Ramanujan was an essentially self-trained Indian mathematician who made substantial and lasting contributions to mathematics. Unfortunatly, he did not seem to prosper well when transplanted to the Enlish climate and died early. One of those great math stories is told by Godfrey H. Hardy (1877-1947) in the book Ramanujan, (London: Cambridge Univesity Press, 1940).
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 Taxicab numbers to any numbers which can be expressed as the sum of two cubes in N different ways. The first few examples are here
T(1) = 2 because 13 + 13 = 2
T(2) = 1729 because 13+123 = 93+103= 1729
T(3) = (discovered in 1957) 87,539,319 = 1673+ 4363
------------------= 2553+ 4143
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 squares in n different ways.