The great mathematician Srinivasa Ramanujan would have been 125 today, 22 December. Mathematicians all over India—and indeed the world—are celebrating his life.
This story: he (Ramanujan) was in hospital in Putney, England. In walked G.H. Hardy, his mentor and a fine mathematician in his own right. He told Ramanujan that he had come in a cab whose number, 1729, “seemed to me rather a dull one.” (I get the feeling Hardy and Ramanujan rather liked playing around with numbers.)
The sick Ramanujan disagreed. “Oh no, not at all!” he said. “It is the smallest number that can be written as the sum of two cubes in two different ways!”
Of course he was right. Here are the two ways:
1³ + 12³ = 1 + 1,728 = 1,729
9³ + 10³ = 729 + 1,000 = 1,729
And 1,729 is indeed the smallest such number. And because of this incident, it is now known as the Ramanujan-Hardy number.
What touches me about this story is though Ramanujan was seriously ill that day, he was sharp enough to remember, and tell Hardy, this little nugget about a random number Hardy mentioned.
It was unfortunate that even the medical practitioners of England couldn’t save Ramanujan. He returned and breathed his last in his own motherland.
Ramanujan had not followed the traditional way of researches. I don’t know if there are any Ramanujan in India, but unfortunately there are no Hardys also in present time.