Indian mathematician Srinivasa Ramanujan went to England at the invitation of British mathematician G.H.Hardy. When Ramanujan fell ill, Hardy went to see him at a hospital riding a taxi. He said to Ramanujan that the cab number 1729 seemed rather dull and hoped that it was not a bad omen. To which Ramanujan replied immediately that it is a very interesting number – "The smallest number expressible as the sum of two cubes in two (positive) different ways".

i.e., 1729 = 1³ + 12³ and also 9³ + 10³.

1729 came to be known as Hardy-Ramanujan number

or as taxicab number.

Two other such numbers are:

4104 (2³ + 16³ and 9³ + 15³)

13,832 (18³ + 20³ and 2³ + 24³)

Considering negative cubes, 91 is the smallest such number.

91 = 6³ + (-5)³ and 4³ + 3³.

1729 is also one of the three positive integers (other two being 81 and 1458) which, when its digits are added together, produces a sum which, when multiplied by its reversal, results in the original number.

1729: 1 + 7 + 2 + 9 = 19

19 reversed is 91.

19 × 91 = 1729!