I remember once going to see him when he was lying 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."From this incident, recreational mathematicians have given the name

T(1) = 2 because 1

T(2) = 1729 because 1

T(3) = (

------------------= 228

------------------= 255

and for more see this Mathworld site.

An article by Ivars Peterson points out that "The first published reference to this property of the integer 1729 is in the writings of 17th-century French mathematician Bernard Frénicle de Bessy (1605–1670). "

He also provided "...For example, you can ask, as Hardy did of Ramanujan, for the smallest number that is a sum of two fourth powers in two ways. Ramanujan couldn't provide an immediate answer, but it was known to Leonhard Euler (1707–1783): 635318657 = 594 + 1584 = 1334 + 1344. ."

Students might want to try to find the equivalent "kiddie-car" numbers; the smallest numbers that can be expressed as the sum of two