Men are X, women are Y. We hear it all the time. Are men and women fundamentally different? And are those differences biological or the result of culture? Physiologically, there are obviously quite a few differences between men and women, so it's reasonable to assume that those differences might extend to the brain. The brains of men and women do exhibit some basic structural differences, and the differences in male and female hormones could contribute to the dissimilarity, as well. But looking at cultures around the world, you find that many of these differences change and blur. The truth is, yes, we're different, but we're not that different. And yes, it's biological, but it's social, too.
The brains of men and women are mostly similar, but there are a few notable differences. Men's brains are larger than women's but that size difference corresponds with the difference in body size and is generally thought to mean little. The gray matter and white matter that composes the brain is also different between the sexes. A 2004 study found that men and women achieve similar results on an IQ test using different brain regions. Men with a higher gray matter volume in the frontal and parietal lobes tended to have higher IQ scores, while the same was true for women with higher gray matter volume in the frontal lobe and Broca's area. Additionally, some studies have found that women have stronger language processing skills on average than men, and that men are consistently better, on average, at math and spatial reasoning tasks than women. Additionally, these strengths are likely to have been reinforced by social stereotypes of men and women, and so it is difficult to make any firm assumptions based on the data.
Another field where it's difficult to separate science from stereotype is the study of interpersonal dynamics. Men are more likely to display aggression than women, but it is not clear whether this is the result of biology or culture. Likewise, women tend to perform better than men on tests of empathy and gauging the emotion of others, and are stereotypically more emotional than men, but this could also be the result of social conditioning. A 2009 study found that the brains of men and women respond differently to negative stimuli, with male brains showing activation of the areas associated with action and female brains showing activation of the areas associated with emotion and memory. This could be the basis for the stereotype that men experience a "fight or flight" response in negative situations, while women are more inclined to take the "tend and befriend" approach. However, these sorts of generalizations are still extremely controversial.