Why is 1729 known as Ramanujan's number?



The number 1729 is known as the Hardy-Ramanujan number after Cambridge Professor Hardy visited Indian mathematician Srinivasa Ramanujan at a hospital. As Hardy called his taxi number 1729 "dull", Ramanujan exclaimed it was "the smallest number expressible as the sum of two cubes in two different ways," as the sum of cubes of 1 & 12 and also 10& 9.

The smallest nontrivial taxicab number, i.e., the smallest number re-presentable in two ways as a sum of two cubes. It is given by

1729=1^3+12^3=9^3+10^3

The number derives its name from the following story G. H. Hardy told about Ramanujan. "Once, in the taxi from London, Hardy noticed its number, 1729. He must have thought about it a little because he entered the room where Ramanujan lay in bed and, with scarcely a hello, blurted out his disappointment with it. It was, he declared, 'rather a dull number,' adding that he hoped that wasn't a bad omen. 'No, Hardy,' said Ramanujan, 'it is a very interesting number. It is the smallest number expressible as the sum of two [positive] cubes in two different ways' ".

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