»In which we stop to admire a Taxicab

Once, in the taxi from London [to Putney], Hardy noticed its number, 1729. He must have thought about it a little because he entered the room where Ramanujan lay in bed and, with scarcely a hello, blurted out his disappointment with it. It was, he declared, "rather a dull number," adding that he hoped that wasn't a bad omen.

"No, Hardy," said Ramanujan. "It is a very interesting number. It is the smallest number expressible as the sum of two [positive] cubes in two different ways."

The Taxicab problem is well-documented, including two entries in the On-Line Encyclopedia of Integer Sequences: A011541 and A047696.

To many mathematicians, the mere mention of the number 1729 recalls the incident involving mathematicians G.H. Hardy and Srinivasa Ramanujan; thus, to commemorate the Hardy-Ramunujan conversation, the least number which is the sum of two positive cubes in n different ways is called the nth taxicab number: For any n >= 1, there indeed exist numbers which are the sum of two positive cubes in n ways, which guarantees the existence of Taxicab(n) for n >= 1. A corollary: Cabtaxi(n) the smallest positive integer which can be written as the sum of two positive or negative cubes in n ways.