The famous mathematician G. H. Hardy wrote a memoir called A Mathematician’s Apology (Amazon, Bookshop). In it, he tells a story about a visit he made to Srinivasa Ramanujan, another brilliant mathematician with whom he collaborated. Ramanujan was in the hospital, dying, and Hardy went to see him. He recalls:
I remember once going to see him when he was lying 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. “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.”
Ramanujan was correct. 1729 is a number that can be written as 1 cubed + 12 cubed and 9 cubed + 10 cubed. There’s no smaller integer that can be written as the sum of two cubes. To this day, this kind of number is called a “Hardy-Ramanujan number” or “taxi-cab number.” Only six other taxi-cab numbers have been found.
I love this story, partly because it’s such an odd conversation to have—the kind of small talk that only two mathematicians would find themselves having.
And partly because it shows that a curious, engaged mind, prepared with knowledge, can look out at the world and find fascination in situations that, to the less well-informed, seem quite dull.