Historical Note on $1729$ (One Thousand, Seven Hundred and Twenty-Nine)
In the opinion of some writers, "among the most famous of all numbers".
He reports the incident thus:
- [ Ramanujan ] could remember the idiosyncrasies of numbers in an almost uncanny way. It was Littlewood who said that every positive integer was one of Ramanujan's personal friends. I remember going to see him once when he was lying ill in Putney. I had ridden in a taxi-cab No. $1729$, and remarked that the number seemed to me a rather dull one, and that I hoped it was not an unfavourable omen. 'No,' he reflected, 'it is a very interesting number; it is the smallest number expressible as the sum of two cubes in two different ways.'
- $1729 = 12^3 + 1^3 = 10^3 + 9^3$
Because of this, $1729$ is often seen referred to as a taxicab number (sometimes hyphenated: taxi-cab).
In fact it is $635 \, 318 \, 657$.
This property of $1729$ appears occasionally in mainstream entertainment either as a subject of mathematics as discussed by supposed mathematicians, or (in more subtle fare) as a mathematical in-joke.
- 1986: David Wells: Curious and Interesting Numbers ... (previous) ... (next): $1729$
- 1997: David Wells: Curious and Interesting Numbers (2nd ed.) ... (previous) ... (next): $1729$