Before his return to India, Srinivasa Ramanujan was lying on the hospital bed of Colinette House, a few miles southwest of London. Hardy came to visit Ramanujam by a taxi-cab, the number of which happened to be 1729.Enquiring after the latter's health, Hardy blurted out that 1729 was rather a dull number, adding that he hoped that wasn't a bad omen.
"No Hardy," said Ramanujan instantly. "It is a very interesting number. It is the smallest number expressible as the sum of 2 cubes in 2 different ways: 12 cubed+1 cubed as well as 10 cubed+9 cubed.
Finding numbers that are the sum of one pair of cubes is easy. For instance, 2 cubed+3 cubed=35. But can we get to 35 by adding some other pair of cubes? We can't. As we try the integers one by one, it is the same story. One pair is easy, two pairs never--never, that is, until we reached 1729.
Hardy was astounded at the lightening insight of Ramanujan's razor-sharp brain even during the worst of his debilitating health and in the face of his imminent death
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