Introduction

The American Mathematical Society (AMS) is the largest mathematics society in the world. According to the AMS, its monthly publication, Notices of the American Mathematical Society (AMS Notices), is one of the most widely-read mathematics publications in the world. In the December 2019 edition of the AMS Notices, a Vice President of the AMS published an invited essay critical of the use of diversity statements in faculty hiring within higher education [1].

In a typical faculty search process, candidates submit the following materials: a cover letter; a curriculum vitae; a research statement, which describes research experience and future plans; and a teaching statement, which discusses teaching experience and philosophy. Many faculty searches now additionally require candidates to submit a diversity statement (or similarly named document). The diversity statement is meant to empower search committees and institutions to identify candidates who have skills, experiences, and/or plans that would support inclusion, diversity, and equity on campus. For an example of an institution’s rationale for and guidelines to writing such a statement, see materials from the University of California, Davis [2].

Ref. [1] argues that the required use of diversity statements in hiring is akin to McCarthyism, the campaign begun by Senator Joseph McCarthy against alleged communists in the United States during the early 1950s. The author writes:

In 1950 the Regents of the University of California required all UC faculty to sign a statement asserting that “I am not a member of, nor do I support any party or organization that believes in, advocates, or teaches the overthrow of the United States Government, by force or by any illegal or unconstitutional means, that I am not a member of the Communist Party.” Eventually thirty-one faculty members were fired over their refusal to sign… Faculty at universities across the country are facing an echo of the loyalty oath, a mandatory “Diversity Statement” for job applicants. The professed purpose is to identify candidates who have the skills and experience to advance institutional diversity and equity goals. In reality it’s a political test, and it’s a political test with teeth.

First, the Institute for the Quantitative Study of Inclusion, Diversity, and Equity published an online post [4]. This post critiques [1] and the AMS’s choice to publish it. Additionally, [4] expresses concern for those in the author’s professional sphere potentially affected by the publication of the essay. Finally, [4] recommends a number of actions that community members could take in response to [1].

Second, a group of concerned mathematical scientists drafted a public letter, hereafter referred to as Letter A [5]. Like [4], this letter expresses dissatisfaction with the publication of [1]. However, Letter A highlights the need for social justice within the mathematical sciences community, assures readers that there are many individuals who see diversity work as integral, and reaffirms the importance of diversity statements in hiring.

Third, a different group of concerned mathematical scientists drafted a public letter in response to [4], hereafter referred to as Letter B [6]. This second public letter expresses displeasure with [4], frames it as an attack on the author of [1], and provides an explicit stance neither on diversity statements nor on diversity in general. Rather, Letter B affirms as its highest priority the need for discussion and debate within the community.

Fourth and last, another letter was drafted, hereafter referred to as Letter C [7]. Unlike Letter B, Letter C does briefly mention the importance of “reducing various difficulties still faced by underrepresented groups.” However, also unlike Letter B, it specifically addresses diversity statements, calling their mandatory use “a mistake” and stating that using them to eliminate candidates during the early stages of a search “diminishes mathematical achievement.” S1 Appendix. contains the full text of all three public letters.

Letter A was made available for signing beginning on November 22, 2019. Unfortunately, we do not have access to the dates that Letters B and C were first made available for signing. As a result of this missing timeline information, we are not able to make meaningful statements comparing the total number of signatories to each letter. All three letters were published online on December 13, 2019, as part of the January 2020 edition of the AMS Notices [5–7]. The purpose of this manuscript is to report on crowdsourced inferences of certain demographic characteristics of the signatories.

We have declared potential conflicts of interest during the submission of this journal article, but we repeat them here in the body of our manuscript because it is an important ethical practice to do so. Co-authors CMT and JAH are co-founders of QSIDE, and CMT wrote the blog post to which Letter B is a response. Additionally, co-authors CMT, CDE, KI, BK, DL, and JL are drafters of and signatories to Letter A, and hence appear in the data set that we construct and study.

Our primary results are as follows. Letter A, which highlights diversity and social justice, was signed by relatively more individuals inferred to be women and/or members of underrepresented ethnic groups. Moreover, this group is diverse with respect to the levels of professional security and types of academic institutions represented. In stark contrast, Letter B, which privileges discussion and debate, was signed by a strong majority of individuals inferred to be white men in professionally secure positions at highly research intensive universities. Letter C speaks out specifically against diversity statements. Individuals who signed both Letters B and C, that is, signatories who privilege debate and oppose diversity statements, are overwhelmingly inferred to be tenured white men at highly research intensive universities. These results are consistent with theories of power from the social sciences, which predict that people from demographic groups in different positions within social power structures (as determined by overrepresentation within larger populations, monetary compensation, or professional security) have divergent perspectives on these structures.

Methods

While Letters A and B were being signed electronically by the public during November and December of 2019, the lists of signatories were publicly accessible via links provided by the letters’ drafters. We retrieved these lists from their respective Google spreadsheets [8, 9] the morning of December 10, 2019. The AMS informed letter drafters that lists of signatories must be submitted by the evening of December 10. Therefore, the final published lists may contain a small number of additional records not included in our present study because they were submitted in the intervening hours. Additionally, for Letters A and B, we removed duplicate signatures, and we removed fake signatures such as “J. Epstein, Department of Children’s Rights” (a reference to public figure Jeffrey Epstein) and “Donald J. Trump, University of Washington, D.C.” It is possible that the AMS removed additional names during the publication process; our data set will include any such names, but based on manual inspection, we believe the number to be statistically negligible. We retrieved the signatories to Letter C once they were published [7]. For all letters, the AMS may update the lists of signatories between the drafting of this manuscript and its publication, and our study will not reflect those changes.

To sign one of the letters, each signatory submitted their name and affiliation. We refer to this textual data as the raw data. To discover information about each signatory, we used the crowdsourcing platform Amazon Mechanical Turk (MTurk). MTurk is a crowdsourcing labor platform. Requesters sign up for the platform to post tasks that they would like completed in return for a small fee. Workers sign up for the platform and earn money by completing these tasks. For further background on MTurk, see, for example [10]. For our study, we served as requesters, posting each raw data record to MTurk. We asked workers to locate information about that signatory, such as personal and academic demographics. We provide details about the information requested later in this section, and we provide the full text of our Amazon Mechanical Turk questionnaire in S1 Appendix. A number of peer-reviewed published studies adopt this crowdsourcing methodology to infer demographics; see, for example, work on diversity in art and diversity on mathematical sciences journal editorial boards [11, 12].

We adopted several strategies to ensure data quality. First, we only hired workers who had previously completed at least 1,000 crowdworking tasks and who had a prior requester approval rating of 99% or higher. Second, we had each signatory initially researched by four independent workers. For each item on our survey instrument, we made a final determination of the answer only if there was a consensus of at least three among the four independent responses. When we could not find a consensus, we deployed the record one additional time to MTurk and sought a consensus of three out of five. If such a consensus still did not exist, we assigned the value NA, meaning that we were not able to make an inference. For most questions, MTurk workers had the option to choose “cannot confidently determine” if they felt unable to make a clear inference, and we coded these responses as NA.

Results

Letter A has 621 signatories, Letter B has 680 signatories, and Letter C has 210 signatories. The overlap between signatories to Letter A and Letter B is six individuals. There is no overlap between the signatories to Letters A and C. There is substantial overlap between the signatories to Letters B and C, namely 74 individuals. The six individuals who signed Letters A and B do not constitute a group large enough to analyze meaningfully, so we leave them in that data set accompanies this manuscript, but we exclude them from our analyses (meaning they are not represented in the tables and charts prsented here). We divide the remaining signatories into four disjoint groups: the 615 signatories to Letter A only, the 600 signatories to Letter B only, the 136 signatories to Letter C only, and the 74 signatories to Letters B and C, for a total of 1,425 signatories. Hereafter, we refer to the groups as Pool A Only, Pool B Only, Pool C Only, and Pool B and C.

We divide our presentation of results into two subsections. First, we examine personal demographics, namely inferred gender and inferred ethnicity. Second, for signatories situated in higher education, which constitute over 95% of the original data, we examine institutional classification, professional role, and academic field. For each of the aforementioned variables except for inferred gender, we also develop a simplified version of the variable by aggregating certain levels of the original one. We describe these aggregations later.

For each demographic variable, we present a two-way contingency table showing proportions of letter signatory pool versus that variable. See Table 1 for personal demographics and Table 2 for academic demographics. Within a given contingency table, for each combination of pool and demographic, the left-hand number gives the column percentage and the right-hand number gives the row percentage. For example, for inferred gender in Table 1, looking down the first column, Pool A Only has 0.2% signatories for whom we did not infer gender, 0.2% of individuals inferred as nonbinary, 50.7% inferred as women, and 48.9% inferred as men. In the same section of Table 1, looking across the row tabulating women, we see that of all individuals inferred to be women in our data set, 69.2% of them are in Pool A Only, 21.1% are in Pool B Only, 8.2% are in Pool C Only, and 1.6% are in Pool B and C.

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Table 1. Two-way contingency tables for letter signatory pool and personal demographics, namely inferred gender, inferred ethnicity, and inferred underrepresented minority (URM) status.

Gender and URM both fail a statistical test for the independence of demographics and pool. Within a given contingency table, for each combination of pool and demographic, the left-hand number gives the column percentage and the right-hand number gives the row percentage. Colors indicate whether a particular cell represents more (blue) or fewer (orange) individuals than we would expect if the variables were independent. For details of statistical tests, see table notes below.

https://doi.org/10.1371/journal.pone.0232075.t001

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Table 2. Two-way contingency tables for letter signatory pool and academic demographics, namely institutional classification, research intensiveness, professional role, professional security, academic field, and simplified academic field.

Research intensiveness, professional security, and simplified field each fails a statistical test for the independence of demographics and pool. Within a given contingency table, for each combination of pool and demographic, the left-hand number gives the column percentage and the right-hand number gives the row percentage. Colors indicate whether a particular cell represents more (blue) or fewer (orange) individuals than we would expect if the variables were independent. For details of statistical tests, see table notes below.

https://doi.org/10.1371/journal.pone.0232075.t002

We perform statistical tests on the contingency tables for gender and for the simplified variables (described below) with NA values excluded. For these tables, we first perform a χ² test of the null hypothesis that the demographic characteristic and letter signatory pool are independent. At the top of the contingency table, we report the value of the χ² test statistic, the degrees of freedom df, the p-value, and Cramér’s effect size V. All χ² tests result in rejection of the null hypothesis. Second, we test for significance of individual cells in the contingency table via a z-test for sample percentage. Colors indicate whether, at the α = 0.05 significance level, a particular cell represents more (blue) or fewer (orange) individuals than we would expect if the variables were independent. We use Holm-adjusted p-values to correct for multiple comparisons. For background on the statistical approaches we use, see reference texts such as [15].

It is important to remember that the population in our statistical tests is the 1,425 letter signatories. As we highlight later, these signatories do not represent a random sample of the mathematical sciences community (or any other group). In the presentation of our results, we will use the words “overrepresented” and “underrepresented.” When we use these words in the following two subsections, we mean over/under-represented as compared to what we would expect if demographics and signatory pool were independent.

Personal demographics

We reiterate that all demographic data are inferred data. This is especially critical for gender and ethnicity. Below, we will use language such as “individuals inferred to be women” and “individuals identified as belonging to underrepresented ethnic groups.” Ideally, gender and ethnicity would be self-identified.

Fig 1(A) displays the inferred gender composition of each letter signatory pool; the percentages shown are column percentages from Table 1. The proportion of individuals inferred to be nonbinary or gender nonconforming is low. We do not conjecture on the true proportion of these individuals within our data, nor within the mathematical sciences community at large. However, we do suspect that the low percentage we observe is attributable at least in part to the limitations of our method of gender inference [16]. As for the remaining (binary) gender categories, Pool A Only achieves approximate gender parity, comprising 50.7% inferred women. In contrast, Pools B Only, C Only, and B and C have low percentages—15.8%, 27.2%, and 9.5% respectively—and hence are dominated by individuals inferred to be men. Compared to what we would expect under the assumption of independence of gender and pool, signatories identified as women are overrepresented in Pool A Only and underrepresented in Pool B Only and Pool B and C.

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Fig 1. Personal demographic characteristics of letter signatory pools.

See Table 1 for details. (A) Inferred gender. Pool A Only achieves (approximate) gender parity, whereas Pools B Only, C Only, and B and C are dominated by people inferred to be men. (B) Inferred underrepresented minority (URM) status. At 12.2%, Pool A Only has a higher than expected percentage of people inferred to belong to ethnic groups traditionally underrepresented in the mathematical sciences. Pools B Only, C Only, and B and C each have approximately 3% or less.

https://doi.org/10.1371/journal.pone.0232075.g001

Fig 1(B) examines inferred ethnicity. Table 1 shows the full results for our original ethnicity variable. However, because there are many ethnicity categories, we perform an additional analysis by grouping together minoritized ethnicities that are considered to be traditionally underrepresented (URM) in mathematics: Black, Latinx, Native American/Alaska Native (NAAN), and Hawaiian Native/Pacific Islander (HNPI). Under this classification, the percentage inferred to be URM is 12.2% for Pool A Only, 3.2% for Pool B Only, 1.5% for Pool C Only, and 2.7% for Pool B and C, as shown in Fig 1(B). The statistical tests of Table 1 indicate that individuals identified as URM are overrepresented in Pool A Only and underrepresented in Pools B Only and C Only.

Academic demographics

We now restrict attention to the signatories situated within higher education (HE). We refer to the pools as Pool A Only HE, Pool B Only HE, Pool C Only HE, and Pool B and C HE. These pools have, respectively, 586, 563, 135, and 73 members, for a total of 1,357 individuals.

Fig 2(A) addresses institutional classification. Table 2 shows the full results for our original institutional classification variable. We perform an additional analysis by creating a collapsed version of this variable as we now describe. The non-U.S. countries appearing most frequently in our data (and their counts) are Israel (47), Canada (37), the United Kingdom (21), Germany (14), and France (13). The specific non-U.S. institutions appearing most frequently in our data (and their counts) are Hebrew University of Jerusalem (20), Technion (15), and University of Toronto (13). We judge that if located in the U.S., these institutions would be classified as Very High Research Activity (R1). Therefore, we aggregate US R1 and international institutions into the category of more research intensive (more RI), and we aggregate US R2 and US other institutions into the category of less research intensive (less RI). As shown in Fig 2(A), Pool A Only HE is composed 57.3% of less RI, whereas Pools B Only HE, C Only HE, and B and C HE have 24.3%, 4.4%, and 1.4% respectively. The latter two pools are especially dominated by individuals from more RI institutions, whereas Pool A Only HE is fairly balanced. Indeed, our statistical tests indicate that less RI institutions are underrepresented in the last three pools.

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Fig 2. Academic demographic characteristics of letter signatory pools.

See Table 2 for details. (A) Research intensiveness. Pool A Only HE shows a balance of signatories. Pools B Only HE, C Only HE, and especially B and C HE are dominated by people from highly research intensive institutions. (B) Professional security. At 51.4%, Pool A Only HE overrepresents individuals with less professional security. Pools B Only HE, C Only HE, and B and C HE underrepresent these individuals, and the latter two contain nearly zero less professionally secure individuals. (C) Academic field. Pool A Only HE contains the highest percentage of signatories from mathematics education, who are overrepresented at 6.0%.

https://doi.org/10.1371/journal.pone.0232075.g002

Fig 2(B) addresses professional security. Table 2 shows the full results for our original professional role variable. We perform an additional analysis by creating a collapsed version of this variable. We aggregate the roles that are not eligible for academic tenure or are eligible but have not yet received tenure (as judged based on title), and refer to these as less professionally secure roles. These roles are undergraduate student, graduate student, staff, non-tenure-track faculty, and Assistant Professor (and their international equivalents). Additionally, we aggregate the roles that do indicate currently or previously held academic tenure, namely Associate Professor, Full Professor, and retired/Emeritus (and their international equivalents). We refer to these as more professionally secure roles. As shown in Fig 2(B), in Pool A Only HE, more professionally secure individuals are in the minority, at 45.4%. Pools B Only HE, C Only HE, and B and C HE are dominated by more professionally secure individuals, at 76.7%, 99.3%, and 97.3% respectively. More professionally secure individuals are statistically overrepresented in these pools. Notably, if we examine Pools C Only HE and B and C HE, we see that almost every signatory to Letter C is tenured (or was at some point).

Finally, Fig 2(C) addresses academic field. Table 2 shows the full results for our original academic field variable. We perform an additional analysis by creating a collapsed version of this variable. We aggregate the mathematics/applied mathematics and statistics/data science categories into one category, and we aggregate computer science/computer engineering and other disciplines into another category, leaving mathematics education as the third category. As shown in Fig 2(C), Pool A Only HE contains the highest percentage of signatories from mathematics education, who are statistically overrepresented at 6.0%. Pool B Only HE contains a substantial group of signatories from computing and other fields, who are statistically overrepresented at 10.8%. Pool B and C HE is composed exclusively of mathematicians and applied mathematicians.

Discussion and conclusions

We have conducted a crowdsourced study of the demographics of signatories to three public letters in the mathematical sciences community. Our key results are as follows. As for personal demographics, we infer Pool A Only to be substantially more diverse than the other pools. We have calculated for each pool the (joint) percentage of signatories who were inferred to be men and who were not inferred to be members of an underrepresented ethnic group. For Pool A Only, this percentage is 40.8%, whereas for Pools B Only, C Only, and B and C, the percentage is 75.8%, 70.6%, and 87.8% respectively. As for academic demographics, Pool A Only represents a broader range of institution types and levels of professional security. We have calculated for each pool the (joint) percentage of signatories who are situated at highly research intensive institutions in more professionally secure positions. For Pool A Only HE, this percentage is merely 11.8%, whereas for Pools B Only HE, C Only HE, and B and C HE, the percentage is 55.6%, 94.8%, and 95.9% respectively. Finally, restricting attention to our HE pools, we have calculated the percentages of individuals who (jointly) are inferred to be men, not members of underrepresented ethnic groups, located at highly research intensive institutions, and in more professionally secure positions. For Pool A Only HE, this percentage is a scant 5.6%. For the remaining pools it is 46.5%, 67.4%, and 83.6%.

In summary, Letter A highlights diversity and social justice and was signed by relatively more people inferred to be women and members of minoritized ethnic groups. These signatories represent a broader range of institution types and levels of professional security. Letter B does not comment on diversity, but rather, argues for discussion and debate. It was signed predominantly by individuals inferred to be men who have ethnicities not underrepresented in the mathematical sciences, and who are in professionally secure positions at highly research intensive institutions. Letter C speaks out specifically against the use of diversity statements. Individuals who signed both Letters B and C, that is, signatories who privilege discussion and debate and who oppose diversity statements, are overwhelmingly inferred to be tenured white men at highly research intensive universities.

We now relate our results to theories of power drawn from scholarship in the social sciences. Our findings are consistent with the idea of positionality. Positionality describes the ways in which individuals’ identities and experiences are consequences of their positions within social structures. These positions shape an individual’s perceptions [21]. More specifically, positionality theory predicts that individuals’ positions within power structures tilt their perceptions of phenomena in patterned ways [22]. Differences in perception are particularly pronounced when individuals’ identities confer unequal levels of power. For example, among students who were shown the same film about race relations, white students were more likely to respond by describing the film as an exaggeration, or “over the top,” while students of color were more likely to respond with reflections on how much the film mirrored their own experiences [23]. In this example, students’ own racial identifications (their positions within social structures) produced very different perceptions about the same film (the phenomenon).

In our present study, positionality theory suggests that people with relatively more power in the mathematical sciences would have very different perspectives from those with relatively less power. This accords with the aggregate patterns we have documented. People in more powerful positions within the mathematical sciences, namely men, white people, people with tenure, and people at highly research intensive universities, tend in aggregate to endorse perspectives on diversity statements that are different from the perspectives endorsed in aggregate by people with relatively less power, namely women, members of underrepresented ethnic groups, people without tenure, and people at institutions that are not highly research intensive.

Some might read tenure and affiliation with highly research intensive universities as proxies for the quality of a mathematician. We are not persuaded that this reading undermines our interpretation above. Regardless of how validly or invalidly tenure status and institution type capture the quality of a mathematician, these professional attributes are face-valid indicators of power. Both tenure and employment at highly research intensive institutions confer substantial monetary benefits. The wage premium associated with highly research intensive universities is especially marked in the natural and mathematical sciences [24]. This premium persists even if one controls for individuals’ research productivity, years of experience, and demographics. All other things being equal, being tenured and affiliated with highly research intensive institutions means more access to social power than not being tenured, or being employed at other types of institutions. Moreover, tenure confers increased academic freedom [25] and professional security. Money, academic freedom, and professional security all help individuals exercise their will, or equivalently, give individuals more power [26].

Additionally, our results are consistent with prior studies that use discourse analysis. When individuals denounce actions that they perceive as harmful to a group, members of other groups often discursively frame this denunciation as an attempt to silence the critiqued actors [27]. Prior research has documented this dynamic in contexts including standup comedy [28], college campus controversies [29], the immigration policy debate [30], and more. The framing of denunciation as an attempt at silencing is consistent with the statements in Letter B, as endorsed by its signatories; see S1 Appendix. Indeed, this letter begins with the sentence “We write with grave concerns about recent attempts to intimidate a voice within our mathematical community.”

In our study, we have reported descriptive statistics and conducted selected statistical tests. Future work could undertake further statistical modeling and inference. Finally, while results of our study are consistent with theories of power, our study is not explanatory. Though Pool A Only has markedly different demographics from the other pools, we do not know why this is case. For instance, demographic differences could arise from the way that news of the letters was disseminated through professional networks, reflecting or even amplifying the (potential) demographic biases of those networks. Alternatively, demographic differences between the pools could reflect contrasting personal and professional values. Professional security could also have played a role in a signing decision of Letters B and C. Of course, these demographic differences could be caused by a combination of the aforementioned factors and others. Investigation using tools and frameworks from the social sciences and humanities might complement our research to provide explanations and further insights.

Supporting information

Acknowledgments

We are grateful to Alicia Prieto Langarica for contributions during the early stages of this work, and to Carina Curto and Joshua Paik for helpful comments regarding our methodology and data.