Why the number 1729 shows up in so many Futurama episodes

It seems like such an ordinary number – so why does it show up so frequently?

Why the number 1729 shows up in so many Futurama episodes
1729 TaxiCab number via MathWorld.

In the episode "Xmas Story," Bender receives a card designating him "Son #1729;" but the number shows up in other places, as well. The registration number on the hull of the starship Nimbus, for example, is BP-1729. In "The Farnsworth Parabox," which involves the members of Planet Express slipping in and out of alternate universes, one of the universes visited is Universe 1729:

Why the number 1729 shows up in so many Futurama episodes

But so then what's the significance behind this seemingly insignificant number? (Fun fact: There's actually no such thing as an uninteresting natural number.) The answer can be traced to a conversation, now famous among numberphiles, that occurred between mathematicians G.H. Hardy and Srinivisa Ramanujan in 1918.

In a BBC News article that explores Hardy and Ramanujan's unlikely friendship and its ties to Futurama's frequent references to 1729, science writer Simon Singh recounts a time when Hardy visited Ramanujan at the nursing home where he lay ill. "I had ridden in taxi cab number 1729 and remarked that the number seemed to me rather a dull one, and that I hoped it was not an unfavorable omen" Hardy later recalled. Ramanujan is said to have countered: "No, it is a very interesting number. It is the smallest number expressible as the sum of two cubes in two different ways."

Ramanujan's point can be expressed mathematically as follows:

1729 = 1³ + 12³ = 9³ + 10³

Why the number 1729 shows up in so many Futurama episodes

1729 has since become known as the Hardy-Ramanujan number. The story behind it is also why the smallest numbers that can be expressed as the sum of two cubes in one or more distinct ways are called "taxicab numbers" – hence the number on the cab pictured here, which makes an appearance in Bender's Big Score (above, the literal taxicab number 87539319 is the smallest number that can be written as the sum of two cubes in three different ways, viz. 87,539,319 = 1673+4363 = 2283+4233 = 2553+4143).

Science jokes, mathematical theorems and other nerdy allusions are, of course, warp and woof of Futurama's style, due in no small part to its team of eminently geeky writers, including J. Stewart Burns, who holds a master's degree in maths from UC Berkeley; Bill Odenkirk, a PhD from U. Chicago in chemistry; Jeff Westbrook, who holds a PhD in computer science from Princeton; Ken Keeler, who earned his PhD in maths at Harvard); and of course head writer David X. Cohen, who majored in applied maths at Harvard and went on to earn a master's in computer science at UC Berkeley.

Why the number 1729 shows up in so many Futurama episodes
Above: A screenshot from The Prisoner of Benda, featuring a novel theorem that Keeler devised and solved for the express purpose of explaining a plot twist in the episode.

Keeler, for his part, makes a direct reference to the Hardy-Ramanujan number in an interview with GotFuturama.

"Well, sure," he replied, when asked whether all his years of education had been worth it. "For example, Bender's serial number is 1729, a historically significant integer to mathematicians everywhere; that 'joke' alone is worth six years of grad school, I'd say." In another interview with mathematician Sarah Greenwald, Keeler explains in greater detail:

We needed a number for plot reasons, and David Cohen asked if I could think of an interesting one, and the Hardy-Ramanujan sum-of-two-cubes story leapt to mind. Afterwards David [X. Cohen] sort of went to town with the idea whenever we needed a serial number.

In the same Greenwald interview, Keeler expands on the idea that pursuing a terminal degree in mathematics can make you a better writer:

Mathematical training makes you good at following logical structure, and I think that's a plus in any field. In writing, it helps you to see the steps you need to lay out to make a story hang together. I also think studying hard math problems teaches you how to just disconnect from your current approach sometimes and force yourself to come up with a radically new one. This is kind of an effective method of coming up with jokes when you're stuck; I guess maybe it helps you achieve the element of surprise. And the way a mathematician will exhaustively explore the consequences of an assumption or a result is kind of similar to the way multipart jokes are occasionally built up; you've started down a road and you want to see how far it'll take you.

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