In this video at 42:06, Daniel Dennett posits that our big brains are:
The human artifice or version of the peacock's tail.
Peacocks have sexual dimorphism - it's males who exhibit the costly signal of showing off a big, colourful tail.
Now, humans are more special, because there are certainly no differences in the cognitive potential of men and women. Yet, there seems to be evidence for each gender being driven by different interests (there are exceptions).
Thus my question: has human intelligence evolved as a costly male signal which has, over time, been passed to females too, but whom are just not as interested to use it to attract mates?