1. The episode “Möbius Dick” concerns a four dimensional space-whale.
The name is not just a pun on Herman Melville’s novel Moby Dick, but also refers to a one-sided mathematical surface known as a Möbius strip. The episode title is the punch line to the obscure joke: “What’s non-orientable and lives in the ocean?”
2. In “The Honking”, Bender visits a haunted castle and sees the digits 0101100101 written in blood on the wall.
Bender is more confused than spooked, but when he sees the digits reflected in the mirror as 1010011010 he is immediately terrified. No explanation is given in the dialogue, but those capable of translating binary to decimal would have appreciated that this is 666, the number of the beast.
3. The registry number of the Nimbus is BP-1729.
This is a tribute to an Indian genius Srinivasa Ramanujan who observed that 1729 is the smallest number that is the sum of two positive cubes in two different ways. (1729 = 10^3 + 9^3 = 12^3 + 1^3.)
Ramanujan first started thinking about the number 1729 when he was visited by the mathematician G. H. Hardy, who had come to see him in a taxi with this number.
5. And 1,729 is the number of the universe Fry jumps out of in “The Farnsworth Parabox”.
6. 87,539,319 appears as a taxicab number in “Bender’s Big Score”.
It’s the smallest number that is the sum of two positive cubes in three different ways
7. In “Put Your Head on My Shoulders”, just behind Amy-Fry’s right hand are two files marked P and NP.
There’s an unsolved mystery in mathematics known as P v NP. In short, P-problems are easy, and NP-problems are hard. But if someone gives you the answer to an NP-problem then it is easy to check if it is right. So are NP-problems really hard, or is there a short cut that would turn them into P-problems?
8. In the same episode a sign states that Bender’s computer dating agency is both “discreet and discrete”.
Discreet implies that Bender will respect his clients’ privacy. Discrete is used in mathematical circles to describe an area of research that deals with data that does not vary smoothly or continuously. The sign might have been inspired by the joke:
Q: What do you call a mathematician who has lots of romantic
liaisons, but who doesn’t like to talk about it?
A: A discrete data.
9. This sign appears in the episode “Rebirth”.
It says “Studio 1^2 2^1 3^3”, which is equivalent to “Studio 1 × 2 × 27” or “Studio 54”, the famous 1970s New York nightclub.
10. This sign appears in “Parasites Lost”.
Instead of “Historic Route 66”.
11. “The Route of All Evil” shows a Klein bottle, a mathematical oddity that has no definable inside or outside.
Incidentally, its inventor, Felix Klein was born on April 25, 1849, which is 4/25/1849, which is 2^2/5^2/43^2. Each element of the date is the square of a prime number.
12. The Loew’s ℵ0-Plex movie theatre, which first appeared in “Raging Bender”, is reference to ℵ0 (pronounced aleph-null).
Mathematicians have proved that there are different scales of infinity, and ℵ0 is smallest, standard type. ℵ1 is even bigger. Which means Buzz Lightyear’s catchphrase “To infinity and beyond” is meaningful, and the “beyond” probably refers to ℵ1.