MesMath

HARDY-RAMANUJAN NUMBER
    1729 is the natural number following 1728 and preceding 1730. 1729 is known as the Hardy–Ramanujan number , named after the British mathematician G.H.Hardy and Srinivasa Ramanujan.
  Now, a little about these great mathematicians:

1) SRINIVASA RAMANUJAN
  Ramanujan was said to be a natural genius by the English mathematician G.H. Hardy, in the same league as mathematicians like Euler and Gauss.During his short lifetime, Ramanujan independently compiled nearly 3900 results. However, the mathematical mainstream has been rather slow in absorbing some of his major discoveries.In Dec 2011, in recognition of his contribution to mathematics, the Government of India declared that Ramanujan's birthday (22 December) should be celebrated every year as National Mathematics Day, and also declared 2012 the National year of mathematics.

2) G.H.HARDY
   Godfrey Harold "G. H." Hardy is usually known by those outside the field of mathematics for his essay from 1940 on the aesthetics of mathematics, A Mathematician's Apology, which is often considered one of the best insights into the mind of a working mathematician written for the layman. When Hardy was asked what his greatest contribution to mathematics was, Hardy unhesitatingly replied that it was the discovery of Ramanujan-it was in an interview by Paul Erdős.

HARDY-RAMANJUAN NUMBER
          It is a very interesting number; it is the smallest number expressible as the sum of two cubes in two different ways.
The two different ways are these:
1729 = 13 + 123 = 93 + 103
In Hardy's words:“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 unfavorable 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."”
Numbers that are the smallest number that can be expressed as the sum of two cubes in "n" distinct ways have been dubbed "taxicab numbers".
    The same expression defines 1729 as the first in the sequence of "Fermat near misses" defined as numbers of the form 1 + z3 which are also expressible as the sum of two other cubes . 1729 has another mildly interesting property: the 1729th decimal place is the beginning of the first occurrence of all ten digits consecutively in the decimal representation of the transcendental number.
Masahiko Fujiwara showed that 1729 is one of four positive integers which, when its digits are added together, produces a sum which, when multiplied by its reversal, yields the original number:
1 + 7 + 2 + 9 = 19
19 × 91 = 1729