Srinivasa Ramanujan was an Indian mathematician and autodidact who, with almost no formal training in pure mathematics, made extraordinary contributions to mathematical analysis, number theory, infinite series, and continued fractions. On the 125th anniversary of his birth, India declared the birthday of Ramanujan, 22 December, as ‘National Mathematics Day.’
The number 1729 is known as the Hardy–Ramanujan number after a famous anecdote of the British mathematician G. H. Hardy regarding a visit to the hospital to see Ramanujan. In Hardy’s words:
“I remember once going to see him when he was 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.’ ”
The two different ways are
1729 = 13 + 123 = 93 + 103.
Generalizations of this idea have created the notion of “taxicab numbers”. Coincidentally, 1729 is also a Carmichael number.