1729

1729 is the smallest number that can be expressed as the sum of two positive cubes in 2 different ways.

1729 = 1^3 + 12^3

1729 = 9^3 + 10^3



A famous anecdote of the British mathematician G. H. Hardy regarding a visit to the hospital to see the Indian mathematician Srinivasa Ramanujan. In Hardy's words:

“

I remember once going to see him when he was ill at Putney. 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. "No," he replied, "it is a very interesting number; it is the smallest number expressible as the sum of two cubes in two different ways."

Ever since then, the lowesat number that can be expressed as the sum of 2 positive cubes in n different ways is called a "taxicab number"  1729 is Taxicab(2) because n is 2.


This property of the number is discussed in the play and in the movie "Proof".


The 2007 play A Disappearing Number by the Théâtre de Complicité company references the number. One of the main characters, Ruth, is a mathematician and 1729 are the last four digits of her phone number, paying homage to two of her heroes: Ramanujan and Hardy.

In the Futurerama movie, "Bender's Big Score", the number of the taxi cab Fry takes home in the past (87539319) is the smallest number expressible as the sum of two cubes in three different ways.