Have different mental strengths evolved in men and women?
There is little neurological evidence that finds a difference between men and women. However there are psychological studies that do find a small difference in mental strengths. This interesting TED talk debunking psychological myths by a lecturer from the University of Liverpool discusses the psychological differences between men and women. 

Males and females are slightly different when it comes to spacial awareness (the top 1/3 of females perform as well as the top 1/2 of men) and language (the top 1/3 of men perform as well as the top 1/2 of women), but the difference is so slight that its not worth taking into consideration.

I moved this answer over from the biology question.