When your TV show's writing staff includes folks with PhDs in maths and sciences, you're bound to end up with some spectacularly nerdy jokes. And if you dig a little deeper into some of the jokes in Futurama, you won't just laugh — you may actually learn something.

The Futurama writers had a rule that the show's more obscure jokes couldn't be central to the plot. So the background is stuffed with nods to mathematics, science, history, and literature. Numbers are often translated into math problems (instead of Studio 54, the crew visits Studio 1²2¹3³). Robot information is conveyed in binary ("The Honking" references the "Redrum" scene in The Shining, when Bender is perplexed to see "0101100101" written in blood on a wall, but then realizes that it reads "1010011010" in the mirror, a series of digits that translates to "666"). And of course, there's the Alienese language. But the writers also built entire episodes around the Banach-Tarski paradox and the premise of three-dimensional characters entering two-dimensional space.

Some of Futurama's smaller jokes require a bit more context to understand, and if you're not already familiar with the mathematic and scientific principles or historical context needed to get the joke, learning a bit more about them can be fascinating and quite rewarding. Here are just a handful of those jokes.

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1. "No fair! You changed the outcome by measuring it!"

In "Luck of the Fryrish," the Planet Express crew goes to the racetrack, where two horses finish a race neck and neck. In order to determine the outcome of the race, the officials use an electron microscope and announce Number 3 is winner in a "quantum finish." The Professor, incensed, shouts, "No fair! You changed the outcome by measuring it." There's a reason this joke is a classic.

The Professor is referencing the observer effect, the impact of observation on the phenomenon being observed. In quantum mechanics, when we measure the state of a quantum system, we know its current state and stop it from being in any of its other possible states. Of course, it's rather bad business for a racetrack to have its winner be a superposition of two different horses at the same time. The Futurama writers also love to reference the famous thought experiment about observation and quantum mechanics, Schrödinger's cat.

2. "What happens in Cygnus X-1 stays in Cygnus X-1"

The opening tagline for "Prisoner of Benda" is obviously a reference to the slogan "What happens in Vegas stays in Vegas." But Vegas has nothing on Cygnus X-1, which is a black hole candidate. No way your photos are getting out of there and ending up on Facebook.

Adding another layer to the joke is the fact that Cygnus X-1 was itself the subject of a wager. In 1975, Stephen Hawking bet fellow physicist Kip Thorne that Cygnus X-1 would not ultimately prove to be a black hole. Eventually, Hawking conceded the bet, and Thorne allegedly won a one-year subscription to Penthouse as his prize.

This isn't even close to the coolest scientific aspect of this episode. After all, writer Ken Keeler, who holds a PhD in applied mathematics, developed a mathematical proof to resolve the episode's core conflict.

3. Loew's ℵ0-Plex

What comes after the multiplex? New New York's premiere movie theater (which shows up in a couple of episodes) is and aleph-nullplex. ℵ0 is the cardinality (measure of elements in a set) of all natural numbers, and therefore describes sets that are countably infinite. We suspect that, even in the year 3000, it's a slight exaggeration for the movie theater to claim it has an infinite number of screens — even if it's a small number of infinity.

The ℵ0-plex was the brainchild of none other than Keeler, who joked in a draft of the "Raging Bender" script that it still wouldn't be big enough to show all the Rocky movies.

In his book The Simpsons and Their Mathematical Secrets, Simon Singh notes that Futurama also references a much larger infinity. In "Möbius Dick," Bender ends up in a four-dimensional space with many copies of himself doing a conga line and later quips, "That was the greatest uncountably infinite bunch of guys I ever met."

4. Happy ln(bΩer)

This is a pun that requires some knowledge of mathematical symbols, scientific symbols, and Jewish holidays. The "ln" refers to a natural logarithm, and the omega is the symbol for ohm, the SI derived unit of electrical resistance. So the sign reads "Happy Logbohmer" or, rather, "Happy Lag BaOmer." Lag BaOmer is a holiday celebrated on the 33rd day of the Counting of Omer, when the mourning of the Counting of Omer is lifted, so the date of Bender's son Ben's Bot-Mitzvah in "The Bots and the Bees" is an auspicious one.

[Hat tip to r/futurama]

5. Taxicab Numbers

Eagle-eyed Futurama viewers may notice that the number 1729 shows up an awful lot in the show. It's part of the Nimbus's registration number. Bender is Mom's son #1729. During "The Farnsworth Parabox," the crew visits Universe 1729.

So what's the deal? 1729 is the Hardy–Ramanujan number, also known as a taxicab number. G.H. Hardy and Srinivisa Ramanujan were mathematicians and unlikely friends. According to Hardy, their interest in 1729 came about when Hardy visited Ramanujan and remarked that he had ridden in a cab numbered 1729. It struck Hardy as a rather dull number, and he worried that it was an ill omen. Ramanujan replied that it was actually quite an interesting number; after all, it's the smallest number that can be expressed as the sum of two positive algebraic cubes in two distinct ways: 1729 = 13 + 123 = 93 + 103

A taxicab number has since been defined as the smallest number that can be expressed as the sum of two positive algebraic cubes in n different ways. For the most part, the number 1729 is used merely as a nod to Hardy and Ramanujan, but in "Bender's Big Score," the taxicab number 87539319 shows up, amusingly enough, on a taxicab. 87539319 is the smallest number that can be written as the sum of two cubes in three distinct ways: 87,539,319 = 1673+4363 = 2283+4233 = 2553+4143

6. Mars University Physics Annex

This is a sight gag that confuses some viewers at first glance. After all, the Mars University Physics Department and the Annex clearly have different masses, but they appear balanced on the lever. But we have to consider the mechanical advantage of the lever. The fulcrum is considerably closer to the main building than the annex, so in order to balance the lever, the force that the annex exerts on the lever must be less than the force that the main building exerts on the lever.

A balanced lever can be expressed with the equation (M1)(a) = (M2)(b), where M1 is the mass at one end of the fulcrum, M2 is the mass at the other end of the fulcrum, a is the distance from the fulcrum to M1, and b is the distance from the fulcrum to M2. Of course, this all goes to hell when Nibbler's ship lands outside the main building.

7. All Those Beers

In the episode "The Route of All Evil," Bender, Fry, and Leela all head to the, ahem, 711 to buy beer. All of the beers are punny — Pabst Blue Robot, Lobrau — but some of them are particularly geeky:

We get a reference to the programming language FORTRAN, which was developed by IBM in the 1950s. Bender drinks it in lieu of Olde English 800, so of course it has a computer language in the name instead of a human one.

The Klein bottles are a non-orientable object, much like a Möbius strip. Its surface is one continuous "side," so you want to watch how you pour that beer.

St. Pauli Girl beer gets mashed up with the Pauli exclusion principle, named for Wolfgang Pauli. The principle states that two identical fermions can't occupy the same quantum state simultaneously. We have no idea how that affects the taste of the beer.

8. Bull Space Moose Party

Not all of Futurama's jokes reference math and science. Some are about history and politics. In "A Head in the Polls," Fry checks out different political parties, and in true Futurama form, the most obscure jokes are lurking in the background. A booth that appears to be manned by Bullwinkle bears the banner "Bully Space Moose Party," a reference to the Progressive Party of 1912. The party was formed by former US President Theodore Roosevelt after he had a falling out with fellow Republican President William Howard Taft. The third party was called the Bull Moose Party because a journalist quoted Roosevelt as saying "I'm feeling like a bull moose." Naturally, though, Fry finds himself drawn to the Apathy Party.

9. Witten's Dog

You may have heard of Schrödinger's cat, but Witten's Dog is entirely an invention of Futurama. It, paired with the phrase "Superdupersymmetric String Theory," is a nod to Ed Witten, one of the fathers of superstring theory and one of the world's greatest living theoretical physicists. In the commentary for this episode, "Mars University," it's explained that a Caltech physicist drew this parody diagram, which is, at its heart, just a classy poop joke.

10. The Cryptic Crypt Inscription

In "The Duh-Vinci Code," the crew flies to Rome to explore the tomb of Saint James and comes across an inscription in Roman numerals that is clearly not a date, but rather part of an equation. In his book, Singh notes that there's nothing random about this particular set of numbers, and that solving the problem gives a very interesting result.

IIXI - (XXIII * LXXXIX) translates to 211 - (23 * 89), which equals one. If we rearrange the equation 211 - (23 * 89) = 1, we get 211 - 1 = 2047. This equation takes the form of a Mersenne prime, in which a prime number is found though 2p - 1, where p is any prime number. The interesting thing about 2047 is that it's not prime. In fact, it's the smallest number described by 2p - 1 that isn't prime.