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1729 is the Hardy-Ramanujan number, known to be the second #taxicab number.

The nth taxicab number, denoted by Ta(n), is the smallest #number representable in n different ways as the sum of positive cubes.

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1729 is known as the Hardy-Ramanujan #number in consequence of a famous anecdote dating back to when the English mathematician G.H. Hardy visited the Putney hospital, where his friend and collaborator #Ramanujan was hospitalized.

#history
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“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”- #Ramanujan replied- "it is a very interesting number;

#maths

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" it is the smallest number expressible as the sum of two cubes in two different ways.” — G.H. Hardy (1918)

Image: #Ramanujan’s manuscript, Trinity College library. The 2 representations of 1729, as the sum of 2 cubes, appear in the bottom right corner.

#History
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So far, six #taxicab #numbers are known.

They are those represented in the image.

(Tap on the image)

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