Women in mathematics

Summary: Historically, women have been underrepresented in mathematics careers and professions.

Questions are raised periodically about women’s participation or lack thereof in mathematics. This issue has been investigated from the perspectives of various disciplines, among them, history, psychology, neuroscience, economics, and statistics. Each of these perspectives has strengths and weaknesses and sheds light on different aspects of the issue.

Differences of era, place, and culture can affect findings; thus, results for one population do not always extend to others and findings from one decade may not hold for the next. In all cases, various forms of bias may affect the selection and interpretation of the information presented—on the part of newspapers, journals, researchers, and writers, as well as their audiences.

Pre-College and College Participation

Historical research has documented how the proportions of women in mathematics and other fields have waxed and waned with changes in societal norms, institutional policies, and mathematical practices.

In the antebellum, nineteenth-century United States, schooling was not compulsory, and most adolescents did not attend school. Mathematics, other than arithmetic, was not a college prerequisite and the adolescent girls enrolled in school did often not study the Greek and Latin required of college-bound boys. By the 1890s, about 7% of 14–17-year-olds attended high school. Girls outnumbered boys in mathematics courses at public high schools, sometimes outperforming them.

The proportion of adolescents attending high school increased rapidly. By 1940, almost three-quarters of 14–17-year-olds attended high school. However, many high schools de-emphasized or eliminated mathematics requirements and smaller proportions of students enrolled in advanced courses. The percentages of girls in these courses declined to parity in the early 1900s and decreased further until the 1950s. By the 1970s, their proportions had increased and 2005 statistics showed them at or above parity.

In every epoch on record, girls have predominated in high school, but before 1900 and between 1930 and 1980, women were a minority of undergraduates. Women’s share of mathematics and statistics baccalaureates was similar to their share of all baccalaureates in 1950 but later lagged, remaining at 40% to 50%, although their overall share has since risen.

Recent Research on College and Pre-College Populations

Cognitive factors such as spatial abilities have been analyzed independently and with respect to mathematical performance. A 1985 meta-analysis by Marcia Linn and Anne Petersen grouped spatial abilities into three categories: spatial perception, spatial visualization, and mental rotation. They found little evidence of gender differences for the first two categories but found large gender differences on mental rotation tasks for which scores depend on speed and accuracy. Subsequent research reports that these differences have diminished and training studies conducted by Nora Newcombe, Sheryl Sorby, and others show this ability can be improved. Mental rotation appears more important for careers such as engineering and fashion design than mathematics.

Another line of research has focused on mathematical aptitude, often as measured by the mathematics section of the Scholastic Aptitude Test (SAT or SAT-M). One finding, frequently cited as evidence for innate gender differences in mathematical aptitude, concerns the SAT-M scores from “talent searches” among middle school student volunteers. Between 1980 and 1982, the ratio of boys to girls scoring 700 or above was 13:1. Later, larger samples have yielded different, smaller ratios; a 2005 ratio is 2.8:1.

Although the first finding received extensive media coverage and is widely cited, the drop has received little publicity and few citations. Underlying causes may be related to those of the file-drawer effect—the tendency for findings that fail to reject a null hypothesis to remain unpublished.

Use of the SAT-M as a measure of mathematical aptitude or ability has been criticized on the grounds of construct validity and predictive validity. Studies of the latter find that the SAT-M underpredicts women’s undergraduate mathematics course grades and overall grade point averages relative to those of men.

Possible reasons for gender gaps in SAT-M scores include differences in strategies (documented by Ann Gallagher and her collaborators) and the phenomenon of stereotype threat identified by Claude Steele and Joshua Aronson. An individual may be vulnerable to stereotype threat in a particular context if the individual is a member of a group that is stereotyped as performing poorly in such contexts. For example, reminding a woman of such stereotypes can hamper her mathematical performance, particularly when she cares about doing well in mathematics.

Using imaging techniques, researchers have found gender differences in brain areas used for processing when subjects were asked to calculate or solve mathematics problems. These have been popularly interpreted as “hard-wired” gender differences. However, the subjects of these studies are adults. Thus, these differences may result from differences in experience. Moreover, the studies are small in scale, and their findings are not always consistent.

International assessments for primary and secondary education are administered by the Trends in Mathematics and Science Survey and the Programme for International Student Assessment. Scores on these assessments, representing 493,495 students, were analyzed in 2010 by Nicole Else-Quest and her colleagues. They concluded that, on average, males and females differ little in mathematical achievement, despite more positive attitudes toward mathematics among males and substantial variability across nations. The most powerful predictors of cross-national variability in gender gaps were gender equity in school enrollment, women’s share of research jobs, and women’s parliamentary representation.

In 2014 the College Board announced that it was redesigning the way the SAT was scored. Instead of a total score range of 600 to 2400 based on equally weighted scores in critical reading, writing, and math, the updated SAT increased the weight of the math section to 50 percent from 33.3 percent and decreased the reading and writing sections to 25 percent from 33.3 percent, respectively. While the overall scoring gap between males and females dropped to 20 points from 24 points, the gap widened among the highest-scoring students to 40 points. The College Board stopped tracking detailed scoring data for each section by race and gender in 2015, making it hard to determine the cause of scoring disparities.

Graduate and Faculty Participation

Since the nineteenth century, a standard credential for professors at four-year academic institutions has been a Doctor of Philosophy degree (Ph.D.). In the United States, a Ph.D. is a terminal degree—the highest degree given in scientific fields. Thus, for modern times, Ph.D. attainment is a frequently used measure of women’s participation in mathematics.

The first American woman to be awarded a Ph.D. in mathematics was Winifred Edgerton Merrill, in 1886. (A decade earlier, Christine Ladd-Franklin had completed a dissertation in mathematics at Johns Hopkins University. However, her Ph.D. was not awarded until 1926.) Before 1890, most Ph.D. programs in the United States did not allow women to enroll, making them less likely to frequent many mathematics departments. Other obstacles were quotas and professors who refused to have women as Ph.D. students. Reflecting societal norms, qualified women were sometimes not considered for academic positions, paid less, promoted more slowly or not at all, or expected to quit their positions if they married. University anti-nepotism rules were often used to exclude wives from paid employment at a spouse’s institution (except during extreme circumstances, such as World War II). Such policies were likely to have affected women in mathematics more than women in many other disciplines. Then, as now, husbands and partners of female mathematicians and scientists tended to also be mathematicians and scientists. Unlike experimental scientists, female mathematicians had few opportunities for professional employment outside academia or as laboratory researchers within academia.

Despite these factors, the numbers and percentages of women earning Ph.D.s in mathematics increased until the 1940s. Between 1950 and 1970, women’s numbers stalled while the numbers of men earning Ph.D.s in mathematics and science increased. Part of this increase was because of the influx of World War II veterans whose college and graduate tuition was supported by the Servicemen’s Readjustment Act of 1944, known as the GI Bill. The lack of any corresponding increase in women’s numbers may have been because of neglect of the female veterans who were nominally beneficiaries of the GI Bill together with changes in social norms and science policy. Consistent with these factors, women who were called to teach at colleges and universities during the war were displaced by men returning from war projects.

Changes in science policy and views of science may have had an especially damping effect on women’s participation in mathematics, intensifying what was often seen as a dichotomy between teaching (associated with women) and research (associated with men). Margaret Murray writes that the “myth of the mathematical life course” became the prevailing model of how a mathematical career should unfold—a trajectory more compatible with societal expectations of men than women. In this view, mathematical talent emerges in childhood—creative achievements begin early and are quickly recognized. The mathematician focuses on research, ignoring distraction or shielded by a spouse or relative. Accomplishments continue, without interruption, until the mathematician’s early 40s.

Faculty Participation After 1970

With the women’s movement of the 1970s, percentages of women in mathematics and other fields increased. In 1971, the American Association of University Professors and the Association of American Colleges issued official policy statements urging that anti-nepotism rules be rescinded. However, the absence of anti-nepotism policies does not always solve a “two-body problem”—finding appropriate professional employment in the same geographical area for two Ph.D.s.

Another important event was the passing of the Educational Amendments Act of 1972. Its Title IX prohibits discrimination against women at educational institutions that receive federal funding and mandates periodic reviews of these grantees by federal agencies.

Elimination of anti-nepotism policies and prohibition of sex discrimination were major changes. However, for two decades, proportions of women had been very small in many mathematics departments and elsewhere in academia. Changes in institutional policies and federal regulations were no guarantee of change in individual expectations and departmental policies.

Individual expectations may be affected by evaluation bias. One example is a study conducted by Linda Fidell in 1970. Sets of 10 fictitious “résumés” of psychologists were sent to psychology department heads with the request to indicate the appropriate professorial rank at which each person described should be hired. Six of the résumés carried a male’s name and the others female names. These were rotated so that the same résumé would sometimes carry a female name and sometimes a male name. The department heads assigned different ranks to identical qualifications, depending on the names they carried. Those with female names received lower ranks than those with male names. Later research suggests that this phenomenon is more complex than originally hypothesized because ratings are affected by social context. An explanatory mechanism identified by Virginia Valian is the notion of “gender schemas”—implicit hypotheses, usually unarticulated, that affect expectations and evaluations of women and men.

Although the percentage of women earning Ph.D.s in mathematics has continued to increase by at least 5% every decade since the 1970s, the presence or absence of departmental policies, such as family leave, may weigh more heavily on women. Moreover, sociological research suggests that women in science have fewer professional interactions within their departments or workplaces and are thus less likely to be aware of expectations conveyed informally. For example, a study of science departments found that departments with written guidelines for graduate students about courses of study, exams, and other expectations tended to have a larger percentage of women who earned Ph.D.s.

A variety of empirical findings suggest that, since the 1970s, the cumulative effects of individual actions, departmental practices, and institutional policies have changed to filter out fewer women. One factor may have been individual and class-action lawsuits brought on the grounds of Title IX violation. In contrast, a 2004 Government Accountability Office study found that federal agencies that fund scientific and mathematical research had not conducted the compliance reviews of their grantees mandated by Title IX.

In 2006, a National Academies report recommended that Title IX and other federal antidiscrimination laws be enforced and that federal agencies work with scientific societies to host mandatory workshops on gender bias. In 2007, the Gender Bias Elimination Act was introduced in Congress, which would have authorized such workshops and directed funding agencies to better enforce federal antidiscrimination laws. This bill did not pass, and similar bills were introduced in 2008 and 2009.

Recent Survey Findings

Every five years, the Conference Board of the Mathematical Sciences (CBMS) surveys a representative sample of two- and four-year academic institutions. The 2005 survey found that women were 50% of the full-time permanent mathematics faculty at two-year colleges (up from 34% in 1990 and 40% in 1995). At four-year institutions, the percentages of women in tenure-track (entry-level) and tenured (permanent) positions also increased, with the exception of tenure-track positions at B.A.-granting institutions (see Table 1).

Table 1. Percentages of Women on Mathematics Faculties of Four-Year Institutions.

	1995	2000	2005
Tenured women (% of tenured faculty)
Ph.D.-granting departments	317 (7%)	346 (7%)	427 (9%)
M.A.-granting departments	501 (15%)	608 (19%)	532 (21%)
B.A.-granting departments	994 (20%)	972 (20%)	1373 (24%)
Tenure-track women (% of tenure-track faculty)
Ph.D.-granting departments	158 (20%)	177 (22%)	220 (24%)
M.A.-granting departments	235 (29%)	276 (32%)	337 (33%)
B.A.-granting departments	748 (43%)	517 (32%)	693 (28%)

Source: Conference Board of the Mathematical Sciences 2000 and 2005 Surveys.

According to the 2010 CBMS Survey, there were 2,740 tenured women (21 percent of tenured faculty) and 1,227 tenure-track women (34 percent of tenure-track faculty) in mathematics departments at four-year universities in the fall of 2010. The 2015 CBMS Survey reported that four-year institutions had 2,688 tenured women (22 percent of tenured faculty) and 1,171 tenure-track women (36 percent of tenure-track faculty) in mathematics departments at four-year universities in the fall of 2015.

The Survey of Doctorate Recipients has collected longitudinal data about 40,000 science and engineering Ph.D. recipients who earned their degrees from institutions within the United States. Recent analysis of data from this survey and the National Survey of Postsecondary Faculty—together with results from surveys of research-intensive departments and faculty members conducted in 2005—found few gender differences on key measures such as grant funding and salary for faculty members. In mathematics, women published fewer articles than men, and the proportions of women applying for jobs were slightly smaller than the proportion earning Ph.D.s. Overall, for the six scientific fields surveyed, the likelihood that a position would have female applicants was affected by institutional characteristics, the presence of family-friendly policies, the proportions of women on search committees, and the gender of the search committee chair. On average, men and women in research-intensive departments reported similar allocations of time on research and teaching but differences in professional interactions. Women were more likely to have mentors; men were more likely to engage with their colleagues on a wide range of topics from research to salary. Women were less satisfied with their jobs, and indirect evidence suggests that women were more likely than men to leave before tenure consideration.

In April 2021, the Pew Research Center reported on the progress made toward increasing gender, racial, and ethnic diversity in science, technology, engineering, and math (STEM) fields by analyzing the 2017–19 American Community Survey. The report, authored by Richard Fry, Brian Kennedy, and Cary Funk, found that progress toward increasing diversity in STEM fields was uneven. While half of the workforce employed in STEM fields were women, their representation in different occupational clusters varied. For example, women held 74 percent of health-related jobs, but only 47 percent of math jobs, 25 percent of computer jobs, and 15 percent of engineering jobs. The Pew researchers also found that, across all racial and ethnic groups in 2019, women in STEM earned about 74 percent of men's median earnings and that the gender pay gap among STEM workers was wider than the gender pay gap among all workers, which has been 80 percent since 2016.

Organizations

Organizations such as the Association for Women in Mathematics (AWM), European Women in Mathematics, and Korean Women in the Mathematical Sciences are dedicated to supporting and promoting women and girls in the mathematical sciences. Student organizations at colleges and universities include AWM chapters and Noetherian Ring groups, the latter named for mathematician Emmy Noether, who is well-known for her pioneering work in abstract algebra.

These and other organizations document women’s participation in mathematics. Biographies of past and present women in mathematics are available online at the MacTutor History of Mathematics Archive, Biographies of Women Mathematicians at Agnes Scott College, and Mathematicians of the African Diaspora. The biographies of 228 women who earned Ph.D.s in mathematics at U.S. institutions before 1940 are maintained at the website for the book Pioneering Women in American Mathematics.

Bibliography

Case, Bettye Anne, and Anne Leggett, eds. Complexities: Women in Mathematics. Princeton, NJ: Princeton University Press, 2005.

Committee on Women in Science, Engineering, and Medicine, et al. Gender Differences at Critical Transitions in the Careers of Science, Engineering, and Mathematics Faculty. Washington, DC: National Academies Press, 2010.

Eliot, Lise. Pink Brain, Blue Brain: How Small Differences Grow Into Troublesome Gaps—And What We Can Do About It. New York: Houghton Mifflin, 2009.

Fry, Richard, Brian Kennedy, and Cary Funk. "STEM Jobs See Uneven Progress in Increasing Gender, Racial and Ethnic Diversity." Pew Research Center, 1 Apr. 2021, www.pewresearch.org/science/2021/04/01/stem-jobs-see-uneven-progress-in-increasing-gender-racial-and-ethnic-diversity/#women-make-up-a-quarter-or-fewer-of-workers-in-computing-and-engineering-are-overrepresented-in-health-related-jobs#women-make-up-a-quarter-or-fewer-of-workers-in-computing-and-engineering-are-overrepresented-in-health-related-jobs#stem-workers-often-earn-more-than-others-but-there-are-sizeable-pay-gaps-for-the-typical-stem-worker-by-gender-race-and-ethnicity. Accessed 23 Dec. 2021.

Green, Judy, and Jeanne LaDuke. Pioneering Women in American Mathematics: The Pre-1940s Ph.Ds. Providence, RI: American Mathematical Society and London Mathematical Society, 2009.

Kenschaft, Patricia. Change Is Possible: Stories of Women and Minorities in Mathematics. Providence, RI: American Mathematical Society, 2005.

Rossiter, Margaret. Women Scientists in America: Before Affirmative Action 1940–1972. Baltimore, MD: Johns Hopkins University Press, 1995.