By Sean Stevens (HxA Research Director) and Jonathan Haidt (HxA Director)

This blog post is a supplement to our main post: The Google Memo: What Does the Research Say About Gender Differences? Please do read at least the introduction to that post before continuing.

As we have scanned the literature to find the major meta-analyses and the most authoritative review articles, we have found one review article that stands above all others, in part for its depth and scope (it is 41 pages long), but especially for its authorship. It was written by a group of psychology’s top experts on these topics, a group that was put together to ensure a diversity of opinion among the authors. The first author is Diane Halpern, a professor emerita at Claremont McKenna College, former president of the American Psychological Association, and the author of the book Sex Differences in Cognitive Abilities. One author is Janet Shibley Hyde, a professor at the University of Wisconsin – Madison, whose publications generally point to small and shrinking gender differences (her meta-analyses feature prominently in our main post). Another author is David Geary, author of Male, Female: The Origin of Human Sex Differences, whose publications generally point to more substantial effects. (Here is Geary on the Damore memo). Also on board is Camilla Benbow, an educational psychologist at Vanderbilt University who researches intellectually gifted students, and who was Vice Chair of the President’s National Mathematics Advisory Panel (which also included Geary); Ruben Gur a clinical psychologist at the University of Pennsylvania who researches brain-behavior relationships, and Morton Ann Gernsbacher, a professor at the University of Wisconsin – Madison, who researches cognitive and neural mechanisms that underlie human communication.  She is also a former president of the Association for Psychological Science.

This august group, this all-star team, came together in part to address the controversy that erupted after Lawrence Summers offered his thoughts, in 2005, on the causes of women’s underrepresentation on the faculty in STEM departments at top universities.

The monograph they produced is magnificent. It is an example of psychology at its best, guiding readers through multiple massive literatures, showing no trace of partisan bias or commitment to any pre-ordained conclusion. The authors find, over and over again, that the sex differences we observe often have a biological basis yet are not direct readouts of biological processes; they emerge in the course of development in interaction with social processes, norms, and stereotypes in ways that can vary across cultures and decades.

We think this paper is the most complete and authoritative statement currently available. We therefore want to bring it to the attention of all those who are interested in the Damore memo, or who are interested in improving diversity policies and the status of women in the tech industry.  The full paper is available online here. But to make it even more accessible, we paste below the full text of its abstract, followed by an outline of its contents, followed by the full text of its conclusion.

We continue the practice from our main blog post of showing text that generally supports Damore’s claims in green, and text that generally supports his critics in red. We do this not to show that he was right or wrong overall, but to show that the science of gender is complicated; Damore was right that there are differences, and that biology is part of the reason for those differences. But it’s tricky to extrapolate out from those findings to conclusions about why women are underrepresented at Google and in tech in general. See the circular model in section 8 of the paper, below. We have also emphasized other important areas of the text in bold font. We do this to draw attention other important findings that may not bear directly on the controversy over the Damore memo.

Citation: Halpern, D.F., Benbow, C.P., Geary, D.C., Gur, R.C., Hyde, J.S., & Gernsbacher, M.A. (2007). The science of sex differences in science and mathematics. Psychological Science in the Public Interest, 8(1), 1-51. (ungated)


Amid ongoing public speculation about the reasons for sex differences in careers in science and mathematics, we present a consensus statement that is based on the best available scientific evidence. Sex differences in science and math achievement and ability are smaller for the mid-range of the abilities distribution than they are for those with the highest levels of achievement and ability. Males are more variable on most measures of quantitative and visuospatial ability, which necessarily results in more males at both high- and low-ability extremes; the reasons why males are often more variable remain elusive. Successful careers in math and science require many types of cognitive abilities. Females tend to excel in verbal abilities, with large differences between females and males found when assessments include writing samples. High-level achievement in science and math requires the ability to communicate effectively and comprehend abstract ideas, so the female advantage in writing should be helpful in all academic domains. Males outperform females on most measures of visuospatial abilities, which have been implicated as contributing to sex differences on standardized exams in mathematics and science. An evolutionary account of sex differences in mathematics and science supports the conclusion that, although sex differences in math and science performance have not directly evolved, they could be indirectly related to differences in interests and specific brain and cognitive systems. We review the brain basis for sex differences in science and mathematics, describe consistent effects, and identify numerous possible correlates. Experience alters brain structures and functioning, so causal statements about brain differences and success in math and science are circular. A wide range of sociocultural forces contribute to sex differences in mathematics and science achievement and ability—including the effects of family, neighborhood, peer, and school influences; training and experience; and cultural practices. We conclude that early experience, biological factors, educational policy, and cultural context affect the number of women and men who pursue advanced study in science and math and that these effects add and interact in complex ways. There are no single or simple answers to the complex questions about sex differences in science and mathematics.

Outline of the paper:

  1. Introduction
  2. Defining Terms
    • Sex and Gender
    • Biological and Innate
    • Abilities and Achievment
    • Intelligence and IQ
    • The Grade-Test Disparity
    • The Size of an Effect
  3. The What, When, and Where of Sex Differences in Math and Science Achievement
  4. Average Sex Differences in Cognitive Abilities
    • Cognitive Sex Differences in Infancy
    • Verbal Abilities
    • Mean Verbal Abilities
    • Variability in Verbal Abilities
    • Visuospatial Abilities
    • Visuospatial Skills and Computer Games
    • Quantitative Abilities
    • Trends Over Time in Average Abilities
    • Racial and Ethnic Differences in Average Abilities
    • A Cognitive-Process Taxonomy of Average Abilities
  5.      Sex Differences in Math and Science Abilities in the Tails of the Distribution
    • Sex Differences in Distributions and Variances
    • Sex Differences in Mathematical Reasoning in Gifted Students
    • Sex Differences in Higher Education
    • Sex Differences in Career Development Choices
    • Visuospatial Ability and Mathematics and Science Careers
    • Additional Factors Influencing Sex Differences in Career Choices of High-Ability Individuals
  6. An Evolutionary Account of Sex Differences in Mathematics and Science
    • Sexual Selection
    • Sex Hormones
    • Within-Sex Variation
    • Development
    • An Evolutionary Understanding of Human Sex Differences
    • Sexual Selection
    • Sex Hormones and Cognitive Sex Differences
    • Within-Sex Variation
    • Development
    • Critiques of Evolutionary Explanations of Sex Differences in Science and Math
  7. Sex Differences in Brain Structure and Function
    • Sex Differences in Brain Structure
    • Sex Differences in Cerebral Volume
    • Sex Differences in Corpus Callosum Structure
    • The Need for Developmental and Longitudinal Studies
    • Sex Differences in Brain Function
    • Sex Differences in Cerebral Blood Flow
    • Sex Differences in Cerebral Glucose Metabolism
    • Sex Differences in Neurotransmitter Function
    • Brain Imaging, Mathematics, and Science
    • Speculative Hypotheses on the Relation of Neural Structures to Science and Mathematics
    • Single-Sex Schools
  8. The Biopsychosocial Model: An Integration of Nature and Nurture

  9. Sociocultural Forces, Sex, and Mathematics and Science
    • Family, Neighborhood, Peer, and Social Influences
    • Stereotype Threat
    • Training Studies
    • Cross-Cultural Analyses
    • Sociocultural Influences on Occupational Culture
    • Sex Discrimination and Occupational Success
    • Women’s Roles
  10. Summary and Conclusions (see below for full text)
    • Average Sex Differences in Cognitive Abilities
    • Sex Differences in Math and Science Performance in the Tails of the Distribution
    • An Evolutionary Account of Sex Differences in Math and Science
    • Sex Differences in Brain Structure and Function
    • Sociocultural Factors, Sex, and Math and Science Abilities



In this review of the current state of the evidence for cognitive and interest differences between the sexes and their putative biological, evolutionary, and social/environmental origins, we have presented a summary of what is known about sex differences and similarities in mathematical and science abilities based on the best available scientific evidence. The popular media have sensationalized findings of sex differences, often presenting the latest finding without assessing the quality of the research that it was based on or using ‘‘person on the street interviews’’ about beliefs about sex differences as though they were as valid as a carefully executed program of research (e.g.,Conlin, 2003). This monograph represents a consensus of expert opinion, from a group of scientists with diverse backgrounds, to the questions about sex and math and science achievement. We addressed questions concerning whether and when (in the lifespan) there are differences between males and females in the cognitive abilities that are important for success in careers requiring aptitude for and achievement in mathematics and science, and the extent to which sex differences in math and science abilities can be attributed to ‘‘innate’’ explanations, socialization, or the way these two types of influences reciprocally influence each other. In this review, we have focused on a wide range of research in which reasonable data have accumulated that address these issues, which we summarize and draw conclusions from below.


Average Sex Differences in Cognitive Abilities


Psychologists often look for sex differences very early in life as clues to the relative contribution of biological and environmental contributions, reasoning that newborns have had fewer social interactions, so the earlier that sex differences are reliably found, the more likely they are assumed to be biological in origin. This assumption is not fully supported by the biological literature because, for many species, sex differences are not evident in infancy and often do not emerge until the age of reproductive maturation. The simple distinction between cognitive sex differences that emerge early in life and those that emerge later does not rule out environmental effects, because the uterine environment affects the development of a fetus. The role of prenatal environmental factors is an excellent example of the interaction of biological and environmental variables, which often become indistinguishable in their effects. It does not necessarily follow that differences found later in life are caused by social or environmental factors, because there are developmental timelines for biological processes, including the timing of puberty, the development of the forebrain, and the aging processes, all of which are also influenced by the environment. Moreover, the tasks that infants can handle may be qualitatively different from tasks designed for adolescents, even if they are both labeled the same. For example, a verbal or spatial task for an infant is qualitatively different than a verbal or spatial task for an adolescent. With these caveats in mind, the usual finding across tasks is that males and females develop equally well in early cognitive skills that relate to quantitative thinking and knowledge of objects in the environment.


By the end of grade school and beyond, females perform better on assessments of verbal abilities when assessments are heavily weighted with writing and the language-usage items cover topics with which females are familiar; sex differences favoring females are much larger in these conditions than when assessments of verbal abilities do not include writing. In contrast, males excel on certain visuospatial-ability measures. Yet, of all the sex differences in cognitive abilities, differences in quantitative abilities have received the most attention because of the marked differences favoring males at the highest end of the ability distribution and because of their importance in so many occupations. Male performance is more variable than that of females in quantitative and visuospatial abilities, which means that there are also more males at the low-ability end of these distributions. Because males tend to be more variable, the average difference in performance between females and males for most assessments is smaller than it is at the high- and low-ability tails of the distributions, and the size of the average between-sex difference is larger for tests such as the GRE that are administered to selective samples than it is for less selective tests such as the SAT or a high-school admissions test. The fact that females achieve higher grades in school-based math and science tests and lower average scores on standardized exams used for college admissions and graduate school may point to differences in the strategies males and females use to solve novel problems (Gallagher & Cahalan, in press) and to the tendency of females to do better in most school contexts (Willingham & Cole,1997). Of course, the factors that enter into earning a high grade in a class are also different from those leading to high test scores on a standardized test.


Sex Differences in Math and Science Performance in the Tails of the Distribution


Substantial evidence suggests that the male advantage in mathematics is largest at the upper end of the ability distribution, a result that could provide important clues to the origin of this sex difference. In addition, a ‘‘tilt’’ favoring visuospatial or mathematical abilities compared to verbal, regardless of level of ability, is more frequently exhibited by males than by females. Females tend to be more balanced in their ability profiles, which may lead them to choose mathematics or science careers less frequently than their male counterparts do. These differences can be seen as early as adolescence, and, therefore, a greater number of males than females may qualify for advanced training in disciplines that place a premium on mathematical reasoning and/or visuospatial abilities. Any differences that exist are increased if interests and activities that are correlated with abilities are considered.


An Evolutionary Account of Sex Differences in Math and Science


From an evolutionary perspective, sex differences in advanced math and science have not evolved in any direct way but could be indirectly related to differences in interests and to specific brain and cognitive systems that differ for females and males. Evolutionary theories predict sex differences that arise from patterns of intrasexual competitions (for both males and females) and intersexual choice (for both females and males), including pressures that accompany the male-biased activities of hunters and warriors who traveled long distances in novel territory. Although a large body of data was presented that supports this theory, numerous criticisms have been raised as well. Many of its predictions remain to be tested, although several patterns are consistent with observed differences in interest and ability profiles.


Sex Differences in Brain Structure and Function


Studies of brain structure and function have suggested some potential biological mechanisms for the observed sex differences in ability. In general, females have a higher percentage of gray-matter brain tissue, whereas males have a higher volume of connecting white-matter tissue—with the exception of the splenium of the corpus callosum, which is more bulbous and, thus, larger in females than in males. Furthermore, male brains show greater volumetric asymmetries than female brains do. The higher white-matter volume seems associated with better spatial performance in males, while the greater bilateral symmetry seems associated with better language processing in females. Although the advent of noninvasive techniques for functional brain imaging has allowed a rapid increase in the number of studies investigating sex differences in the regional functional specialization for cognition, these studies are in their infancy. Future research of this type should involve larger and more carefully selected sample populations to avoid strong and potentially confounding cohort effects, and should employ longitudinal designs. Finally, hormones have been documented to affect cognition through their organizing effects on the brain.


Sociocultural Factors, Sex, and Math and Science Abilities


Sociocultural forces also influence sex differences in math and science abilities, academic-course choices, occupational choices, and occupational success in math and science careers. Compared with girls, boys seem to benefit more from enriched neighborhoods and to be hurt more by deprived neighborhoods. Schools certainly influence students’ learning and performance; research has documented systematic, subtle differences in the ways that teachers treat males compared with the ways they treat females in math and science classrooms. Cross-cultural research demonstrates that the magnitude of sex differences in math performance varies across nations. In no country is the overall sex difference large prior to the end of secondary school, when the size of the sex difference begins to increase, although larger differences sometimes emerge earlier in specific mathematical areas (e.g., geometry). Moreover, the magnitude of the sex difference correlates negatively with measures of gender equality in the country. Many women in math and science areas do report significant sex discrimination, and these experiences likely shape the direction their careers take. Finally, women’s roles may be part of the equation, as women still bear more responsibility for child care than do men and they work fewer hours. It also seems that being successful in a nontraditional career, such as engineering, may penalize women in the marriage market.

Closing comment, from Stevens and Haidt:

The Damore memo has elicited a great deal of controversy. In most written commentaries, you can tell what conclusions the author will reach after reading the first few sentences. Our goal in our posts here at Heterodox Academy is to help those who sincerely want to figure out the truth, and who therefore want to read competing analyses, and analyses by groups of experts that included some viewpoint diversity. When passions run high, viewpoint diversity is most needed. 

As John Stuart Mill wrote, in On Liberty:

the only way in which a human being can make some approach to knowing the whole of a subject, is by hearing what can be said about it by persons of every variety of opinion, and studying all modes in which it can be looked at by every character of mind. No wise man ever acquired his wisdom in any mode but this; nor is it in the nature of human intellect to become wise in any other manner.

To read the whole review paper, click here.

Opinions expressed are those of the author(s). Publication does not imply endorsement by Heterodox Academy or any of its members. We welcome your comments below. Feel free to challenge and disagree, but please try to model the sort of respectful and constructive criticism that makes viewpoint diversity most valuable. Comments that include obscenity or aggression are likely to be deleted.