I wish I was special

March 24, 2010

There’s a great story in the beautiful, tragic, triumphant story of Ramanujan. Ramanujan emerged from India in the early 1900s (out of nowhere as far as Western mathematicians were concerned), and quickly emerged as the greatest natural mathematician of all time. He teemed up with Hardy and produced incredibly novel results. I have heard it said that he had a personal relationship with every number less than 10,000. Think about that. A personal relationship. These were his friends. And he needed them… he was out of place in England, sick in its winters, stranger to its customs. He died young, at the age of 32.

The classic story is that Hardy visited Ramanujan in the hospital during one of his bouts of illness, and remarked, making conversation, that he had taken a taxicab with a very boring number to get there. The number was 1729. Ramanujan responded, “No, Hardy! No, Hardy! 1729 is the first number that can be written as the sum of cubes in two different ways.”

What’s truly impressive about this, when you stop to think about it, is not that he knew that 1729 had this property… it’s that little word ‘first.’ No number below it has that property, and Ramanujan knew that. He had already checked them all. Or he just knew, the way we know which friend we need to go see when we need cheering up.

I was thinking about this because someone just asked this question: what’s the smallest positive integer that isn’t special? And that took me to this very interesting webpage, which shows that most integers have something special about them. There’s a paradox here, actually: the smallest number that isn’t special… that’s pretty special, isn’t it?

So right now I’m wondering: what’s special about the number 424?

Meanwhile, my little brother was playing this very song on the ukulele this morning.

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