The episode “The Prisoner of Benda” revolves around a mind-switching machine invented by Professor Farnsworth so that characters within their episode can live out their fantasies by taking on the physical identity of another. One unfortunate side effect of the experiment is that the machine can’t be used to reverse the effect on the same two people.
For this episode, writer Ken Keeler, who also has a doctorate from Harvard University in applied mathematics, devised a proof, which appears on a holographic blackboard during the episode, to set things right and put each character back into their original bodies.
The proof works by restoring each character’s mind to the original body provided that two additional people who have not previously had their identities switched to assist with the process.
Although Keeler himself refers to his equation as a proof, it has since become known as the “Futurama Theorem.” (Click here for a full description of how the theorem works.)
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