In 1919, the legendary British mathematician GH Hardy visited his ailing friend Srinivasa Ramanujan at a hospital in Putney, London. He arrived in a taxi bearing the number 1729, and joked that it seemed “rather a dull” number.

Ramanujan, with a spark of brilliance, countered:

“No, Hardy, it is a very interesting number. It is the smallest number expressible as the sum of two positive cubes in two different ways.”

That offhand remark transformed 1729 from a casual cab number into a monument in number theory—later dubbed the Hardy–Ramanujan number.

TWO CUBES, TWO WAYS

What Ramanujan meant was this:

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

No smaller positive integer can be split into two cubes in two distinct ways.

This unique property placed 1729 at the front of a class of numbers known

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