Reduce the clutter in a discussion: I'm not saying everyone should abstract everything away, but I've found mathematicians have a knack for seeing what is pertinent to the discussion and putting the other things aside for the time being. I see this particularly on university committees, where mathematicians seem to be the best at both getting things done and getting near optimal solutions. All over the world we see parties in a discussion holding grudges and settling into opposing camps based on historical disagreements. I see the same behavior on university committees but mathematicians seem to be better about ignoring the disagreements of last week and focusing solely on the problem at hand.

In a similar vein, mathematicians seem to be able to take positive action quickly in these discussions rather than getting disheartened by the difficulty of the problem at hand. I suspect this is because we train ourselves to build theorems out of lemmas and to see the whole structure of a proof before starting. So I suppose this point is more about making an outline or plan of attack (and many fields train you to do this), but we seem particularly good at it because we do such problem-solving for a living and we know how to break a problem down into easier pieces.