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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.

To know more about Srinivasa Ramanujan click here.

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. Vedant Mittal · 3 years, 5 months ago

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

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@Nanayaranaraknas Vahdam Carmichael numbers are also great!! Shivamani Patil · 2 years, 10 months ago

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@Nanayaranaraknas Vahdam yeah you are right Vedant Mittal · 3 years, 5 months ago

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