Dynamics of Gender Representation in Academic Mathematics

SIAM Conference on Applications of Dynamical Systems
Minisymposium on Data, Inference, and Dynamics in Complex Social Systems
Denver, CO || May 13th, 2025

Phil Chodrow
Department of Computer Science
Middlebury College

Questions for today

What mechanisms drive ongoing lack of gender representation in academic mathematics?

What can we expect to happen in our profession if these mechanisms continue to operate as is?

What could the effects of interventions be on long-term gender representation?

Inspiration from…

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

Some early caveats

This talk represents work-in-progress using data about our mathematics community. All results are preliminary!

This talk focuses on the production of PhD graduates and therefore almost exclusively considers doctoral universities.

Gender is not binary, but unfortunately our data (and therefore our story and our model) are.

Quantitative work complements, but never replaces: voices of marginalized scholars, qualitative research and critical theory, activism, and implementation of initiatives and policies.

Representation varies across mathematical subfields

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.

Leadership A small number of influential women can dramatically change the culture of a department or research community.

Our data

Our data

Ben Brill, UCLA ’21

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

Nonrandom missing data

Various shenanigans

We have more than counts – we have relationships

We could treat this as a branching process and read off parameters, but this would assume that we are already at stationarity – our predictions would just be averages over the recent past.

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.

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

The vector \(\color{#F25C54}{\boldsymbol{\theta}}\) contains the parameters to be estimated.

We do this using a hybrid expectation-maximization algorithm: some parameters can be estimated efficiently via EM, while others must be estimated by hill-climbing.

Men have estimated careers ~4 years longer

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

We hypothesize that greater student production per year 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.

\[ \begin{aligned} \log (\text{odds F}) = & \beta_0 + \beta_a \times (\text{advisor gender}) + \beta_f \times (\text{subfield}) \\ & \beta_g \times (\text{proportion F advisees in group}) + \\ & \gamma_{p} \times (\text{proportion F in subfield}) \end{aligned} \]

We tried a lot of other models with other features (e.g. decade, nonlinear transformations, etc) but this one was best in cross-validation.

Homophily effects: advisor-student and student-student

Numerical estimation of stationary proportion

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

• \(\sigma_g(p^*)\): probability that the 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 represent the subfield as a whole.

Long-run behavior

Two strategies: compute the numerical stationary proportion of female advisors or simulate the model forwards.

We can do both of these either with or without parameter uncertainty.

Long-run behavior

What could we do to make math a more inclusive profession?

Two candidate interventions:

Improve retention and resourcing of female advisors

We can model this by setting the career and student production parameters of women equal to men in the advisor production model.

Train men as equally-appealing mentors for female PhD students:

We can model this by setting the propensity of men to produce female PhD advisees equal to women in the advisee gender model.

Limitations of scenario modeling: we are not explicitly modeling the supply of female students entering graduate school (“the pipeline”).

Estimating the effect of interventions on long-run proportions

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.	Leadership A small number of influential women can dramatically change the culture of a department or research community.
Yes! Female advisors are substantially more likely than male advisors to produce female PhD graduates.	Yes! Subfields/advisor groups with greater representation of women tend to attract more women.	Yes, but… Resourcing and retaining female faculty is an inclusive, equitable goal to pursue but may not lead to large-scale change.	We’re exploring… We’re developing models and data analysis to try to detect these effects in our data set.

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 😬😬😬