User:Charles Matthews/1729 (anecdote)

1729 is known as the Hardy-Ramanujan number, after a famous anecdote of the British mathematician G. H. Hardy regarding a hospital visit to the Indian mathematician Srinivasa Aiyangar Ramanujan. In Hardy's words [1]:

I remember once going to see him when he was lying 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."

In fact

1729 = 1³+12³ = 9³+10³

as both men would have verified mentally; but it is much less obvious that this is the smallest example.

Two things have been observed regarding the anecdote, both of which detract from the surprise element. Firstly, Ramanujan didn't discover the taxicab property on-the-spot; it has been found in one of his notebooks dated years before the incident. Secondly, Hardy possibly knew it as well, and pretended not to only to cheer up the ailing Ramanujan. Indeed, such behaviour would have been in keeping with Hardy's self-deprecating character.

Quote

"Every positive integer is one of Ramanujan's personal friends" -- J. E. Littlewood, on hearing of the taxicab incident.

External links

• Mathworld: Hardy-Ramanujan number
• Mathworld: Taxicab number

See also

• Interesting and uninteresting numbers
• 1729 (number)