The number $1729$ has a reputation of its own. The reason is the famous exchange between G. H. Hardy, a famous British mathematician (1877-1947), and Srinivasa Ramanujan , one of India's greatest mathematical geniuses (1887-1920):

In 1917, during one visit to Ramanujan in a hospital (he was ill for much of his last three years), Hardy mentioned that the number of the taxi cab that had brought him was $1729$ which, as numbers go, Hardy thought was ``rather a dull number''. At this, Ramanujan perked up, and said ``No, it is a very interesting number; it is the smallest number expressible as a sum of two cubes in two different ways.''

Indeed: $$1729=1+12^3=9^3+10^3.$$ Moreover, there are other reasons why $1729$ is far from dull. $1729$ is the third Carmichael number. Even more strange, beginning at the $1729$ decimal digit of the transcental number $e$ the next ten successive digits of $e$ are 0719425863. This is the first appearance of all ten digits in a row without repititions.

More generally, the smallest natural number which can be expressed as the sum of $n$ positive cubes is called the $n$ taxicab number. The first taxicab numbers are: $$2=1^3+1^3,\ 1729 =1^3+12^3=9^3+10^3,\ 87539319=167^3+436^3=228^3+423^3=255^3+414^3$$ followed by $6963472309248$ (found by E. Rosenstiel, J.A. Dardis, and C.R. Rosenstiel in 1991) and $48988659276962496$ (found by David Wilson on November 21st, 1997).