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