As I was contemplating yesterday, I stopped at Matthew 10:16 -- I am sending you out like sheep among wolves. Therefore be as shrewd as snakes and as innocent as doves. (NIV)
Referring to other verses about the serpent, we find that serpents have the symbol of shrewdness and intellectual cunning.
Now the serpent was more crafty than any other beast of the field that the LORD had made. (ESV)
They have venom like the venom of a serpent, like the deaf adder that stops its ear, so that it does not hear the voice of charmers or the cunning enchanter. (ESV)
Doves represents simple innocence, though Hosea does not paint a very good picture about it.
Ephraim is like a dove, silly and without sense. (ESV)
But can one have both shrewdness and innocence? ESV translated it as being crafty, which means being skilled in deception. But how can one deceive and yet be innocent? Is there a good kind of deception? NIV and NASB translated it as shrewd, KJV and RSV as wise.
I suppose we cannot just be innocent and not be crafty enough to realise underlying issues and motivation of other people. So I would take it as being wise, discerning but innocent. A very good combination of qualities to have for sure.