I’m supposed to explain this to a person. Please tell me in a simple way as simple as possible.
In: Mathematics
It’s the smallest number that can be written as a sum of two cubes in two different ways:
* 1^(3)+12^(3) = 1729 = 9^(3)+10^(3)
A similar number for squares is 65: It is the smallest number that can be written as a sum of distinct squares in two different ways:
* 1^(2) + 8^(2) = 65 = 7^(2) + 4^(2)
Ramanujan was interested in it because it pops up as a “near miss” for a counterexample to Fermat’s Last Theorem. Fermat’s Last Theorem says that there is no integer solution to x^(n)+y^(n)=z^(n) when n is bigger than 2. 1729 is *almost* gives a solution since it says that
* 9^(3) + 10^(3) = 12^(3) (+1)
So its a “near miss”. Ramanujan found a way to find infinitely many such numbers.
> 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.”
https://en.wikipedia.org/wiki/1729_(number)
The significance is that Ramanujan had been exploring numbers so long and in such depth that he could come up with this oddball bit of trivia off the top of his head.
*I’*d be left saying, well, it’s one off from 1728 (which *is* one of the ways you get the sum of two cubes).
Latest Answers