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# Hardy–Ramanujan number

Srinivasa Ramanujan (22 December 1887 – 26 April 1920) was an Indian mathematician and autodidact.

1729 is the natural number following 1728 and preceding 1730. 1729 is known as the Hardy–Ramanujan number after a famous anecdote of the British mathematician G. H. Hardy regarding a visit to the hospital to see the Indian mathematician Srinivasa Ramanujan. 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. (instantly)"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." The two different ways are these:

$$1729 = 1^{3} + 12^{3} = 9^{3} + 10^{3}$$

With almost no formal training in pure mathematics, made extraordinary contributions to mathematical analysis, number theory, infinite series, and continued fractions, Ramanujan developed his own mathematical research in isolation. As a result, he rediscovered known theorems in addition to producing new work. Ramanujan was said to be a natural genius by the English mathematician G. H. Hardy, in the same league as mathematicians such as Euler and Gauss.

Note by Vedant Mittal
3 years, 5 months ago

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After reading about Ramanujan, I have become a fan of him. He was truly a genius. · 3 years, 5 months ago

In fact, 1729 is also special because it is the third Carmichael number, which can disprove Fermat's Little Theorem · 3 years, 5 months ago

Carmichael numbers are also great!! · 2 years, 10 months ago