Hardy-Ramanujan number 1729 is the natural number following 1728 and preceding 1730. It is a taxicab number, and is variously known as Ramanujan's number and the Ramanujan-Hardy number, after an anecdote of the British mathematician G. H. Hardy when he visited Indian mathematician Srinivasa Ramanujan in hospital. He related their conversation: I remember once going to see him when he was 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 unfavourable 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."

1. Hardy-
Ramanujan
Number

2. Srinivasa Ramanujan

3. THE SMALLEST NONTRIVIAL TAXICAB NUMBER,
I.E., THE SMALLEST NUMBER REPRESENTABLE IN TWO
WAYS AS A SUM OF TWO CUBES. IT IS GIVEN BY
1729 = 103 + 93 = 123 + 13

4. HISTORY
THE NUMBER DERIVES ITS NAME FROM THE FOLLOWING STORY G. H. HARDY
TOLD ABOUT RAMANUJAN. "ONCE, IN THE TAXI FROM LONDON, 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' "

5. Taxicab Number

6. • IN MATHEMATICS, THE NTH TAXICAB NUMBER, TYPICALLY DENOTED
TA(N) OR TAXICAB(N), ALSO CALLED THE NTH HARDY–RAMANUJAN
NUMBER, IS DEFINED AS THE SMALLEST INTEGER THAT CAN BE
EXPRESSED AS A SUM OF TWO POSITIVE INTEGER CUBES IN N DISTINCT
WAYS. THE MOST FAMOUS TAXICAB NUMBER IS 1729 = TA(2) = 13 +
123 = 93 + 103.
• THE NAME IS DERIVED FROM A CONVERSATION IN ABOUT 1919
INVOLVING MATHEMATICIANS G. H. HARDY AND SRINIVASA
RAMANUJAN.

7. Known Taxicab Numbers