Futurama - Hidden Math Gems

Many of my students love watching certain cartoons such as The Simpsons or Futurama.  I know there is lots of wonderful math in The Simpsons but what about Futurama?  What math does it have shared in the 14 years it was on television?

There are lots of math jokes running through the show.  In fact almost every episode has a math reference, some are only known to mathematicians.  Three of the show's writers have PhD's including Ken Keeler who has one in applied mathematics.

Let's look at some of those jokes sprinkled through the series.  Some are puns and some are out right jokes.  So lets take a look at some of the wonderful references.

1.  "What's non-orientatable and lives in the ocean?"  A Mobius Dick of course referring to a four dimensional whale based on a Mobius Strip. 

2. In another episode, one of the characters sees 1010011010 written in blood on a mirror in a haunted castle.  Most people do not read binary but if you did, you would know the number is actually 666 associated with the beast.

3. One of the space ships has the registry number of BP-1729.  1729 is the smallest sum from two different positive cubes combined in two different ways.  The same number is assigned to a unit of soldiers.  Furthermore, it is assigned to the universe in Farnsworth Paradox. 

4.  A taxi cab has the number 87,539,319 which is the smallest number made from three positive cubes combined in three different ways.

5. In another episode, the artists snuck P vs NP on two books found in a bookcase of books.  P problems are easy to solve, NP are not but answers to NP problems can be checked.

6. How about a dating agency that advertises that is is both discreet and discrete.  Remember discreet refers to protecting client identities while discrete refers to data that does not vary smoothly or continuously.

7. Then there is the episode with the club "1^2   2^1    3^3 which is a play on Club 54, a very famous night club.

8. One of the writers ended up proving a theorem from the episode where the brains of two people were switched in "Prisoner of Brenda" but cannot be switched back.  The theorem known as Keeler's Theorem proved that no matter how mixed up people's brains are, all you need to do is bring in two new brains and everyone can get their own brain back.

9.  The local theater is Loews  ℵ0 plex with an infinite number of screens.  Alepha naught or ℵ0 refers to the different sizes of infinite sets which change based on the scale.  Since ℵ0 is the smallest cardinal number for the set, every one has an ℵ0.  

10. In an episode with a horse race, the track uses a quantum finish to determine the winner but all that means is when they measure results, the results are changed because its based on the observer. 

There are other references to Banach Tarski theoretical paradox, a beer called Klein's with an odd-shaped bottle based on Klein's bottle, and other unique things.  There are lots of fun references, many of which are only understood by math people straight off but knowing this, one can play clips from the show and then brig the math into the classroom this way.

Let me know what you think, I'd love to hear.  Have a great day.