# Quantifying and Documenting Inequity in PhD-granting Mathematical Sciences
Departments in the United States

Ron Buckmire111Corresponding author<EMAIL_ADDRESS>Carrie Diaz Eaton  Joseph E.
Hibdon, Jr  Jakini Kauba  Drew Lewis  Omayra Ortega  José L. Pabón  Rachel
Roca  Andrés R. Vindas-Meléndez

###### Abstract

We provide an example of the application of quantitative techniques, tools,
and topics from mathematics and data science to analyze the mathematics
community itself in order to quantify and document inequity in our discipline.
This work is a contribution to the new and growing interdisciplinary field
recently termed “mathematics of Mathematics,” or “MetaMath.” Using data about
PhD-granting institutions in the United States and publicly available funding
data from the National Science Foundation, we highlight inequalities in
departments at U.S. institutions of higher education that produce PhDs in the
mathematical sciences. Specifically, we determine that a small fraction of
mathematical sciences departments receive a large majority of federal funding
awarded to support mathematics in the United States. Additionally, we identify
the extent to which women faculty members are underrepresented in mathematical
sciences PhD-granting institutions in the United States. We also show that
this underrepresentation of women faculty is even more pronounced in
departments that received more federal grant funding.

##  1 Introduction

The kinds of problems mathematics and data science can be used to solve are
extremely varied, running the gamut from theoretical with no foreseen
applications to those that are immediately applicable to important real-world
phenomena like climate change, epidemiology, and social networks. There is a
rapidly growing body of work using tools from the mathematical sciences to
analyze the mathematical sciences itself that has recently been described as
the “mathematics of Mathematics” or “MetaMath” [5]. This term was chosen as an
allusion to the broader field of “science of Science” [12] or “SciSci” that
uses scientific and mathematical tools to analyze science as a whole as well
as its individual disciplines.

In this paper, we present a contribution to the mathematics of Mathematics to
introduce readers to the kinds of questions that can be asked and the types of
tools and techniques that can be used in the emerging MetaMath area. We are
inspired by the work of Wapman, Zhang, Larremore, and Clauset [37] published
in Nature in 2022 that quantified hierarchy in faculty hiring and retention in
a wide array of academic disciplines in the United States by analyzing a very
large dataset of nearly 300,000 faculty members in over 10,000 departments at
almost 400 PhD-granting institutions from 2011 to 2020. The research we
present here builds on and leverages the ideas and analyses presented in
Wapman et al. [37], but focuses on specific disciplines in the mathematical
sciences that are available in their dataset [36], namely, mathematics,
statistics, and operations research. This results in a dataset which includes
nearly 10,000 faculty members in well over 200 departments that granted PhDs
in the mathematical sciences from 2011 to 2020.

Using mathematical tools from network science [21], Wapman et al. produced a
“prestige ranking” for every department at every PhD-granting institution in
their dataset and quantified hierarchy in faculty hiring and retention in a
large number of academic disciplines. In particular, Wapman et al. constructed
a directed graph of PhD-granting departments with an edge from department A to
department B corresponding to a faculty member who earned a Ph.D. at
department A being hired into department B. Unlike other rankings like those
published by U.S. News & World Report that purport to assign prestige based on
an arbitrary selection of attributes, Wapman et al.’s prestige rankings are
based upon the characteristics of the directed graph of departments. It is
assumed that “prestigious” departments will prefer to hire faculty from other
“prestigious” departments, and then the overall hierarchy of departments is
inferred from the topology of the network using the SpringRank algorithm [9].
We will refer to the definition of prestige from Wapman et al. [37] as
“Wapman-prestige.”

We utilize Wapman’s quantification of prestige to produce a definition of
“elite,” which we will use to help us quantify and document inequity in PhD-
granting departments in the United States. We define “elite” institutions as
those that are within the top quartile as defined by Wapman-prestige. In this
paper we will use Hasty et al.’s anthropological definition of inequity. They
say inequity is “the unequal distribution of resources due to an unjust power
imbalance. It is a type of inequality caused by this unequal distribution,
often as a result of injustices against historically excluded groups of
people” [18]. In the mathematical sciences, the underrepresentation of
historically marginalized demographic groups at all levels results in an
unjust power imbalance (see the brief literature review in Section 2 for
further details). Because of the nature of the dataset [36], which contains
gender data but not other demographic data (and in particular no data on race
or ethnicity), we are only able to conduct analyses using gender and not other
identity characteristics. However, by combining this dataset with publicly
available data from the National Science Foundation (NSF) on awards made by
the Division of Mathematical Sciences (DMS) [14], which is the primary funder
of mathematical sciences research in the United States, we can investigate
relationships among gender equity, Wapman-prestige, and NSF DMS funding.

Our thesis is that we can quantify and document inequity in mathematical
sciences PhD-granting departments in the United States. Specifically, in this
paper we will address the following research questions:

  * •

RQ1: What is the relationship between the percentage of women in a department
and that department’s Wapman-prestige?

  * •

RQ2: What is the relationship between Wapman-prestige and funding received
from the National Science Foundation Division of Mathematical Sciences?

  * •

RQ3: What is the relationship between the percentage of women in a Mathematics
department and funding received from the National Science Foundation Division
of Mathematical Sciences?

The rest of this paper is organized as follows. In Section 2, we provide some
examples of recent research that uses data science and mathematics to analyze
the mathematics and science communities. We describe the data and methods used
in our research in Section 3. Specifically, in this section we describe the
processing of the Wapman et al. data and the NSF funding data that is required
so that we can investigate our research questions that support the thesis of
this paper, i.e. that inequity exists in PhD-granting mathematical sciences in
the United States. We provide details about the statistical data analysis
performed to establish the existence of quantifiable relationships between our
variables of interest, gender percentage of faculty in mathematical sciences
PhD-granting departments, amount of funding received from NSF from 2011-2020,
and departmental Wapman-prestige. The results of the data analysis and
discussion of these results are given in Section 4 and Section 5,
respectively. We end the paper by discussing in Section 6 some limitations of
the work presented here and recognizing that there is a lot more work that can
(and should) be done to quantify and document inequity in the mathematical
sciences.

##  2 Existing work on inequity and hierarchy in mathematics

In this section, we provide a short survey of selected recent work that uses
tools, topics, and techniques from mathematics and data science to describe,
document, and discuss inequity in the mathematical sciences. We organize our
summary of the literature in this area into three topics: 1) analysis of the
(lack of) diversity in the mathematical sciences; 2) existence of hierarchy in
mathematics and other academic disciplines; and 3) evidence of inequity in the
mathematical sciences. For a longer survey of the areas discussed here, as
well as the broader field of the mathematics of Mathematics, we refer the
reader to the recent paper by Buckmire et al. [5].

###  2.1 The Demographics and Diversity of the Mathematics Community.

It is well-documented that women are underrepresented at all levels in the
mathematics community, and that their representation declines as they progress
through the academic system [29]. Women made up approximately 42.6% of
recipients of bachelor’s degrees in mathematics between 2013 and 2018 [2].
However, only 29% of doctorate recipients in mathematical sciences were women
(in 2017-2018) [17]. Women were 28% of hires in doctoral-granting mathematical
sciences departments in 2019 [19].

Underrepresentation in the mathematical sciences based on race and ethnicity
is profound and persistent [11]. For example, from 2013 to 2018, the racial
and ethnic makeup of undergraduate math graduates ranged from 64.9% White,
7.5% Latino/Hispanic, and 5.0% Black to 52.5% White, 9.9% Latino/Hispanic and
4.2% Black [2]. Between 1993 and 2002, less than 5% of those who earned
doctoral degrees in mathematics were Black, Latino/Hispanic, or Indigenous,
even though those communities made up a quarter of the general population of
the United States at that time [24].

Vitulli [35] examined the representation of women being hired by mathematics
departments, based upon data from annual surveys conducted by the American
Mathematical Society (AMS). Prior to 2012222The AMS changed how they report
this data in 2012, as the newest National Research Council report no longer
provided a total ordering of departments, instead reporting multiple measures
for each department., the AMS reported this data by dividing departments into
three Groups based on the reputational rankings in the 1995 (or previously,
1982) National Research Council report on doctoral departments [7, 8]. Group I
contained the highest rated 25.9% of the departments. Group II was the next
highest 30.3% while Group III contained the remaining departments. Vitulli
found that from 1991-2011, 20.5% of the faculty hired by Group I departments
were women, while 26.3% of the faculty hired by the remaining departments were
women. We acknowledge that this is just a small sample of the research in the
literature analyzing the demographics and diversity of the mathematical
sciences community.

###  2.2 The Existence of Hierarchy in Mathematics and Science.

Recently, researchers have used available data on faculty positions at
institutions of higher education in the United States to document the
existence of hierarchies in faculty hiring networks in academia. These
hierarchical structures [21] in mathematics and science demonstrate that some
institutions have greater influence on faculty hiring than others [28]; this
is the essential characteristic of what we call Wapman-prestige. Institutions
nearer the top of the hierarchy that are “more prestigious” (i.e., they have
greater Wapman-prestige) are more likely to have graduating doctoral students
go on to obtain faculty positions at institutions that are “less prestigious”
and lower in the hierarchy. Clauset et al. [6] demonstrated the existence of
hierarchy in faculty hiring in a study involving departments in computer
science, business, and history. Wapman et al. [37] expanded this analysis to
cover 295,089 faculty in 10,612 departments at 368 PhD-granting institutions
and all academic disciplines for the years 2011-2020. FitzGerald et al. [10]
built upon Wapman et al.’s research and partially replicated their results by
using data from the Mathematics Genealogy Project (MGP) to restrict their
analysis to mathematics faculty. These results confirm that hierarchies exist
in faculty hiring networks in the mathematical sciences.

###  2.3 Evidence of inequity in Mathematics.

There are multiple research articles that use quantitative tools and
techniques to analyze and highlight examples of inequity in the mathematics
community. Topaz et al. [34] analyzed the editorial boards of 435 mathematical
science journals and found that women accounted for a mere 8.9% of editorial
positions. Editorial positions play important gatekeeping roles and represent
status in the mathematics community, so the underrepresentation of women in
this area demonstrates inequity based on gender in the area of power over
knowledge production. Brisbin and Whitcher [1] found that women are
underrepresented as authors among papers in the mathematical sciences uploaded
to the arXiv preprint repository, and that there are certain subfields
(particularly concentrated within “pure” or theoretical mathematics) with even
larger discrepancies. Researchers have analyzed data describing different
aspects of academic activity and demonstrated myriad ways that gender can
negatively mediate opportunity for advancement, participation, and achievement
in science and mathematics [25, 31, 33, 22]. Schlenker [32] notes that fields
with applications to the social or physical sciences such as numerical
analysis, mathematical modeling, or statistics (i.e. fields seen as being in
applied mathematics) seem to be viewed by some as having low status in the
wider mathematical community. A large study investigating class backgrounds in
academia by Morgan et al. [26] found that faculty are much more likely than
the general population to have a parent with a PhD, with the effect being even
more pronounced at institutions in the top quintile of U.S. News and World
Report rankings.

##  3 Data and Methods

In this section, we will describe the data and explain the methodology used to
obtain our results. Our data and code is publicly available at [3]. We
utilized two datasets, one sourced from Wapman et al. [36] and the second from
awards made by the Division of Mathematical Sciences (DMS) at the United
States National Science Foundation (NSF) between 2011 and 2020 [13].

The Wapman et al. dataset required some nuance to interpret. The dataset
consisted of a census of tenured or tenure-track faculty employed at all PhD-
granting institutions in the United States from the years 2011–2020. Faculty
were only included in this sample if they were employed in the majority of the
years under review. This dataset is centered on departments, rather than on
faculty, and these departments are each assigned to a field such as
“Mathematics.” In particular, a department may be accounted for in multiple
fields; a “Department of Mathematics and Statistics” would have its faculty
included twice, in the fields of “Mathematics” and “Statistics.”

Because our goal is to quantify and document inequity in the mathematics
community as a whole, we choose to define the mathematical sciences as broadly
as possible (see [4]). This choice results in a reduction of Wapman et al.’s
original dataset of 295,089 faculty in all academic disciplines offering PhDs
in the United States to 9,814 faculty that are distributed among the fields of
Mathematics, Statistics, or Operations Research (Table 1). We adopt the
convention of capitalizing these three terms when referring to these fields
present in the data throughout the rest of this paper.

Table 1: Faculty present in the Wapman et al. dataset in the fields of Mathematics, Statistics, and Operations Research. Field | Departments | Faculty Members | Percentage of women
---|---|---|---
Mathematics | 223 | 7328 | 16.8%
Statistics | 122 | 2576 | 20.9%
Operations Research | 51 | 1034 | 19.3%

In our analysis, we incorporate the department prestige rankings from Wapman
et al. [36] which we refer to as Wapman-prestige. Because of the way these are
computed (a department has more Wapman-prestige if its PhD-graduates are hired
by departments that also have Wapman-prestige), some departments do not have a
Wapman-prestige ranking. This could happen if the department does not have a
PhD program in one of the three fields (recall the Wapman dataset began with
institutions that grant PhDs), or if none of its PhD-graduates were hired by
departments with Wapman-prestige rankings. In Mathematics, for example, there
are 223 departments listed, but only 161 of these have a Wapman-prestige
ranking. Departments without Wapman-prestige rankings were not included in the
data analyses involving Wapman-prestige below, but were included in the
analysis of NSF funding later in the paper.

Since the Group I departments—in the groupings used by the AMS historically to
divide departments by perceived quality (see Section 2.1 above)—constituted
about 25% of departments, in our analysis we consider the upper quartile (in
terms of Wapman-prestige rankings) as “elite” departments and compare this
group to the remaining 75% of departments, which we refer to as “non-elite.”

As stated earlier in the paper, the Wapman et al. dataset does not have
information on race or ethnicity but does include gender. However, gender is
only included as a binary variable in their dataset. In fact, gender is self-
reported for a small percentage (6%) of faculty in their initial dataset. They
then attempted to infer the gender of the remaining faculty based on their
names and the use of software that claims to assign gender based on names
relatively accurately; ultimately binary gender was ascribed to a total of 85%
of the faculty listed in their dataset. We include only these faculty who were
ascribed a binary gender in our analyses,which eliminates roughly 15% of the
total due to the inability to accurately ascribe a gender to these data
entries.

We separately obtained data from the NSF’s publicly available data on awards
made by the Division of Mathematical Sciences (DMS) in the Directorate of
Mathematical and Physical Sciences (MPS) from 2011-2020 [13]. These data were
aggregated by institution. Since the institution names in the Wapman et al.
dataset typically did not match the formal organization names listed by the
NSF, we manually adjusted these in order to compare the two datasets. On
average, DMS awarded $235 million per year towards achieving its mission to
support “a wide range of research in mathematics and statistics aimed at
developing and exploring the properties and applications of mathematical
structures” [14]. Of the awards to institutions, 80% were matched to the
departments of interest in the following analysis. The NSF, and DMS in
particular, is the primary source of funding for mathematics research in the
United States [14]. While some mathematicians (such as several authors of this
paper) receive funding from NSF divisions other than DMS and directorates
other than MPS (e.g., the Division of Undergraduate Education and the
Directorate for STEM Education) as well as from other federal agencies (e.g.,
the National Institutes of Health), we consider DMS funding a reasonable
measure for overall financial support of mathematics by the federal
government.

There are two major caveats to our use of the NSF DMS funding data. First, NSF
awards are made to institutions rather than specifically to departments, which
is the unit of analysis provided by the Wapman et al. data. Second, since
faculty in Statistics and Operations Research typically have more varied
sources of funding, we only considered the field of Mathematics in our
analyses of funding discussed below.

Some of the institutions in the NSF data with the largest amount of funding
were not included in our analysis because they were mathematics research
institutes, not PhD-granting institutions. For example, the Mathematical
Sciences Research Institute (MSRI, now known as the Simons Laufer Mathematical
Sciences Institute or SLMath) and the Institute for Advanced Study (IAS) were
awarded funds as separate entities from their associated universities, the
University of California at Berkeley and Princeton University, respectively.
We chose to treat MSRI and IAS as separate, non-PhD-granting institutions and
therefore they are not included in our analyses.

##  4 Results

In this section, we present the primary results of our research into the
distribution of faculty and funding at mathematical sciences PhD-granting
institutions in the United States. In Figure 1, the percentage of women in the
fields of Mathematics, Statistics, and Operations Research from 2011 to 2020
is given. We note that the percentage of women in Mathematics lags behind
Operations Research and Statistics throughout the time period of the dataset,
mirroring the lower percentage of women that earn PhD’s in Mathematics versus
the other two fields [17]. We further note the percentage of women in
Mathematics, Statistics, and Operations Research is far below the percentage
of women in Academia as a whole for the time period covered by the dataset.

Figure 1: Fraction of women in the fields Mathematics, Statistics, and
Operations Research, as well as academia as a whole, over the ten year period
of the dataset.

Next, we computed the percentages of faculty in each department inferred to be
women, and plotted these according to Wapman-prestige rank in the fields of
Mathematics, Statistics, and Operations Research in Figure 2. To compute this
percentage, we used as a denominator the total number of faculty in a
department for which a gender was inferred, in effect removing from our sample
any faculty members whose gender could not be inferred. In Figure 2, the blue
circles are clustered in the lower-left corner of all three subfigures; this
corresponds to the data demonstrating that elite departments (in the top
quartile of Wapman-prestige) also have a low percentage of women (below 20%
for Mathematics).

Figure 2: Percentage of women by department in the fields of Mathematics,
Statistics, and Operations Research. Color distinguishes the upper quartile of
Wapman-prestige (blue circles) from the lower three quartiles (orange
squares).

In order to address RQ1, we then considered the elite institutions as a group
and calculated the percentage of faculty at these institutions that are women
(Table 2); in each case, we see that the percentage of women among these elite
institutions is lower than among non-elite institutions. A chi-squared test
for each field was conducted, finding only the difference in Mathematics to be
significant ($p<0.001$). We also conducted a Kendall tau test to determine if
there is an association between the percentage of women and Wapman-prestige
rank of Mathematics departments; we found a significant negative association
between Wapman-prestige rank and rank by percentage of women ($\tau=-0.23$,
$p<0.001$). In other words, higher Wapman-prestige of Mathematics department
is associated with having a lower percentage of women.

Table 2: The percentage of faculty at elite and non-elite institutions who are women in each field. Field |  Percentage of women among elite institutions |  Percentage of women among non-elite institutions
---|---|---
Mathematics | 12.5% | 18.1%
Statistics | 21.3% | 21.6%
Operations Research | 17.0% | 18.7%

To address RQ2, we then explored the distribution of DMS funding to
Mathematics departments with Wapman-prestige rankings from 2011-2020. The
elite institutions (i.e., the upper quartile by Wapman-prestige) were awarded
in aggregate $119M per year in grant funding, while the non-elite
institutions, of which there are three times as many, were awarded only $70M
in aggregate of NSF money per year. We plotted this funding by Wapman-prestige
of each department in Figure 3. Note that the two subfigures in Figure 3
depict total funding and per capita funding versus Wapman-prestige and yet
they are remarkably similar in appearance. This demonstrates that we can use
NSF funding to distinguish between different mathematical sciences PhD-
granting institutions without worrying about individual outlier faculty
members in Mathematics departments of those institutions. We also computed the
total amount of funding received by elite (top quartile by Wapman-prestige)
and non-elite (lower 3 quartiles by Wapman-prestige) departments over the time
period in question. Elite departments received 64.7% of funding in our
dataset, compared to 35.3% for the non-elite departments (despite these being
thrice as numerous). Here we also conducted a Kendall tau test, finding a
significant positive relationship between Wapman-prestige rank and DMS funding
rank ($\tau=0.68$, $p<0.001$). In other words, higher Wapman-prestigeis
associated with more DMS funding.

Another metric that can be used to quantify inequity in NSF DMS funding
received by Mathematics departments in the United States is the Gini
coefficient, a well-known measure of inequality often used to characterize
wealth inequality on a scale from 0 to 1. A uniform distribution of wealth
would result in a Gini coeffient value of 0 and a case where one individual
holds all the wealth would result in a Gini coefficient of 1. The Gini
coefficient of NSF DMS funding for the Mathematics departments in our dataset
is 0.63. For more information on the Gini coefficient, refer to [27].

We also analyzed the full DMS-funded portfolio (excluding fellowships which
are given to people instead of institutions) to avoid a possible sampling
effect due to our focus on PhD-granting departments. In this more
comprehensive dataset, the top 20% holds 86.1% of all DMS funding. The Gini
coefficient of this distribution is 0.80. Thus, the larger set of all DMS
funding recipients demonstrates greater inequality than the subset of PhD-
granting institutions.

(a) Total funding

(b) Funding per faculty

Figure 3: Average annual grant funding for Mathematics departments by the
prestige rank of the department, displayed by total funding to the department
(a), and on a per capita basis accounting for the varying number of faculty in
each department (b).

To address RQ3, we plotted the annual grant funding received by Mathematics
departments against the percentage of women in those departments in Figure 4.
We note an interesting effect in Figure 4, where none of the 29 departments
(which are all non-elite with respect to Wapman-prestige) with at least 25%
women received more than $1.1M in average annual funding from the DMS. We
conducted a Kendall tau test to determine if there is an association between
annual funding received from DMS and the percentage of women in Mathematics
departments and found a significant negative relationship ($\tau=-0.22$,
$p<0.001$). In other words, a higher percentage of women is associated with
less annual DMS funding,

Figure 4: Average annual grant funding for Mathematics departments by the
percentage of women faculty in the department. The upper quartile (by
prestige) departments are represented by blue circles, while the remainder are
orange squares.

In addition to the statistical analyses above, we also ran a k-means
clustering analysis on the dataset that contained NSF DMS funding and faculty
gender percentage for mathematical sciences PhD-granting departments. We are
particularly interested in the extent to which clusters produced by this
analysis would reflect the Wapman-prestige rankings.

After normalizing the data, we ran an analysis to determine the optimal
clustering number. Using the cluster [23] and factoextra [20] packages in the
R programming language, we identified three as a consistent optimal number in
the “bend-in-the-knee” analyses. These analyses identify the point at which
increasing cluster number does not return significant advantages in lowering
measures such as within-cluster variation. A visualization of the resulting
three clusters is found in Figure 5. Cluster 1 in the bottom left, designated
by red squares, identifies academic institutions with low representation of
women and with low funding amounts. Cluster 2 in the bottom right, designated
by blue diamonds, identifies institutions with high representation of women,
but with low funding amounts. Cluster 3 in the top left, designated by green
triangles, identifies institutions with low representation of women, but high
funding amounts.

Figure 5: The clustering analysis of total NSF DMS funding amount versus the
fraction of women by institution reveals three clusters. Cluster 1 in the
bottom left, designated by red squares, identifies academic institutions with
low representation of women and with low funding amounts. Cluster 2 in the
bottom right, designated by blue diamonds, identifies institutions with high
representation of women, but low funding amounts. Cluster 3 in the top left,
designated by green triangles, identifies institutions with low representation
of women, but high funding amounts.

Note that there is no high gender diversity with high funding cluster, nor are
there any institutions in the upper right area of Figure 5. In Table 3 the
number of elite and non-elite institutions in each cluster are aggregated. We
then conducted a chi-squared test to see if cluster membership and “eliteness”
(being in the top 25% of Wapman-prestige rankings) were independent; they were
not ($p<0.001$). In fact, Cluster 2 (blue diamonds) did not contain a single
elite department, while 75% of Cluster 3 (green triangles) were elite
departments. The red cluster of institutions with low gender diversity and low
funding includes a mix of elite and non-elite institutions. Every institution
identified in the gender diverse blue cluster was also ascribed to the lower
75% of the Wapman-prestige ranking list. The vast majority of institutions in
the high funding green cluster were elite (in the top quartile by Wapman-
prestige ranking). This cluster identified 68% of upper quartile (elite)
institutions and only 7% of the lower three quartile (non-elite) institutions.

Table 3: The distribution of elite and non-elite Departments among the clusters identified using k-means clustering (see Figure 5). Cluster Name | Elite Departments | Non-elite Departments
---|---|---
Cluster 1 (red squares) | 13 | 80
Cluster 2 (blue diamonds) | 0 | 32
Cluster 3 (green triangles) | 27 | 9

##  5 Discussion

In this section we shall discuss the results presented above that demonstrate
inequalities exist in faculty composition with respect to gender and the
distribution of federal funding to mathematical sciences PhD-granting
institutions in the United States.

The data shows that almost all PhD-granting institutions have Mathematics
departments which are composed of faculty that are disproportionately male. In
fact, not a single Mathematics department represented in this dataset was
majority women. We found that the underrepresentation of women is more
pronounced among elite Mathematics departments (recall that we defined “elite”
departments as those in the upper quartile of departments in the prestige
ranking generated by Wapman et al.).

We believe in the fundamental principle that mathematical talent is
distributed equally among all groups of people who do mathematics. In the
context of this paper, we therefore assume an equal distribution of
mathematical talent among men and women. Under that assumption, the results
presented here highlight the extreme level of underrepresentation of women in
PhD-granting mathematical sciences departments.

Our analysis of NSF DMS funding identifies inequality in the amount of
financial support for mathematics PhD-granting departments depending on
Wapman-prestige. Pareto models, also popularized as the “20/80” economic
model, predict that approximately 80 percent of assets are held, gained or
earned by only 20 percent of the population being studied [30]. We found that
in the elite institutions, the top 25% in our dataset by Wapman-prestige
ranking, garnered 65% of the total funds given to the subset of PhD-granting
institutions with a Wapman-prestige ranking. When we examine all NSF DMS
funding, the top 20% of awardees receive 86% of all funds, with a Gini
coefficient of 0.8. This result demonstrates a larger inequality than the
classic “20/80” proportion.

The procedures and policies that NSF uses to determine which institutions
receive funding may actually reinforce inequity in the mathematical sciences.
NSF uses a process called merit review, where anonymous reviewers are asked to
read, rate, and review funding proposals submitted to the agency. They are
instructed to assess the intellectual merit and broader impacts of all
proposals under five elements [16]. Two of these elements in particular may
bolster inequity in the mathematical sciences. First, reviewers are asked “How
well qualified is the individual, team, or organization?” This question is
likely to skew reviewers towards considering institutional reputations since
the information provided about qualifications typically includes individuals’
institutional affiliation(s). Second, reviewers are asked “Are there adequate
resources available to the PI (either at the home organization or through
collaborations) to carry out the proposed activities?” This second question is
likely to skew reviewers to more positively rate proposals from well-resourced
institutions, which contributes to a rich-get-richer phenomenon that could
explain the extremely inequitable, “Pareto-like” distribution we found in our
analysis of NSF DMS funding data.

Even more troubling are the systemic effects that are propagated over time by
this inequality in the distribution of NSF DMS funding. The cliché “the rich-
get-richer” is a colloquial distillation of how systems that
disproportionately allocate resources then have an easier time justifying
disproportionate funding. For example, well-resourced universities have
significant funds internally for pilot projects. They have teams of grant
departments that assist in the writing and administration of grants, funded by
high indirect cost rates. They also have research support teams devoted to
data gathering and processing as well as communications teams devoted to
disseminating the results. We also note that expectations in obtaining grant
funds vary widely between departments and institutions, and are often higher
at the elite institutions (those in the top quartile using Wapman-prestige) in
our dataset. This likely affects the number of proposals that are submitted by
different institutions. In short, the effect we are seeing in NSF DMS funding
is likely a result of a complicated collection of processes which reinforce
and exacerbate the status quo that is a demonstrably unequal system, despite
often being presented as a meritocracy.

To summarize, we have analyzed data on faculty in mathematical sciences PhD-
granting departments and NSF DMS funding to institutions with these
departments. We found that higher Wapman-prestige is associated with a lower
percentage of women in Mathematics departments (RQ1). We also found, perhaps
unsurprisingly, that NSF DMS funding was associated with higher Wapman-
prestige (RQ2). Finally, we found that NSF DMS funding to departments was
associated with a lower percentage of women (RQ3).

In this paper, we have shown that being an elite institution is an indicator
of a disproportionately high allocation of financial resources from the
federal government and a low proportion of women; this documents the existence
of systemic inequality, i.e inequity, in the mathematical sciences community.
We advocate for the redefinition of “prestige” (separate from Wapman-prestige)
in mathematics in a way that better reflects equity for excellence [15]. For
example, one could define institutions that are more prestigious to be
institutions that “reflect the diversity of the US population” [15] among
their faculty and doctoral graduates in mathematics. Using this re-envisioned
idea of prestige, we present the ten most prestigious PhD-granting Mathematics
departments based on representation of women in Table 4. Here, we
intentionally choose to turn away from Wapman-prestige, but provide an
alternative definition of prestige based on gender representation. One could
also define “prestige” in the contribution that one makes not just to
mathematics or academia, but in service to society. This is a cultural shift,
but one that could have significant advantages to producing a vision for
science and mathematics that improves all lives.

Table 4: The top ten PhD-granting Mathematics departments by percentage of women. Institution | Percentage of Women
---|---
Bryn Mawr College | 50.0%
Louisiana Tech University | 50.0%
University of California Merced | 50.0%
Teachers College Columbia | 45.8%
University of Texas at Tyler | 40.0%
University of New Hampshire | 38.9%
Cleveland State University | 38.1%
Drew University | 37.5%
Illinois State University | 37.5%
Case Western Reserve University | 37.5%

###  5.1 Limitations.

There are a number of limitations that accompany the research presented in
this paper that we want to highlight below. The primary limitation is that the
there is a paucity of publicly available, comprehensive, self-reported
demographic data about the mathematics community. The data we used was part of
a dataset shared publicly by Wapman et al. [36] after they had processed it,
and the raw data was not available to us. Their methodology of determining
Wapman-prestige means that only PhD-granting departments are represented in
the prestige data; a large number of faculty in the mathematical sciences who
are at community colleges and predominantly undergraduate institutions are not
included. Additionally, because of the way disciplines in the mathematical
sciences are defined in the Wapman et al. dataset, faculty who are in
“Mathematics and Statistics” departments are counted in “Mathematics” and
again in “Statistics.”

Another important limitation is the way gender is ascribed to individuals in
the Wapman et al. dataset. Recall that this dataset included gender, but only
a small percentage were determined by the individuals themselves, with the
rest inferred based on names. While we acknowledge this practice is common,
there are multiple issues with name-based gender inference. There is some
degree of selection bias in which names can be ascribed to a particular
(binary) gender; we note, again, that in the dataset used here, 15% of entries
were omitted due to an inability to confidently ascribe them a gender.
Furthermore, the reduction of gender to a binary erases the experiences of
gender-diverse mathematical scientists from this work.

We also lament the lack of race/ethnicity in the data; there are important
questions to be answered about the interaction of race/ethnicity and inequity
in the mathematical sciences. A similar argument can be made about the absence
of available data about LGBTQ+ identity. The Wapman et al. dataset is limited
to only tenured or tenure-track faculty. Without comprehensive demographic
data, an intersectional analysis involving multiple identity characteristics
is not possible. As discussed below, we hope other researchers will collect or
generate additional data that can be used to address important outstanding
questions about the mathematical sciences discipline.

##  6 Future Directions.

There are many other directions in which the research presented here could be
extended. It is important to study the questions addressed in this paper with
respect to other dimensions of diversity, particularly marginalized social
identities including race/ethnicity, sexual orientation, national origin, and
disability status, among others. This future work should be done in a way that
allows analysis using intersections of multiple identity characteristics.

The addition of geographic location to the analysis of the gender diversity of
PhD-granting institutions as well as of the distribution of federal funding is
a possible direction of future research.

Another future direction is to expand this work to a wider range of
institutions and faculty appointments. A study encompassing all types of
institutions, and particularly community colleges, minority-serving
institutions, and primarily undergraduate institutions, is necessary.
Additionally, future work should investigate related questions about all types
of faculty employed at these institutions, especially the increasing
percentage of non-tenure track faculty.

This work’s primarily goal has been to document inequity in the mathematical
sciences. Future work could involve developing mathematical models that are
informed by the data we have that documents inequity in the mathematical
sciences and lead to a better understanding of the mechanisms involved.
Specifically, the data [2, 19, 17] showing the underrepresentation of women in
new hires versus their underrepresentation in tenure-stream positions in PhD-
granting institution raises some interesting questions that could also be
addressed in future research.

We conclude by inviting interested researchers to join us in the ongoing
MetaMath project to use mathematics and data science to analyze our discipline
in order to promote social justice and enhance equity within all fields of the
mathematical sciences.

###  6.1 Author Contributions.

All the listed co-authors contributed equally to the creation of this article;
the order of attribution is alphabetical, as is customary in mathematics and
is not intended to demonstrate any distinction in credit or effort.

### Acknowledgements.

This material is based upon work supported by the National Science Foundation
under Grant No. DMS-1929284 while all authors were in residence at the
Institute for Computational and Experimental Research in Mathematics in
Providence, RI, during the Data Science and Social Justice: Networks, Policy,
and Education program. The content is solely the responsibility of the authors
and does not necessarily represent the official views of the National Science
Foundation. The authors would like to thank Phil Chodrow and Victor Piercey
for fruitful conversations that pushed this work forward, and Sam Zhang for
contributions to a first draft of this work.

Buckmire acknowledges sabbatical support provided by the Office of the Dean of
the College at Occidental College in Los Angeles, California.

Diaz Eaton was supported in part by the Bates Enhanced Sabbatical Fund and
Faculty Professional Development Fund.

Hibdon was supported, in part, by the National Institutes of Health’s National
Cancer Institute, Grant Numbers U54CA202995, U54CA202997, and U54CA203000. The
content is solely the responsibility of the authors and does not necessarily
represent the official views of the National Institutes of Health.

Kauba is partially supported by the National Science Foundation South Carolina
LSAMP Bridge to Doctorate Fellowship HRD-2005030.

Pabón is partially supported by the National Science Foundation under Awards
DMS-2108839 and DMS-1450182.

Vindas-Meléndez is partially supported by the National Science Foundation
under Award DMS-2102921.

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Ron Buckmire

received his PhD in mathematics from Rensselaer Polytechnic Institute in 1994
and has been on the faculty of Occidental College in Los Angeles, California
ever since. He is a passionate advocate for broadening the participation of
people from historically marginalized and currently underrepresented groups in
the mathematical sciences. Dr. Buckmire believes that: 1) mathematics is a
human endeavor; 2) mathematics is created, discovered, learned, researched,
and taught by people; 3) the identities and experiences of “who does math” are
important and that everyone and anyone can be and should be welcome in the
mathematics community.

Mathematics Department, Occidental College, Los Angeles, CA 90032
<EMAIL_ADDRESS>
Carrie Diaz Eaton

has M.A. and PhD degrees in mathematics from University of Maine and
University of Tennessee. She is now an associate professor of digital and
computational studies, where her mixed methods teaching and research focus on
social justice, complex adaptive systems and leadership, and their
intersection with society, STEM culture, and higher education. They are
committed to fostering a new STEM ecosystem in which the current marginalized
and oppressed are instead the liberated.

RIOS Institute, Digital & Computational Studies, Bates College, Lewiston, ME
04240
<EMAIL_ADDRESS>
Joseph E. Hibdon, Jr.

received his PhD in Applied Mathematics from Northwestern University in 2011.
He is an associate professor of mathematics at Northeastern Illinois
University, a Hispanic Serving Institutions in Chicago, Illinois. Dr. Hibdon
works in many interdisciplinary teams across the country to increase diversity
in STEM and broadening the participation of students in research at the
undergraduate level. Dr. Hibdon’s recent research is in mathematical modeling,
with a focus on public health and biological phenomena.

Department of Mathematics, Northeastern Illinois University, Chicago, IL 60625
<EMAIL_ADDRESS>
Jakini Kauba

is a PhD student in mathematical sciences at Clemson University. Her interests
lie in stochastics and data science with an emphasis in interdisciplinary
social justice work that addresses the many inequities of our nation. She
believes in using mathematics to better serve underrepresented and
marginalized communities.

School of Mathematical and Statistical Sciences, Clemson University, Clemson,
SC, 29634
<EMAIL_ADDRESS>
Drew Lewis

received his PhD in mathematics from Washington University in St. Louis in
2012 and most recently served on the faculty at the University of South
Alabama. He now works primarily in education research and faculty development.
<EMAIL_ADDRESS>
Omayra Ortega

received her PhD in Applied Mathematics & Computational Sciences from the
University of Iowa in 2008. She is an Associate Professor of Applied
Mathematics & Statistics and the Assistant Dean of Research and Internships in
the School of Science and Technology at Sonoma State University. Using the
tools from statistics, mathematics, data science, public health and
epidemiology, Dr. Ortega tackles the emerging health issues. She is deeply
committed to broadening the participation of underrepresented minorities in
STEM and mentoring students through the challenges of academia.

Department of Mathematics & Statistics, Sonoma State University, Rohnert Park,
CA 94928
<EMAIL_ADDRESS>
José L. Pabón

is a PhD candidate in mathematics at the New Jersey Institute of Technology in
Newark, N.J. He received his A.B. degree in mathematics from Princeton
University in 2019 and has a particular affinity for working with
disenfranchised populations, having first-hand experience with these given he
was born and raised in Puerto Rico.

Department of Mathematical Sciences, Newark, New Jersey, 07102
<EMAIL_ADDRESS>
Rachel Roca

is a PhD student in computational mathematics, science, and engineering at
Michigan State University. Her interests lie in topological data analysis and
computing education with an emphasis in social good. She believes in
leveraging mathematical and data science tools for both advocacy and activism.

Department of Computational Mathematics, Science, and Engineering, Michigan
State University, East Lansing, MI 48824
<EMAIL_ADDRESS>
Andrés R. Vindas-Meléndez

received their PhD in mathematics from the University of Kentucky in 2021.
Andrés is an NSF Postdoctoral Fellow and Lecturer at UC Berkeley and will
begin as a tenure-track Assistant Professor at Harvey Mudd College in July
2024. Andrés’ research interests are in algebraic, enumerative, and geometric
combinatorics and have expanded to include applications of data science and
mathematics for social justice.

Department of Mathematics, University of California, Berkeley, CA 94720
Department of Mathematics, Harvey Mudd College, Claremont, CA 91711
<EMAIL_ADDRESS><EMAIL_ADDRESS>