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Women and Math – Part 2

by T.J. Nelson


On the Internet, no one can tell whether you're a dolphin or a porpoise
by T.J. Nelson

Women and Math, Part 2

Science has made many advances in the past decade documenting cognitive and neuroanatomic differences between men and women. Part 1 of this article gave an overview and personal observations. Below is Part 2, which gives a brief review of the scientific literature on the subject.

Mathematicians and career choice

F ar and away the greatest number of articles on the Internet and the popular literature about male and female mathematicians are devoted to “famous female mathematicians.” The same is true for the psychology and sociology literature. Clearly there is a strong desire in popular culture to see greater female participation in science and mathematics. However, the subjective and biased nature of these articles makes them useless in determining what brain differences may actually exist. Identifying such differences is critical in adapting education to maximize the benefit to both sexes.

As mentioned in Part 1, almost all the simultaneous translators at the U.N. are females. The reason for this is undoubtedly the greater lateralization of language function in males. Adult females process speech on both sides of the brain [1, 2] while males process speech on only one side, and are consequently more strongly affected by a stroke in that area. This is a slight oversimplification for the sake of brevity. But clearly, having two speech centers, and using one for English and the other for Urdu, would be a big convenience for a translator.

In 2003 there were 12,675 males and 3,305 female members of the American Mathematical Society, a voluntary association of professional mathematicians, who resided in the U.S. (ratio=3.83). Since math skill is a strong component of IQ, this would seem to indicate that males tend to be predominant in job choices requiring long-term dedication to difficult intellectual tasks involving mathematics.

The best available data consistently show that men and women have nearly identical IQ, but there is a greater variation in men. That is, there are more men in the extremely intelligent group, and more men in the lowest IQ group. IQ is pretty much a verboten topic for research these days, so there is less new hard information on results using standard IQ tests. However, the past decade has seen an explosion of data from functional MRI and other techniques for measuring the brain. But first, we should mention autism and ADHD, which are sometimes mentioned as evidence for gender-brain differences.


Autism is diagnosed 4.6 times more in males than females [3,4], while women have higher incidences of stress-related disorders such as depression and anxiety-related disorder [5]. Neither of these conditions is fully understood, which makes it difficult to make inferences about brain differences from these statistics. Autism, in particular, is not a single disorder, but a general term for a spectrum of disorders, so it almost certainly has many different causes.

Attention-deficit hyperactivity disorder

ADHD is diagnosed by purely behavioral criteria: inattention, hyperactivity, and impulsive behavior. Some studies [6,7] report that males are diagnosed four times as often with ADHD than females. Another study reported that in adolescents (age 13-18) the male/female is 3.6, while in children (age 7-13) the ratio is 2.46 [8]. The biggest problem with ADHD is referral bias. At its root, ADHD is essentially a behavior problem in school. The teacher, who is usually a female, finds she is unable to discipline the male child and “refers” him for drug treatment. Thus we end up with “referral bias”, in which the overwhelming number of patients are male, but the symptoms are more acute in females.

When attempts are made to eliminate referral bias, the actual male/female ratio is reduced to 2.28 or less [8]. This is consistent with the idea that ADHD is partly, and maybe even primarily, a social phenomenon. The overall prevalence of ADHD using DSM-IV criteria is said to be 11.7% in children, 9.7% in adolescents, and 6.4% in adults [8]. The percentages are expected to be even higher in DSM-5.

Structural brain differences

Unfortunately, the fact that there are fewer female mathematicians, ADHD sufferers, and autism sufferers tells us little about brain differences. Males could simply be choosing more frequently to become mathematicians for cultural or historical reasons, and ADHD is first diagnosed by teachers, who are untrained in making diagnoses, and who are predominantly female, and therefore potentially less familiar with the needs of male students.

Likewise, autism could be caused by other factors in the child's environment that discriminate against the male. Moreover, since the only criteria in ADHD and career choice are behavioral, even the prevalence data are unreliable and uninformative. Thus, our most reliable data on male-female brain differences come from medical studies of healthy children and adults that use functional magnetic resonance imaging, or fMRI. What do these fMRI studies tell us?

Wu et al [9] did a resting-state functional MRI study of 51 healthy children, and found that although the IQs of the male and female children were similar, there were marked differences in brain network properties and topological organization.

In terms of their network properties, males had significantly higher global efficiency, while females had a longer characteristic path length. This means that the boys benefited from more rapid transfer of information across remote brain regions that constitute the basis of cognitive processing [10], while girls had a more organized neuronal network. Global efficiency and path length are both associated with higher intellectual performance [11]. So, in layman's terms, both boys and girls were equally smart, but in quite different ways.

Studies on children showed that females had a marginally higher overall clustering coefficient [10, 12], while studies of young adults showed that males had higher values in the right hemisphere and lower values in the left hemisphere [13] due to differences in cross-hemisphere communication [14]. This means that boys had more lateralization and a more optimal configuration for globally distributed processing, which would be necessary for executive functioning, while girls were optimized for locally distributed processing, which would benefit aspects of visual input analysis.

Electroencephalographic studies also reveal functional connectivity. To give an idea what these terms mean, a short characteristic path length represents a more closely integrated network. Characteristic path length decreases with age [15]. Even though this is only one single parameter, and there's a vast amount about the brain that we don't yet understand, it indicates unequivocally that the brains of males and females are wired differently in terms of how they integrate information between multiple brain regions. A nice review of brain networks is given here [11].

Studies on children are confounded by well-established differences in rates of physical development. Females tend to mature earlier than males. (This is not a sign of either inferiority or superiority as sometimes claimed in the popular literature—it should be remembered that larger and more complex animals tend to develop more slowly.) Nevertheless, brain differences in children may have a large impact on how they are treated, and on later career choice. These differences are inborn and follow a pre-programmed path. They increase during puberty, and are carried on into adulthood.

Males and females also develop significantly differently in their visuospatial, language, and emotion processing [16, 17, 18]. fMRI studies have identified significant differences in the trajectories of intellectual development and functional connectivity between males and females [19, 20, 21], as well as anatomical connectivity [22] and brain structure [23, 24, 25].

fMRI and Math

So what about math, then? An interesting paper by Lyons and Beilock [26] found that math anxiety increases brain activity in regions associated with visceral threat detection, as well as in bilateral dorso-posterior insula, which are regions associated with perception of pain. They found that only anticipating math, but not actually doing math, activated the pain regions. Evidently, in high-math-anxiety patients, just thinking about math produces pain.

An fMRI study of 24 males and 25 females [27], using voxel-based morphometry measurements, found significant gender differences in functional brain activation in the right dorsal and ventral visuospatial information processing streams. Males showed greater activation in the right intra-parietal sulcus, which is important for numerical cognition. All gender differences were lateralized to the right hemisphere. Males had a higher brain volume and a higher percentage of white matter, which is involved in communication between neurons, while females had a higher percentage of gray matter [28].

The larger brain size in males has been known for some time, and is usually attributed to their larger body mass. All the scientists in these studies went out of their way to emphasize the same thing: not better or worse, just clearly different.

A study in Turkey found that mathematicians have a higher gray matter density in the parietal cortex, which correlated with the number of years spent working as a mathematician [29]. So doing math problems seems to increase one's quantity of gray matter. (Or, possibly more likely, having more gray matter increases the length of time mathematicians remain in their career.) The left-inferior frontal and bilateral parietal regions, say the authors, are involved in arithmetic processing, while inferior parietal regions are involved in high-level mathematical thinking, such as mental creation and manipulation of three-dimensional objects. This study didn't compare males and females, but gender differences in neural correlates of mental rotation were found in a German study by Hoppe et al. [30].

In this study, the authors say that mental rotation ability is reliably correlated with both gender and math talent. Mental rotation produces activation of the parietal lobe, which they measured using fMRI. Even though the IQ and school grades of the subjects were identical, big gender differences were found in both performance and in activation of the parietal lobe. In the right superior parietal lobe, for instance, males had a relative activation level of 0.77±0.15 and females had an activation of 0.46±0.06. However, owing to the small number of subjects (34), the difference was only significant at p<0.1. (It turns out that if they had just added two more in each group, they would have found a significant change. This happens often: you realize after it's too late that you used too small a population.)

Language skills

Studies of language ability are more difficult, and have focused mainly on lateralization. Sex differences in lateralization have been found in processing of nonwords and stories with global language structure, but not in processing of real individual words [31].

It is surprising that any difference at all can be measured, either in math or in language, since the prevailing hypothesis is that gender differences would exist mainly among the highest and lowest performers, while the mean performance should be identical. This hypothesis would predict that much larger populations are needed before any difference becomes apparent. That still may be true for IQ, but for math skills, it seems that we are seeing not just a broader population distribution, but differences in average ability.

The reason for these differences is even harder to identify. The relative importance of genetic programming vs. sex hormones is unknown. Population sizes have sometimes been too small. Some studies have used college psychology students, raising the possibility that none of the subject population might be particularly good at math. Yet despite the difficulties, there are unequivocal, measurable differences between male and female brains.

So, yes, I lied about there being no math. Math is tough. So is neuroanatomy. Nonetheless, the scientific evidence for gender differences in both math skill and brain neuroanatomy is overwhelming. But just as clearly, we still have much to learn about the brain. Oh, and I almost forgot: more research is needed™.


[1]. Clements AM, Rimrodt SL, Abel JR, Blankner JG, Mostofsky SH, et al. (2006) Sex differences in cerebral laterality of language and visuospatial processing. Brain Lang 98: 150-158.

[2]. Wang L, Shen H, Tang F, Zang Y, Hu D (2012) Combined structural and resting-state functional MRI analysis of sexual dimorphism in the young adult human brain: an MVPA approach. Neuroimage 61: 931-940.

[3]. Werling DM, Geschwind DH. Sex differences in autism spectrum disorders. Curr Opin Neurol. 2013 Apr;26(2):146-53.

[4]. MMWR Surveill Summ. 2012 Mar 30;61(3):1-19. Prevalence of autism spectrum disorders--Autism and Developmental Disabilities Monitoring Network, 14 sites, United States, 2008. Autism and Developmental Disabilities Monitoring Network Surveillance Year 2008 Principal Investigators; Centers for Disease Control and Prevention.

[5]. Hodes GE. Sex, stress, and epigenetics: regulation of behavior in animal models of mood disorders. Biol Sex Differ. 2013 Jan 21;4(1):1.

[6]. Ramtekkar UP, Reiersen AM, Todorov AA, Todd RD. Sex and age differences in Attention-Deficit/Hyperactivity Disorder symptoms and diagnoses: Implications for DSM-V and ICD-11. J Am Acad Child Adolesc Psychiatry. 2010 March; 49(3): 217-28.e1-3.

[7]. Cantwell DP. Attention deficit disorder: a review of the past 10 years. J Am Acad Child Adolesc Psychiatry. 1996 Aug; 35(8):978-87.

[8]. Gaub M, Carlson CL. Gender differences in ADHD: a meta-analysis and critical review. J Am Acad Child Adolesc Psychiatry. 1997 Aug;36(8):1036-45.

[9]. Wu K, Taki Y, Sato K, Hashizume H, Sassa Y, Takeuchi H, Thyreau B, He Y, Evans AC, Li X, Kawashima R, Fukuda H. Topological organization of functional brain networks in healthy children: differences in relation to age, sex, and intelligence. PLoS One. 2013;8(2):e55347. Epub 2013 Feb 4.

[10]. Sporns O, Zwi J (2004) The small world of the cerebral cortex. Neuroinformatics 2: 145-162.

[11]. van den Heuvel M, Stam CJ, Kahn RS, Hulshoff Pol HE (2009). J. Neurosci 29(23): 7619-7624. Efficiency of Functional Brain Networks and Intellectual Performance.

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[14]. Tian L, Wang J, Yan C, He Y (2011) Hemisphere- and gender-related differences in small-world brain networks: a resting-state functional MRI study. Neuroimage 54: 191-202

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[18]. Bussey K, Bandura A (1999) Social cognitive theory of gender development and differentiation. Psychol Rev 106: 676-713.

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[20]. Rubia K, Hyde Z, Halari R, Giampietro V, Smith A (2010) Effects of age and sex on developmental neural networks of visual-spatial attention allocation. Neuroimage 51: 817-827

[21]. Schmithorst VJ, Holland SK (2007) Sex differences in the development of neuroanatomical functional connectivity underlying intelligence found using Bayesian connectivity analysis. Neuroimage 35: 406-419

[22]. Schmithorst VJ (2009) Developmental Sex Differences in the Relation of Neuroanatomical Connectivity to Intelligence. Intelligence 37: 164-173.

[23]. Lenroot RK, Gogtay N, Greenstein DK, Wells EM, Wallace GL, et al. (2007) Sexual dimorphism of brain developmental trajectories during childhood and adolescence. Neuroimage 36: 1065-1073.

[24]. Shaw P, Greenstein D, Lerch J, Clasen L, Lenroot R, et al. (2006) Intellectual ability and cortical development in children and adolescents. Nature 440: 676-679

[25]. De Bellis MD, Keshavan MS, Beers SR, Hall J, Frustaci K, et al. (2001) Sex differences in brain maturation during childhood and adolescence. Cereb Cortex 11: 552-557

[26]. Lyons IM, Beilock SL. (2012). When math hurts: math anxiety predicts pain network activation in anticipation of doing math. PLoS One. 2012;7(10) e48076. Epub 2012 Oct 31.

[27]. Keller K, Menon V. Gender differences in the functional and structural neuroanatomy of mathematical cognition. Neuroimage. 2009 Aug 1;47(1):342-52. Epub 2009 Apr 17.

[28]. Cosgrove KP, Mazure CM, Staley JK. Evolving knowledge of sex differences in brain structure, function, and chemistry. Biol Psychiatry. 2007 Oct 15;62(8):847-55. Epub 2007 Jun 4.

[29]. Aydin K, Ucar A, Oguz KK, Okur OO, Agayev A, Unal Z, Yilmaz S, Ozturk C. Increased gray matter density in the parietal cortex of mathematicians: a voxel-based morphometry study. AJNR Am J Neuroradiol. 2007 Nov-Dec;28(10):1859-64. Epub 2007 Oct 5.

[30]. Hoppe C, Fliessbach K, Stausberg S, Stojanovic J, Trautner P, Elger CE, Weber B. A key role for experimental task performance: effects of math talent, gender and performance on the neural correlates of mental rotation. Brain Cogn. 2012 Feb;78(1):14-27. Epub 2011 Nov 15.

[31]. Kansaku K, Kitazawa S. Imaging studies on sex differences in the lateralization of language. Neurosci Res. 2001 Dec;41(4):333-7.

Click here to go back to Part 1

See also:

Science Commen­tary

Women and Math, Part 1

Book Reviews

P.C., M. D by Sally Satel

Experiments Against Reality by Roger Kimball

Science Left Behind: Feel-Good Fallacies and the Rise of the Anti-Scientific Left by Alex Berezow and Hank Campbell

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aug 18, 2013; updated aug 22, 2013