It seems highly likely that the average woman and man do have varying abilities based on the brain. But, we currently do not have the knowledge to 100% accurately determine what these are. And, of course there will always be exceptions. Personally, I use these uncertainties to explore notions of gender in all of my novels.
Jared Angel, Betraying the God of Light (Silver Leaf Books, 2012)
Jerry Bergman, “Darwin’s Teaching of Women’s Inferiority” (Institute Creation Research,
Charles Darwin, The Descent of Man
Cordelia Fine, Delusions of Gender (W. W. Norton & Company, 2011)
Sarah Blaffer Hrdy, The Woman That Never Evolved (Harvard University Press, 2000)
Janet Hyde, et al., “Gender Similarities Characterize Math Performance” (Science, Vol.
321, July 2008, Pp. 494-495)
Weiwei Men, et al., “The corpus callosum of Albert Einstein’s brain: another clue to his
high intelligence?” (Brain: A Journal of Neurology, Vol. 137, Issue 4, 2013, http://brain.oxfordjournals.org/content/137/4/e268
Nikhil Swaminathan, “Girl Talk: Are Women Really Better at Language?” (Scientific
American, 2008, http://www.scientificamerican.com/article/are-women-really-better-with-language/