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One thousand seven hundred and twenty nine

1729 is a number 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.

During one visit to Ramanujan in the hospital at Putney, Hardy mentioned that the number of the taxi cab that had brought him was 1729, which, as numbers go, Hardy thought was "rather a dull one", and that this was a bad omen. At this, Ramanujan perked up, and said "No, it is a very interesting number; it is the smallest number expressible as a sum of two cubes in two different ways."

Owing to this, numbers such as 1729 = 13+123 = 93+103 which can be expressed as the sum of cubes in distinct ways have been dubbed Taxicab Numbers.

The issue of classifying numbers as "dull" and "interesting" leads to an interesting paradox (strictly speaking, an antinomy). In a classification of numbers as to whether they had interesting properties or not, there would be a smallest number with no interesting properties (for instance, 38 could be a candidate). This in itself would be an interesting property of the number, making it interesting, thus excluding it from the list. Closely related paradoxes/antinomies are the Berry paradox and the Liar paradox.

This article is about the number 1729. For the year AD 1729, see 1729.

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