Post by dividavi on Feb 21, 2020 20:07:02 GMT
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."
The two different ways are:
1729 = 1^3 + 12^3 = 9^3 + 10^3
That was a great discovery but I admire Ramanujan even more for his practice of expressing mathematical truths through poetry instead of standard notations.
The truth Ramanujan revealed to Hardy is my second favorite equation. Numero uno in my book is this masterpiece:
π^4 + π^5 ≈ e^6 , about 403 if I recall correctly.
Here's something else about the number 1729 I didn't know:
Masahiko Fujiwara (same wikipedia article as above) showed that 1729 is one of four positive integers (with the others being 81, 1458, and the trivial case 1) 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