Since they are including TV shows, how could they have missed Futurama? Episode 6ACV10, "The Prisoner of Benda" involved a machine that could swap the minds of two people. However, it turned out a given pair could only be swapped once. So if A and B swapped, and then wanted to swap back, they could not just use the machine together again. They would need to find some intermediate bodies to swap through--but then those people might no longer all be in the right bodies, and they would need to find some intermediaries, and so on. Thus, the question arose if, given a group of people who have done assorted swaps, is it always possible, with the help of a finite number of volunteers, to get everyone back to their original body and also leave the volunteers in their original bodies? And if so, how many volunteers do you need?
The Harlem Globetrotters are called in to help, and they prove that any group of swapped people can be restored to their bodies with the help of two volunteers. Their proof of this appears on a blackboard in the episode, and it is fact a correct proof.
Furthermore, not only is it correct, it was a new result, proved by Futurama writer Ken Keeler (who has a PhD in mathematics). This is, as far as anyone as been able to determine, the first and only time that a new theorem has been first published as part of a TV show.
I haven't dug into the proof to deeply, but that does not seem like something that would be that difficult to prove. It seems more like Keeler simply put mathematically correct writing into the show, and that math happens to be something that no one has bothered to formally show. Not to say that it is not an impressive level of detail to put into a cartoon, but the fact that it was first published in the show only shows that it is not a difficult or interesting result.
The Harlem Globetrotters are called in to help, and they prove that any group of swapped people can be restored to their bodies with the help of two volunteers. Their proof of this appears on a blackboard in the episode, and it is fact a correct proof.
Furthermore, not only is it correct, it was a new result, proved by Futurama writer Ken Keeler (who has a PhD in mathematics). This is, as far as anyone as been able to determine, the first and only time that a new theorem has been first published as part of a TV show.
Details, including the theorem and proof, here: http://en.wikipedia.org/wiki/The_Prisoner_of_Benda