students graduating during the intervention period and thereafter.

Looking Back on Our Hypotheses

Looking Back on Our Hypotheses

Mentorship: Female advisors are more effective in attracting or retaining female graduate students.	Yes! Female advisors are ~30% more likely than male advisors to produce female PhD graduates.
Belonging: Representation in the grad student community attracts women to programs and subfields.	Yes! Subfields/advisor groups with greater representation of women tend to attract more women.
Attrition:Addressing disparities in career attrition for female faculty would help to close the gender gap.	Yes! This is an intrinsically inclusive goal AND may accelerate progress by 10-20 years.

Next?

Thanks everyone!

	Heather Brooks Harvey Mudd		Harlin Lee UNC Chapel Hill		Mason Porter UCLA
	Juan G. Restrepo CU Boulder		Anna Haensch Tufts		Ben Brill UCLA ’22

National Science Foundation

ICERM @Brown Two summer programs!

Preprint coming soon 😬😬😬

Extra Slides

Many math subfields are on
qualitatively similar trajectories.

Six largest subfields
by record count.