Here’s an interesting study.
“Sex differences in the brain are irresistible to those looking to explain stereotypic differences between men and women,” said Dr. Eliot. “They often make a big splash, in spite of being based on small samples. But as we explore multiple datasets and are able to coalesce very large samples of males and females, we find these differences often disappear or are trivial.” […]
“Many people believe there is such a thing as a ‘male brain’ and a ‘female brain,'” Dr. Eliot said. “But when you look beyond the popularized studies — at collections of all the data — you often find that the differences are minimal.”[…]
Meta-analyses by other investigators have also disproved other purported sex differences in the brain, Dr. Eliot noted. There is no difference in the size of the corpus callosum, white matter that allows the two sides of the brain to communicate, nor do men and women differ in the way their left and right hemispheres process language.
The link doesn’t explain it very well, but the point is this: many previous studies had suggested that women had a larger hippocampus than men. Few of them controlled for brain size, however, which is an issue as bigger people tend to have bigger brains, and men are typically bigger than women. Once you factor that in, there’s no difference.
To be honest, I’m kind of conflicted about this. I’ll explain by retreading old ground.
Here’s one dataset detailing the height differences between men and women. The light green area has the two distributions overlapping one another, while the dark green area is their sum. You can see the distribution peaks quite clearly, and if I provided you with a height plucked at random from the dataset, you’d be able figure out with 83% accuracy the person’s gender.
Math ability shows no gender divide in the general population. If you delve into sub-groups, though, you can find a difference as big as the one I pictured above. This is a pretty good indicator of what we can explain by societal factors; if I plucked a random person’s score out of there, you’d guess the sex correctly 60% of the time.
So let’s bring up those spatial differences.
If you delve into sub-populations, you can get a result this big. Ever heard of mental rotation? It’s a huge deal in the scientific study of gender, because it persistently shows greater sex differences than almost any other metric, including other spatial measures.* Yet it’s on the same scale as what socialization can deliver, and only 60% predictive.
The sex difference in spatial ability is either trivially small or non-existent. So when the authors state “Sex differences in memory and spatial skills further suggest that males and females differ in hippocampal structure and function” in the abstract, my first thought is “what sex differences?” My second thought is to scan through the intro of the paper, looking for a citation showing these differences. Maybe I missed a major study, somehow?
Human studies similarly suggest that prenatal testosterone enhances spatial skills (Puts et al., 2008 and Vuoksimaa et al., 2010) although post-pubertal testosterone fluctuations do not (Puts et al., 2010). It is possible, then, that early androgen exposure enhances HCV and later spatial and navigational skills in males.
On the other hand, female rats exhibit an increase in dendritic spine density in hippocampal neurons in response to estrogen, an effect associated with changes in spatial learning and synaptic plasticity across the estrous cycle (Cooke and Woolley, 2005). High levels of estrogens in females have been associated with greater spine density in rhesus monkeys (Hao et al., 2003) and with the size and synaptic density of hippocampal subregions in both rats (Galea et al., 1999) and humans (Protopopescu et al., 2008), all findings suggesting HCV may be specifically enhanced in reproductive-aged women.
That’s all of the relevant bits. Would you be shocked to learn that “spatial ability” was equivocated with “mental rotation?” And that only two of the studies cited actually measured mental rotation performance, the ones I highlighted? Here’s the sex difference according to Puts et. al. (2008)… 
The alternative socialization explanation for our result is that females with twin brothers are exposed to different sex-typed activities than are females with twin sisters and are thus masculinized in their mental rotation ability. For example, a previous study showed that short-term training in action video games reduced the gender difference in MRT performance (Feng, Spence, & Pratt, 2007). However, computer-game playing, a possible indicator of practice effects, had a trivial association to MRT performance in our study, and this suggests that our results are not explained fully by the possible tendency of sisters of twin brothers to engage in more male-typical activity than other females do.
The effect of having a male co-twin on females’ MRT performance remained even when we controlled for pregnancy-related variables and compared only dizygotic twins. This supports the inference that our results were not caused by differences related to monozygotic and dizygotic twinning. Interestingly, gestational age was associated with MRT performance only in females. Because this measure relates to prenatal development, this result may suggest that prenatal events affect mental rotation ability differently in females and males.
Well there you go: the authors only found a small association between video games and mental rotation ability, so social factors are ruled out.
To sum up: these authors tried to dispel a physical association to a specific task which is reliably linked to gender, but the sex differences in said task are about the same size as what we could explain by socialization. This study is a decent result stacked on top of nonsense, and like hundreds of other studies over gender differences blindly accepts the existence of a difference that may not actually be there.
But remember that chart which showed significant differences in height between men and women?
Adult male brains are some 14% larger than female brains, with bigger ventricles, a higher ratio of white:gray matter, and a longer period of growth during adolescence (e.g., Lenroot et al., 2007). These differences are reliable enough that most brain morphometry studies now use sex as a covariate when analyzing mixed-sex samples.
Bigger people have bigger brains. Bigger brains should lead to some difference in cognition; otherwise, we’re stuck arguing brain connectivity and/or volume doesn’t have much effect on our computational abilities. Men are bigger than women, on average, hence they have bigger brains. So we’d expect a difference in cognition.
And on things like math, there’s no difference in computation ability between men and women. “Legit” differences only persist in very specific tasks like mental rotation, not global measures, and even then the gap isn’t hard to explain by socialization instead of biology. There seems to be little-to-no correlation between brain hardware and brain output, at least with the tools we have now.
So if we do find a sex difference in brain hardware, we’re not justified in saying it has an effect on behavior. Why the hell are we still looking for sex differences in human brains, then?!
… Maybe you shouldn’t answer that one.
- Masterbation rates are higher.
 Anh Tan, Wenli Ma, Amit Vira, Dhruv Marwha, Lise Eliot. The human hippocampus is not sexually-dimorphic: Meta-analysis of structural MRI volumes. NeuroImage, 2016; 124: 350 DOI: 10.1016/j.neuroimage.2015.08.050
 Hyde, Janet S., et al. “Gender similarities characterize math performance.” Science 321.5888 (2008): 494-495. http://dericbownds.net/uploaded_images/hyde.pdf
 Hyde, Janet S., Elizabeth Fennema, and Susan J. Lamon. “Gender differences in mathematics performance: a meta-analysis.” Psychological bulletin 107.2 (1990): 139.
 Voyer, Daniel, Susan Voyer, and M. Philip Bryden. “Magnitude of sex differences in spatial abilities: a meta-analysis and consideration of critical variables.” Psychological bulletin 117.2 (1995): 250.
 Puts, David A., Rodrigo A. Cárdenas, Drew H. Bailey, Robert P. Burriss, Cynthia L. Jordan, and S. Marc Breedlove. “Salivary Testosterone Does Not Predict Mental Rotation Performance in Men or Women.” Hormones and Behavior 58, no. 2 (July 2010): 282–89. doi:10.1016/j.yhbeh.2010.03.005.
 Vuoksimaa, Eero, Jaakko Kaprio, William S. Kremen, Laura Hokkanen, Richard J. Viken, Annamari Tuulio-Henriksson, and Richard J. Rose. “Having a Male Co-Twin Masculinizes Mental Rotation Performance in Females.” Psychological Science 21, no. 8 (August 1, 2010): 1069–71. doi:10.1177/0956797610376075.
 Oliver, Mary B., and Janet S. Hyde. “Gender differences in sexuality: a meta-analysis.” Psychological bulletin 114.1 (1993): 29.