1729 is known as the Hardy-Ramanujan Number. Godfrey Hardy was a professor of Mathematics at Cambridge university. Once he decided to visit his friend’s place, the brilliant Indian Mathematician Srinivasa Ramanujan , when he was ill.
When hardy came he tell Ramanujan he had come in a taxi. Then he asked him what the number of the taxi was. Hardy said it was just a boring number 1729.
But Ramanujan explained him 1729 is not a boring number: – It is very interesting number because it was the smallest number that could be expressed by the sum of the two cubes in two different ways.
There are two ways to say that 1729 is the sum of two cubes.
1x1x1=1; 12x12x12=1728. So 1+1728=1729 but also: 9x9x9=729; 10x10x10=1000. So 729+1000=1729 there are other numbers that can be shown to be the sum of two cubes in more than one way, but 1729 is the smallest of them.
Ramanujan was not the one who discovered this fact. It was known in 1657 by a French mathematician Bernard Frenicle de Bessy.
But it is got famous by the conversation between Ramanujan and Hardy and famously named as Ramanujan Number.