Another Matt Groening cartoon TV show (like the Simpsons) that includes many mathematical "in jokes". The website simpsonsmath.com/futuramamath includes discussion of these jokes and the mathematical training of the show's writers. Contributed by
Anonymous
The depth of the mathematical content is quite remarkable  very interesting equations, etc, to explore, although you don't have a category for this. Math or scientific references occur in almost every show, so I'm giving this a 3. I wish you had a category for depth and a separate category for content.

December 2007: Futurama seemed to have died a quiet death when no contract was offered to renew it several years ago. But, fans are now excited to learn that the original cast and crew were reunited for one more blast, producing enough material for a DVD which will also be shown in segments on the Comedy Channel. In addition, the DVD will have an extra feature: a lecture by mathematician Sarah Greenwald. For more information, see this press release from the American Mathematical Society:
Contributed by
AMS Headlines & Deadlines
MATH LECTURE ON NEW "FUTURAMA" DVD
One of the special features on the DVD "Futurama: Bender's Big Score" is
Sarah Greenwald (Appalachian State University) talking about the
mathematical references in the television show "Futurama," which ran on
FOX from 1999 to 2003. The show's writers, who often included
mathematical jokes in the show, have advanced degrees in mathematics,
computer science, and physics. They haven't lost their enthusiasm for
"in" jokes: One scene in the new straighttoDVD film features the
fictional Greenwaldian Theorem. Greenwald's "Futurama" web page is at
http://www.mathsci.appstate.edu/~sjg/futurama/ . At the upcoming Joint
Mathematics Meetings in San Diego, Greenwald and Christopher Goff
(University of the Pacific) are coorganizers of a panel, "Mathematics
and Hollywood," sponsored by the MAA Special Interest Group on
Mathematics and the Arts, which includes Hollywood writers and
mathematics faculty (Sunday afternoon at 2:15). More on the panel is at
http://www.ams.org/amsmtgs/2109_maasess.html#sun .

The Prisoner of Benda: From the point of view of mathematical fiction, the most notable episode of Futurama was "The Prisoner of Benda" (2011). In that episode, a machine which exchanges minds between two bodies is created, and only after it has been used they discover that the machine can only exchange the minds of a given pair of individuals once. In response to Amy's question about whether it will be possible to return to their original bodies, the Professor answers (ominously) "We will have to use....math!" In the middle of the episode there is a reference to a "reverse Turing test" for determining if a being in a human body is actually a robot, but the real mathematics shows up later. Towards the end, two Harlem Globetrotters prove a theorem at the board (a result about permutations) guarantees that there will be a way to restore all individuals to their original bodies provided two additional individuals who have not previously used the machine are available. (The professor makes a comment about pure math finally finding a real application.)
In fact, regular Futurama writer Ken Keeler really proved such a theorem in preparing the episode. (See The Infosphere for more information.) This makes "The Prisoner of Benda" very interesting to me. I know of many works of fiction that include references to a real mathematical result that existed before, and many that include references to imaginary mathematical results created specifically for inclusion in the work of fiction. At the moment, however, I am not aware of any other examples of a real mathematical result created only for inclusion in a work of fiction. (Many thanks to Lauren Tubbs for bringing "The Prisoner of Benda" to my attention.)
2D Blacktop: This episode from season 10 (2013) written by Michael Rowe and directed by Raymie Muzquiz was also mathematically/topologically interesting. Professor Farnsworth invents a device that looks like a tesseract and takes his "hot rod" into the fourth dimension. When he collides with Leela's ship during a drag race on a giant Möbius strip, they end up in a 2dimensional "flatland". In addition to referencing the classic mathematical fiction novel Flatland, they make intriguing observations about life in such a world (e.g. that creatures could not have a digestive tract like animals in our world do, because that would divide them into two unconnected pieces). The Professor uses his device again to return to 3dimensions, passing briefly through an existence of fractional dimensional objects, fractals, before returning them home to New New York.
