http://www.youtube.com/watch?v=I7tYwnqot6M
> or serve me food while playing a violin at a restaurant at my tenth wedding anniversary,
http://www.youtube.com/watch?v=EOLL59nIkrA
> or perform a moving and/or erotic song and dance at a concert.
http://www.youtube.com/watch?v=-kM3n64WJmo
> Well, we could, but none of those things would go over well or have the desired effect.
People seem to be enjoying the last 2 robots plenty. As for the first one, robot nurses, I think they'll massively prefer it over not having anyone. Baby boomers didn't have nearly enough kids, so they won't have any reasonable amount of attendants during old age. People that were never born can't take care of them. This is especially true in Europe, but even in America it's a pretty reasonable argument to make.
> We also can't make a robot to make startling leaps like "hey, I think the PHASES OF THE MOON are controlling the strength of the tides! Holy crap!"
I think you need to visit a university. Or even better, a pharma company, or an oil company. The times of people making those associations are long, long over. Now people clean databases before they get fed into the computers that make the real discoveries, and fix any blockages in the equipment. Oh and implement the bureaucracy, of course.
Mathematical discoveries, it's been 2 years now since one was actually made by a human. It's been decades since the last real mathematical discovery that wasn't at least "proof-assisted". Same goes for physics and it's becoming more and more true in chemistry (it's already true in commercial chemistry and pharma).