1729 (number)

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

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.

Table of contents

1 Interesting and Uninteresting Numbers
2 See also
3 External links
4 References

Interesting and Uninteresting Numbers

A tongue-in-cheek proof by contradiction exists showing that all numbers are "interesting." 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, and thus excluding it from the list. Therefore, all numbers must be interesting.

External links

Mathworld: Hardy-Ramanujan number
Mathworld: Taxicab number

References

The Dullness of 1729

Martin Gardner, Mathematical Puzzles and Diversions, 1959