What is special about the number 1729?
The number 1729 is known as the Hardy���Ramanujan number after a famous visit by Hardy to see Ramanujan at a hospital. 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."
 
 Immediately before this anecdote, Hardy quoted Littlewood as saying, "Every positive integer was one of [Ramanujan's] personal friends."
 
 The two different ways are:
 
 1729
 =
 1
 3
 +
 12
 3
 =
 9
 3
 +
 10
 3
 .
 {\displaystyle 1729=1^{3}+12^{3}=9^{3}+10^{3}.}
 Generalisations of this idea have created the notion of "taxicab numbers".
1729, known as the Hardy���Ramanujan number, is the smallest integer that can be expressed as the sum of the cubes of two unique pairs of integers.